Popović, Jovan K; Atanacković, Milica T; Pilipović, Ana S; Rapaić, Milan R; Pilipović, Stevan; Atanacković, Teodor M
2010-04-01
This study presents a new two compartmental model and its application to the evaluation of diclofenac pharmacokinetics in a small number of healthy adults, during a bioequivalence trial. In the model the integer order derivatives are replaced by derivatives of real order often called fractional order derivatives. Physically that means that a history (memory) of a biological process, realized as a transfer from one compartment to another one with the mass balance conservation, is taken into account. This kind of investigations in pharmacokinetics is founded by Dokoumetzidis and Macheras through the one compartmental models while our contribution is the analysis of multi-dimensional compartmental models with the applications of the two compartmental model in evaluation of diclofenac pharmacokinetics. Two experiments were preformed with 12 healthy volunteers with two slow release 100 mg diclofenac tablet formulations. The agreement of the values predicted by the proposed model with the values obtained through experiments is shown to be good. Thus, pharmacokinetics of slow release diclofenac can be described well by a specific two compartmental model with fractional derivatives of the same order. Parameters in the model are determined by the least-squares method and the Particle Swarm Optimization (PSO) numerical procedure is used. The results show that the fractional order two compartmental model for diclofenac is superior in comparison to the classical two compartmental model. Actually this is true in general case since the classical one is a special case of the fractional one.
Compartmental modeling and tracer kinetics
Anderson, David H
1983-01-01
This monograph is concerned with mathematical aspects of compartmental an alysis. In particular, linear models are closely analyzed since they are fully justifiable as an investigative tool in tracer experiments. The objective of the monograph is to bring the reader up to date on some of the current mathematical prob lems of interest in compartmental analysis. This is accomplished by reviewing mathematical developments in the literature, especially over the last 10-15 years, and by presenting some new thoughts and directions for future mathematical research. These notes started as a series of lectures that I gave while visiting with the Division of Applied ~1athematics, Brown University, 1979, and have developed in to this collection of articles aimed at the reader with a beginning graduate level background in mathematics. The text can be used as a self-paced reading course. With this in mind, exercises have been appropriately placed throughout the notes. As an aid in reading the material, the e~d of a ...
International Nuclear Information System (INIS)
Charkes, N.D.
1984-01-01
Using compartmental analysis methods, a mathematical basis is given for the measurement of absolute and fractional cardiac output with diffusible tracers. Cardiac output is shown to be the product of the blood volume and the sum of the rate constants of tracer egress from blood, modified by a factor reflecting transcapillary diffusibility, the transfer fraction. The return of tracer to the blood and distant (intracellular) events are shown to play no role in the solution. Fractional cardiac output is the ratio of the rate constant of tracer egress from blood to an organ, divided by the sum of the egress constants from blood. Predominantly extracellular ions such as sodium or bromide are best suited for this technique, although theoretically any diffusible tracer whose compartmental model can be solved may be used. It is shown that fractional cardiac output is independent of the transfer fraction, and therefore can be measured accurately by tracers which are not freely diffusible
A Calculus for Modelling, Simulating and Analysing Compartmentalized Biological Systems
DEFF Research Database (Denmark)
Mardare, Radu Iulian; Ihekwaba, Adoha
2007-01-01
A. Ihekwaba, R. Mardare. A Calculus for Modelling, Simulating and Analysing Compartmentalized Biological Systems. Case study: NFkB system. In Proc. of International Conference of Computational Methods in Sciences and Engineering (ICCMSE), American Institute of Physics, AIP Proceedings, N 2...
Compartmentalization analysis using discrete fracture network models
Energy Technology Data Exchange (ETDEWEB)
La Pointe, P.R.; Eiben, T.; Dershowitz, W. [Golder Associates, Redmond, VA (United States); Wadleigh, E. [Marathon Oil Co., Midland, TX (United States)
1997-08-01
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
Analytical properties of a three-compartmental dynamical demographic model
Postnikov, E. B.
2015-07-01
The three-compartmental demographic model by Korotaeyv-Malkov-Khaltourina, connecting population size, economic surplus, and education level, is considered from the point of view of dynamical systems theory. It is shown that there exist two integrals of motion, which enables the system to be reduced to one nonlinear ordinary differential equation. The study of its structure provides analytical criteria for the dominance ranges of the dynamics of Malthus and Kremer. Additionally, the particular ranges of parameters enable the derived general ordinary differential equations to be reduced to the models of Gompertz and Thoularis-Wallace.
Compartmental transport model of microbicide delivery by an intravaginal ring
Geonnotti, Anthony R.; Katz, David F.
2010-01-01
Topical antimicrobials, or microbicides, are being developed to prevent HIV transmission through local, mucosal delivery of antiviral compounds. While hydrogel vehicles deliver the majority of current microbicide products, intravaginal rings (IVRs) are an alternative microbicide modality in preclinical development. IVRs provide a long-term dosing alternative to hydrogel use, and might provide improved user adherence. IVR efficacy requires sustained delivery of antiviral compounds to the entire vaginal compartment. A two-dimensional, compartmental vaginal drug transport model was created to evaluate the delivery of drugs from an intravaginal ring. The model utilized MRI-derived ring geometry and location, experimentally defined ring fluxes and vaginal fluid velocities, and biophysically relevant transport theory. Model outputs indicated the presence of potentially inhibitory concentrations of antiviral compounds along the entire vaginal canal within 24 hours following IVR insertion. Distributions of inhibitory concentrations of antiviral compounds were substantially influenced by vaginal fluid flow and production, while showing little change due to changes in diffusion coefficients or ring fluxes. Additionally, model results were predictive of in vivo concentrations obtained in clinical trials. Overall, this analysis initiates a mechanistic computational framework, heretofore missing, to understand and evaluate the potential of IVRs for effective delivery of antiviral compounds. PMID:20222027
Efficient Vaccine Distribution Based on a Hybrid Compartmental Model.
Directory of Open Access Journals (Sweden)
Zhiwen Yu
Full Text Available To effectively and efficiently reduce the morbidity and mortality that may be caused by outbreaks of emerging infectious diseases, it is very important for public health agencies to make informed decisions for controlling the spread of the disease. Such decisions must incorporate various kinds of intervention strategies, such as vaccinations, school closures and border restrictions. Recently, researchers have paid increased attention to searching for effective vaccine distribution strategies for reducing the effects of pandemic outbreaks when resources are limited. Most of the existing research work has been focused on how to design an effective age-structured epidemic model and to select a suitable vaccine distribution strategy to prevent the propagation of an infectious virus. Models that evaluate age structure effects are common, but models that additionally evaluate geographical effects are less common. In this paper, we propose a new SEIR (susceptible-exposed-infectious šC recovered model, named the hybrid SEIR-V model (HSEIR-V, which considers not only the dynamics of infection prevalence in several age-specific host populations, but also seeks to characterize the dynamics by which a virus spreads in various geographic districts. Several vaccination strategies such as different kinds of vaccine coverage, different vaccine releasing times and different vaccine deployment methods are incorporated into the HSEIR-V compartmental model. We also design four hybrid vaccination distribution strategies (based on population size, contact pattern matrix, infection rate and infectious risk for controlling the spread of viral infections. Based on data from the 2009-2010 H1N1 influenza epidemic, we evaluate the effectiveness of our proposed HSEIR-V model and study the effects of different types of human behaviour in responding to epidemics.
Compartmental models for assessing the fishery production in the Indian Ocean
Digital Repository Service at National Institute of Oceanography (India)
Dalal, S.G.; Parulekar, A.H.
Compartmental models for assessing the fishery production in the Indian Ocean is discussed. The article examines the theoretical basis on which modern fishery sciences is built. The model shows that, large changes in energy flux from one pathway...
Compartmental distribution of radiotracers
International Nuclear Information System (INIS)
Robertson, J.S.; Colombetti, L.G.
1983-01-01
This book examines the use of radioisotopes in medical diagnosis. Topics considered include compartmental analysis, data processing in nuclear medicine, historical aspects, basic principles, mathematical methods, the application of computers in obtaining numerical solutions to compartmental models, the SAAM and CONSAM programs, some statistical principles in compartmental analysis, and applications
Compartmental distribution of radiotracers
International Nuclear Information System (INIS)
Roberton, J.S.
1983-01-01
Emphasizes applications of compartmental analysis in physiology, pharmacology, and other areas of biology and medicine. Details of computer methods and applications of statistical principles as they apply to compartmental analysis are presented. Of special interest is a step-by-step discussion of Berman's SAAM program in modeling at several different levels of difficulty. Extensive references and sources of additional information in mathematical methods and in applications to specific problems are provided. Contents: Historical Development. Basic Principles, Mathematical Methods. Application of Computers for Obtaining Numerical Solutions to Compartmental Models. Use of Computers in Compartmental Analysis: SAAM and CONSAAM Programs. Some Statistical Principals in Compartmental Analysis. Applications. Index
Compartmental modeling approach to the radiation dosimetry of radiolabeled antibody
International Nuclear Information System (INIS)
Zanzonico, P.B.; Bigler, R.E.; Primus, F.J.; Alger, E.; DeJager, R.; Stowe, S.; Ford, E.; Brennan, K.; Goldenberg, D.M.
1986-01-01
Essential for the calculation of absorbed doses from systemically administered radiolabled antibody is the determination of the total number of nuclear transformations in specified source regions. Compartmental analysis (using biodistribution data augmented with a priori physiological information), unlike simply integrating empirical time-activity curves, may enable one to calculate the cumulated activity in unsampled as well as sampled source regions. These may include microscopic source regions (e.g. the intracellular space, cell surface, and extracellular space) important for microdosimetry calculations. Of particular importance is the interaction between the anti-tumor antibody and the tumor antigen. 30 references, 9 figures, 2 tables
Global identifiability of linear compartmental models--a computer algebra algorithm.
Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C
1998-01-01
A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.
International Nuclear Information System (INIS)
Dimitrov, L.; Tzvetkova, A.; Nikolov, A.
1997-01-01
The compartmental models have a variety of applications in the analysis of the transport of radioactive and non-radioactive material in complex systems as atmosphere, hydrosphere, food chains, human body. The analysis of the biokinetic behaviour of the radioactive material into a human body gives a possibility for correct assessment of the dose from internal irradiation. Skrable has given a decision of non-cyclic linear compartmental models in case of a single intake of material in the compartments as an initial condition. The main purpose of our article is to write down a procedure for analysis of a general compartmental model in case of continuous intake of material into the compartments. This procedure is related to retain function concept and had developed on the base of Laplace transform. On the base on the proposed procedure a non-cyclic linear compartmental model decisions are given in case of both a single and a continuous intake. The Laplace images of cyclic and circular linear compartmental model decisions and their originals in some cases are given too. (author)
Modeling influenza-like illnesses through composite compartmental models
Levy, Nir; , Michael, Iv; Yom-Tov, Elad
2018-03-01
Epidemiological models for the spread of pathogens in a population are usually only able to describe a single pathogen. This makes their application unrealistic in cases where multiple pathogens with similar symptoms are spreading concurrently within the same population. Here we describe a method which makes possible the application of multiple single-strain models under minimal conditions. As such, our method provides a bridge between theoretical models of epidemiology and data-driven approaches for modeling of influenza and other similar viruses. Our model extends the Susceptible-Infected-Recovered model to higher dimensions, allowing the modeling of a population infected by multiple viruses. We further provide a method, based on an overcomplete dictionary of feasible realizations of SIR solutions, to blindly partition the time series representing the number of infected people in a population into individual components, each representing the effect of a single pathogen. We demonstrate the applicability of our proposed method on five years of seasonal influenza-like illness (ILI) rates, estimated from Twitter data. We demonstrate that our method describes, on average, 44% of the variance in the ILI time series. The individual infectious components derived from our model are matched to known viral profiles in the populations, which we demonstrate matches that of independently collected epidemiological data. We further show that the basic reproductive numbers (R 0) of the matched components are in range known for these pathogens. Our results suggest that the proposed method can be applied to other pathogens and geographies, providing a simple method for estimating the parameters of epidemics in a population.
Compartmental Model For Uptake Of 137cs By Pine In Forest Soil ...
African Journals Online (AJOL)
A compartmental model of soil to pine tree transfer of 137Cs following the Chernobyl nuclear accident is presented. The model was validated using data collected in 1996 at five sites in Northern Ukraine. The transfer constants of 137Cs between model compartments are estimated using a semi-empirical method.
Elbert, Donald L; Patterson, Bruce W; Bateman, Randall J
2015-03-01
Amyloid beta (Aβ) peptides, and in particular Aβ42, are found in senile plaques associated with Alzheimer's disease. A compartmental model of Aβ production, exchange and irreversible loss was recently developed to explain the kinetics of isotope-labeling of Aβ peptides collected in cerebrospinal fluid (CSF) following infusion of stable isotope-labeled leucine in humans. The compartmental model allowed calculation of the rates of production, irreversible loss (or turnover) and short-term exchange of Aβ peptides. Exchange of Aβ42 was particularly pronounced in amyloid plaque-bearing participants. In the current work, we describe in much greater detail the characteristics of the compartmental model to two distinct audiences: physician-scientists and biokineticists. For physician-scientists, we describe through examples the types of questions the model can and cannot answer, as well as correct some misunderstandings of previous kinetic analyses applied to this type of isotope labeling data. For biokineticists, we perform a system identifiability analysis and a sensitivity analysis of the kinetic model to explore the global and local properties of the model. Combined, these analyses motivate simplifications from a more comprehensive physiological model to the final model that was previously presented. The analyses clearly demonstrate that the current dataset and compartmental model allow determination with confidence a single 'turnover' parameter, a single 'exchange' parameter and a single 'delay' parameter. When combined with CSF concentration data for the Aβ peptides, production rates may also be obtained. Copyright © 2015 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Mazoyer, B.M.; Huesman, R.H.; Budinger, T.F.; Knittel, B.L.
1986-01-01
Over the past years a major focus of research in physiologic studies employing tracers has been the computer implementation of mathematical methods of kinetic modeling for extracting the desired physiological parameters from tomographically derived data. A study is reported of factors that affect the statistical properties of compartmental model parameters extracted from dynamic positron emission tomography (PET) experiments
A new method to estimate parameters of linear compartmental models using artificial neural networks
International Nuclear Information System (INIS)
Gambhir, Sanjiv S.; Keppenne, Christian L.; Phelps, Michael E.; Banerjee, Pranab K.
1998-01-01
At present, the preferred tool for parameter estimation in compartmental analysis is an iterative procedure; weighted nonlinear regression. For a large number of applications, observed data can be fitted to sums of exponentials whose parameters are directly related to the rate constants/coefficients of the compartmental models. Since weighted nonlinear regression often has to be repeated for many different data sets, the process of fitting data from compartmental systems can be very time consuming. Furthermore the minimization routine often converges to a local (as opposed to global) minimum. In this paper, we examine the possibility of using artificial neural networks instead of weighted nonlinear regression in order to estimate model parameters. We train simple feed-forward neural networks to produce as outputs the parameter values of a given model when kinetic data are fed to the networks' input layer. The artificial neural networks produce unbiased estimates and are orders of magnitude faster than regression algorithms. At noise levels typical of many real applications, the neural networks are found to produce lower variance estimates than weighted nonlinear regression in the estimation of parameters from mono- and biexponential models. These results are primarily due to the inability of weighted nonlinear regression to converge. These results establish that artificial neural networks are powerful tools for estimating parameters for simple compartmental models. (author)
Venkatakrishnan, Vaidehi
1995-01-01
Physical and mathematical models provide a systematic means of looking at biological systems. Radioactive tracer kinetic studies open a unique window to study complex tracee systems such as protein metabolism in humans. This research deals with compartmental modeling of tracer kinetic data on leucine and apolipoprotein metabolism obtained using an endogenous tritiated leucine tracer administered as a bolus, and application of compartmental modeling techniques for dosimetric evaluation of metabolic studies of radioiodinated apolipoproteins. Dr. Waldo R. Fisher, Department of Medicine, was the coordinating research supervisor and the work was carried out in his laboratory. A compartmental model for leucine kinetics in humans has been developed that emphasizes its recycling pathways which were examined over two weeks. This model builds on a previously published model of Cobelli et al, that analyzed leucine kinetic data up to only eight hours. The proposed model includes different routes for re-entry of leucine from protein breakdown into plasma accounting for proteins which turn over at different rates. This new model successfully incorporates published models of three secretory proteins: albumin, apoA-I, and VLDL apoB, in toto thus increasing its validity and utility. The published model of apoA-I, based on an exogenous radioiodinated tracer, was examined with data obtained using an endogenous leucine tracer using compartmental techniques. The analysis concludes that the major portion of apoA-I enters plasma by a fast pathway but the major fraction of apoA-I in plasma resides with a second slow pathway; further the study is suggestive of a precursor-product relationship between the two plasma apoA-I pools. The possible relevance of the latter suggestion to the aberrant kinetics of apoA-I in Tangier disease is discussed. The analysis of apoA-II data resulted in similar conclusions. A methodology for evaluating the dosimetry of radioiodinated apolipoproteins by
Robust global identifiability theory using potentials--Application to compartmental models.
Wongvanich, N; Hann, C E; Sirisena, H R
2015-04-01
This paper presents a global practical identifiability theory for analyzing and identifying linear and nonlinear compartmental models. The compartmental system is prolonged onto the potential jet space to formulate a set of input-output equations that are integrals in terms of the measured data, which allows for robust identification of parameters without requiring any simulation of the model differential equations. Two classes of linear and non-linear compartmental models are considered. The theory is first applied to analyze the linear nitrous oxide (N2O) uptake model. The fitting accuracy of the identified models from differential jet space and potential jet space identifiability theories is compared with a realistic noise level of 3% which is derived from sensor noise data in the literature. The potential jet space approach gave a match that was well within the coefficient of variation. The differential jet space formulation was unstable and not suitable for parameter identification. The proposed theory is then applied to a nonlinear immunological model for mastitis in cows. In addition, the model formulation is extended to include an iterative method which allows initial conditions to be accurately identified. With up to 10% noise, the potential jet space theory predicts the normalized population concentration infected with pathogens, to within 9% of the true curve. Copyright © 2015 Elsevier Inc. All rights reserved.
A Residual Approach for Balanced Truncation Model Reduction (BTMR of Compartmental Systems
Directory of Open Access Journals (Sweden)
William La Cruz
2014-05-01
Full Text Available This paper presents a residual approach of the square root balanced truncation algorithm for model order reduction of continuous, linear and time-invariante compartmental systems. Specifically, the new approach uses a residual method to approximate the controllability and observability gramians, whose resolution is an essential step of the square root balanced truncation algorithm, that requires a great computational cost. Numerical experiences are included to highlight the efficacy of the proposed approach.
Abrams , Robert H.; Loague, Keith
2000-01-01
This paper, the first of two parts [see Abrams and Loague, this issue], takes the compartmentalized approach for the geochemical evolution of redox zones presented by Abrams et al. [1998] and embeds it within a solute transport framework. In this paper the compartmentalized approach is generalized to facilitate the description of its incorporation into a solute transport simulator. An equivalent formulation is developed which removes any discontinuities that may occur when switching compartments. Rate‐limited redox reactions are modeled with a modified Monod relationship that allows either the organic substrate or the electron acceptor to be the rate‐limiting reactant. Thermodynamic constraints are used to inhibit lower‐energy redox reactions from occurring under infeasible geochemical conditions without imposing equilibrium on the lower‐energy reactions. The procedure used allows any redox reaction to be simulated as being kinetically limited or thermodynamically limited, depending on local geochemical conditions. Empirical reaction inhibition methods are not needed. The sequential iteration approach (SIA), a technique which allows the number of solute transport equations to be reduced, is adopted to solve the coupled geochemical/solute transport problem. When the compartmentalized approach is embedded within the SIA, with the total analytical concentration of each component as the dependent variable in the transport equation, it is possible to reduce the number of transport equations even further than with the unmodified SIA. A one‐dimensional, coupled geochemical/solute transport simulation is presented in which redox zones evolve dynamically in time and space. The compartmentalized solute transport (COMPTRAN) model described in this paper enables the development of redox zones to be simulated under both kinetic and thermodynamic constraints. The modular design of COMPTRAN facilitates the use of many different, preexisting solute transport and
Davidson, Natalie R; Godfrey, Keith R; Alquaddoomi, Faisal; Nola, David; DiStefano, Joseph J
2017-05-01
We describe and illustrate use of DISTING, a novel web application for computing alternative structurally identifiable linear compartmental models that are input-output indistinguishable from a postulated linear compartmental model. Several computer packages are available for analysing the structural identifiability of such models, but DISTING is the first to be made available for assessing indistinguishability. The computational algorithms embedded in DISTING are based on advanced versions of established geometric and algebraic properties of linear compartmental models, embedded in a user-friendly graphic model user interface. Novel computational tools greatly speed up the overall procedure. These include algorithms for Jacobian matrix reduction, submatrix rank reduction, and parallelization of candidate rank computations in symbolic matrix analysis. The application of DISTING to three postulated models with respectively two, three and four compartments is given. The 2-compartment example is used to illustrate the indistinguishability problem; the original (unidentifiable) model is found to have two structurally identifiable models that are indistinguishable from it. The 3-compartment example has three structurally identifiable indistinguishable models. It is found from DISTING that the four-compartment example has five structurally identifiable models indistinguishable from the original postulated model. This example shows that care is needed when dealing with models that have two or more compartments which are neither perturbed nor observed, because the numbering of these compartments may be arbitrary. DISTING is universally and freely available via the Internet. It is easy to use and circumvents tedious and complicated algebraic analysis previously done by hand. Copyright © 2017 Elsevier B.V. All rights reserved.
A mechanistic compartmental model for total antibody uptake in tumors.
Thurber, Greg M; Dane Wittrup, K
2012-12-07
Antibodies are under development to treat a variety of cancers, such as lymphomas, colon, and breast cancer. A major limitation to greater efficacy for this class of drugs is poor distribution in vivo. Localization of antibodies occurs slowly, often in insufficient therapeutic amounts, and distributes heterogeneously throughout the tumor. While the microdistribution around individual vessels is important for many therapies, the total amount of antibody localized in the tumor is paramount for many applications such as imaging, determining the therapeutic index with antibody drug conjugates, and dosing in radioimmunotherapy. With imaging and pretargeted therapeutic strategies, the time course of uptake is critical in determining when to take an image or deliver a secondary reagent. We present here a simple mechanistic model of antibody uptake and retention that captures the major rates that determine the time course of antibody concentration within a tumor including dose, affinity, plasma clearance, target expression, internalization, permeability, and vascularization. Since many of the parameters are known or can be estimated in vitro, this model can approximate the time course of antibody concentration in tumors to aid in experimental design, data interpretation, and strategies to improve localization. Copyright © 2012 Elsevier Ltd. All rights reserved.
Compartmental modeling alternatives for kinetic analysis of pet neurotransmitter receptor studies
International Nuclear Information System (INIS)
Koeppe, R.A.
1991-01-01
With the increased interest in studying neurotransmitter and receptor function in vivo, imaging procedures using positron emission tomography have presented new challenges for kinetic modeling and analysis of data. The in vivo behavior of radiolabeled markers for examining these neurotransmitter systems can be quite complex and, therefore, the implementation of compartmental models for data analysis is similarly complex. Often, the variability in the estimates of model parameters representing neurotransmitter or receptor densities, association and dissociation rates, or rates of incorporation or turnover does not permit reliable interpretation of the data. When less complex analyses are used, these model parameters may be biased and thus also do not yield the information being sought. Examination of trade-offs between uncertainty and bias in the parameters of interest may be used to select a compartmental model configuration with an appropriate level of complexity. Modeling alternatives will be discussed for radioligands with varying kinetic properties, such as those that bind reversibly and rapidly and others that bind nearly irreversibly. Specific problems, such as those occurring when a radioligand is open-quotes flow limitedclose quotes also will be discussed
Abrams , Robert H.; Loague, Keith; Kent, Douglas B.
1998-01-01
The work reported here is the first part of a larger effort focused on efficient numerical simulation of redox zone development in contaminated aquifers. The sequential use of various electron acceptors, which is governed by the energy yield of each reaction, gives rise to redox zones. The large difference in energy yields between the various redox reactions leads to systems of equations that are extremely ill-conditioned. These equations are very difficult to solve, especially in the context of coupled fluid flow, solute transport, and geochemical simulations. We have developed a general, rational method to solve such systems where we focus on the dominant reactions, compartmentalizing them in a manner that is analogous to the redox zones that are often observed in the field. The compartmentalized approach allows us to easily solve a complex geochemical system as a function of time and energy yield, laying the foundation for our ongoing work in which we couple the reaction network, for the development of redox zones, to a model of subsurface fluid flow and solute transport. Our method (1) solves the numerical system without evoking a redox parameter, (2) improves the numerical stability of redox systems by choosing which compartment and thus which reaction network to use based upon the concentration ratios of key constituents, (3) simulates the development of redox zones as a function of time without the use of inhibition factors or switching functions, and (4) can reduce the number of transport equations that need to be solved in space and time. We show through the use of various model performance evaluation statistics that the appropriate compartment choice under different geochemical conditions leads to numerical solutions without significant error. The compartmentalized approach described here facilitates the next phase of this effort where we couple the redox zone reaction network to models of fluid flow and solute transport.
A compartmental model of the cAMP/PKA/MAPK pathway in Bio-PEPA
Directory of Open Access Journals (Sweden)
Federica Ciocchetta
2009-11-01
Full Text Available The vast majority of biochemical systems involve the exchange of information between different compartments, either in the form of transportation or via the intervention of membrane proteins which are able to transmit stimuli between bordering compartments. The correct quantitative handling of compartments is, therefore, extremely important when modelling real biochemical systems. The Bio-PEPA process algebra is equipped with the capability of explicitly defining quantitative information such as compartment volumes and membrane surface areas. Furthermore, the recent development of the Bio-PEPA Eclipse Plug-in allows us to perform a correct stochastic simulation of multi-compartmental models. Here we present a Bio-PEPA compartmental model of the cAMP/PKA/MAPK pathway. We analyse the system using the Bio-PEPA Eclipse Plug-in and we show the correctness of our model by comparison with an existing ODE model. Furthermore, we perform computational experiments in order to investigate certain properties of the pathway. Specifically, we focus on the system response to the inhibition and strengthening of feedback loops and to the variation in the activity of key pathway reactions and we observe how these modifications affect the behaviour of the pathway. These experiments are useful to understand the control and regulatory mechanisms of the system.
DEFF Research Database (Denmark)
Vahidi, O; Kwok, K E; Gopaluni, R B
2016-01-01
We have expanded a former compartmental model of blood glucose regulation for healthy and type 2 diabetic subjects. The former model was a detailed physiological model which considered the interactions of three substances, glucose, insulin and glucagon on regulating the blood sugar. The main...... variations of blood glucose concentrations following an oral glucose intake. Another model representing the incretins production in the gastrointestinal tract along with their hormonal effects on boosting pancreatic insulin production is also added to the former model. We have used two sets of clinical data...... obtained during oral glucose tolerance test and isoglycemic intravenous glucose infusion test from both type 2 diabetic and healthy subjects to estimate the model parameters and to validate the model results. The estimation of model parameters is accomplished through solving a nonlinear optimization...
International Nuclear Information System (INIS)
Yahaghi, E.; Movafeghi, A.; Askari, M. A.; Karimi Diba, G.; Mohammadzadeh, N.
2012-01-01
Cs-137 is one of the fission products that is usually released in environment after nuclear accidents. This contamination remains in environment for a long time due to long half life of Cs-137 (30 years) and can enter easily into the human food chain. A two-compartmental model was implemented to describe caesium intake and its distribution in Dicentrarchus Labrax, using a proposed differential equation model. The model included two compartments, the first compartment was the blood and the second one was the tissue. The activity of Cs-137 was undertaken in each compartment by means of a numerical method and the activity of Cs-137 was considered as an input of compartmental equations. We obtained the transfer coefficients between fish tissues by comparing the radiation curves with the actual data. In the light of the differences with the transfer coefficients, the calculation by the COMKAT software was found to be about 2%. Then, we provided the activity curves of Cs-137 and their characteristics (feature extractions) by changing the transfer coefficients and they were utilized to train the neural network. The network was trained for six data groups, and the results of the network testing had about 99% correct response, therefore it can be employed to estimate the transfer coefficients in fish tissue, the salinity range, and the activity of Cs-137 in water.
Estimation of guinea pig tracheobronchial transport rates using a compartmental model
International Nuclear Information System (INIS)
Velasquez, D.J.; Morrow, P.E.
1984-01-01
Mucociliary clearance in the tracheobronchial tree of guinea pigs was examined using monodisperse 7.9 μm MMAD polystyrene particles. Animals were exposed for approximately 1 h by inhalation via an intratracheal tube to aerosols tagged with gold-198 and fluorescent dyes. Following exposure, animals were radioactively monitored and sacrificed at predetermined times. The lungs were removed, freeze-dried, sectioned completely, and examined with a fluorescent microscope. Measurements were made of airway diameters where particles were found. An anatomic model for guinea pig lung morphology was used to assign ranges of airway diameters to five zones, which were incorporated into a compartmental model for lung clearance. Kinetic analysis of particle distributions in the zones led to development of first-order equations describing the compartmental clearance. Rate constants obtained from the kinetic analysis were used to estimate mucociliary transport rates in specific bronchial generations, which ranged from approximately 0.001 mm/min in the distal bronchioles to approximately 8 mm/min in the trachea, and resulted in a calculated 24-h clearance time for tracheobronchial clearance in the guinea pig. No evidence for either bronchial penetration by particles or relatively prolonged bronchial retention of particles was found in this study. 22 references, 3 figures, 3 tables
Fatigue in isometric contraction in a single muscle fibre: a compartmental calcium ion flow model.
Kothiyal, K P; Ibramsha, M
1986-01-01
Fatigue in muscle is a complex biological phenomenon which has so far eluded a definite explanation. Many biochemical and physiological models have been suggested in the literature to account for the decrement in the ability of muscle to sustain a given level of force for a long time. Some of these models have been critically analysed in this paper and are shown to be not able to explain all the experimental observations. A new compartmental model based on the intracellular calcium ion movement in muscle is proposed to study the mechanical responses of a muscle fibre. Computer simulation is performed to obtain model responses in isometric contraction to an impulse and a train of stimuli of long duration. The simulated curves have been compared with experimentally observed mechanical responses of the semitendinosus muscle fibre of Rana pipiens. The comparison of computed and observed responses indicates that the proposed calcium ion model indeed accounts very well for the muscle fatigue.
Koldsø, Heidi; Reddy, Tyler; Fowler, Philip W; Duncan, Anna L; Sansom, Mark S P
2016-09-01
The cytoskeleton underlying cell membranes may influence the dynamic organization of proteins and lipids within the bilayer by immobilizing certain transmembrane (TM) proteins and forming corrals within the membrane. Here, we present coarse-grained resolution simulations of a biologically realistic membrane model of asymmetrically organized lipids and TM proteins. We determine the effects of a model of cytoskeletal immobilization of selected membrane proteins using long time scale coarse-grained molecular dynamics simulations. By introducing compartments with varying degrees of restraints within the membrane models, we are able to reveal how compartmentalization caused by cytoskeletal immobilization leads to reduced and anomalous diffusional mobility of both proteins and lipids. This in turn results in a reduced rate of protein dimerization within the membrane and of hopping of membrane proteins between compartments. These simulations provide a molecular realization of hierarchical models often invoked to explain single-molecule imaging studies of membrane proteins.
Kevin T. Smith
2006-01-01
For more than 30 years, the compartmentdization concept has helped tree care practitioners and land managers interpret patterns of decay in living trees. Understanding these patterns can help guide the selection of treatments that meet the needs of people and communities while respecting the underlying tree biology. At its simplest, compartmentalization resists the...
International Nuclear Information System (INIS)
King, C.M.; Wilhite, E.L.; Root, R.W. Jr.
1985-01-01
The Savannah River Laboratory DOSTOMAN code has been used since 1978 for environmental pathway analysis of potential migration of radionuclides and hazardous chemicals. The DOSTOMAN work is reviewed including a summary of historical use of compartmental models, the mathematical basis for the DOSTOMAN code, examples of exact analytical solutions for simple matrices, methods for numerical solution of complex matrices, and mathematical validation/calibration of the SRL code. The review includes the methodology for application to nuclear and hazardous chemical waste disposal, examples of use of the model in contaminant transport and pathway analysis, a user's guide for computer implementation, peer review of the code, and use of DOSTOMAN at other Department of Energy sites. 22 refs., 3 figs
International Nuclear Information System (INIS)
Toal, M.E.; Copplestone, D.; Johnson, M.S.; Jackson, D.; Jones, S.R.
2001-01-01
A study was undertaken to quantify the activity concentrations of 137Cs in Apodemus sylvaticus (the woodmouse) in two woodland sites, Lady Wood and Longrigg Wood, adjacent to British Nuclear Fuels Ltd. (BNFL) Sellafield, Cumbria, UK. A deterministic dynamic compartmental food chain model was also constructed to predict 137Cs activity concentration [Bq kg -1 dry weight (dw)] in A. sylvaticus on a seasonal basis given the activity concentrations in its diet. Within the coniferous woodland site (Lady Wood), significant differences were found between seasons (P x / 2.3 Bq kg -1 dw) being attributed to mycophagy. Fungal concentrations ranged from 2-3213 Bq kg -1 dw. The modelled activity concentrations fell between the confidence intervals of the observed data in four of the six seasonal cohorts sampled. Disparities between predicted and observed activity concentrations are attributed to uncertainties surrounding the fundamental feeding ecology of small mammals
The construction of next-generation matrices for compartmental epidemic models.
Diekmann, O; Heesterbeek, J A P; Roberts, M G
2010-06-06
The basic reproduction number (0) is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation of (0) where finitely many different categories of individuals are recognized. We clear up confusion that has been around in the literature concerning the construction of this matrix, specifically for the most frequently used so-called compartmental models. We present a detailed easy recipe for the construction of the NGM from basic ingredients derived directly from the specifications of the model. We show that two related matrices exist which we define to be the NGM with large domain and the NGM with small domain. The three matrices together reflect the range of possibilities encountered in the literature for the characterization of (0). We show how they are connected and how their construction follows from the basic model ingredients, and establish that they have the same non-zero eigenvalues, the largest of which is the basic reproduction number (0). Although we present formal recipes based on linear algebra, we encourage the construction of the NGM by way of direct epidemiological reasoning, using the clear interpretation of the elements of the NGM and of the model ingredients. We present a selection of examples as a practical guide to our methods. In the appendix we present an elementary but complete proof that (0) defined as the dominant eigenvalue of the NGM for compartmental systems and the Malthusian parameter r, the real-time exponential growth rate in the early phase of an outbreak, are connected by the properties that (0) > 1 if and only if r > 0, and (0) = 1 if and only if r = 0.
Evaluation of a compartmental model for estimating tumor hypoxia via FMISO dynamic PET imaging
International Nuclear Information System (INIS)
Wang Wenli; Nehmeh, Sadek A; O'Donoghue, Joseph; Zanzonico, Pat B; Schmidtlein, C Ross; Lee, Nancy Y; Humm, John L; Georgi, Jens-Christoph; Paulus, Timo; Narayanan, Manoj; Bal, Matthieu
2009-01-01
This paper systematically evaluates a pharmacokinetic compartmental model for identifying tumor hypoxia using dynamic positron emission tomography (PET) imaging with 18 F-fluoromisonidazole (FMISO). A generic irreversible one-plasma two-tissue compartmental model was used. A dynamic PET image dataset was simulated with three tumor regions-normoxic, hypoxic and necrotic-embedded in a normal-tissue background, and with an image-based arterial input function. Each voxelized tissue's time activity curve (TAC) was simulated with typical values of kinetic parameters, as deduced from FMISO-PET data from nine head-and-neck cancer patients. The dynamic dataset was first produced without any statistical noise to ensure that correct kinetic parameters were reproducible. Next, to investigate the stability of kinetic parameter estimation in the presence of noise, 1000 noisy samples of the dynamic dataset were generated, from which 1000 noisy estimates of kinetic parameters were calculated and used to estimate the sample mean and covariance matrix. It is found that a more peaked input function gave less variation in various kinetic parameters, and the variation of kinetic parameters could also be reduced by two region-of-interest averaging techniques. To further investigate how bias in the arterial input function affected the kinetic parameter estimation, a shift error was introduced in the peak amplitude and peak location of the input TAC, and the bias of various kinetic parameters calculated. In summary, mathematical phantom studies have been used to determine the statistical accuracy and precision of model-based kinetic analysis, which helps to validate this analysis and provides guidance in planning clinical dynamic FMISO-PET studies.
Vahidi, O; Kwok, K E; Gopaluni, R B; Knop, F K
2016-09-01
We have expanded a former compartmental model of blood glucose regulation for healthy and type 2 diabetic subjects. The former model was a detailed physiological model which considered the interactions of three substances, glucose, insulin and glucagon on regulating the blood sugar. The main drawback of the former model was its restriction on the route of glucose entrance to the body which was limited to the intravenous glucose injection. To handle the oral glucose intake, we have added a model of glucose absorption in the gastrointestinal tract to the former model to address the resultant variations of blood glucose concentrations following an oral glucose intake. Another model representing the incretins production in the gastrointestinal tract along with their hormonal effects on boosting pancreatic insulin production is also added to the former model. We have used two sets of clinical data obtained during oral glucose tolerance test and isoglycemic intravenous glucose infusion test from both type 2 diabetic and healthy subjects to estimate the model parameters and to validate the model results. The estimation of model parameters is accomplished through solving a nonlinear optimization problem. The results show acceptable precision of the estimated model parameters and demonstrate the capability of the model in accurate prediction of the body response during the clinical studies.
Modelling altered fractionation schedules
International Nuclear Information System (INIS)
Fowler, J.F.
1993-01-01
The author discusses the conflicting requirements of hyperfractionation and accelerated fractionation used in radiotherapy, and the development of computer modelling to predict how to obtain an optimum of tumour cell kill without exceeding normal-tissue tolerance. The present trend is to shorten hyperfractionated schedules from 6 or 7 weeks to give overall times of 4 or 5 weeks as in new schedules by Herskovic et al (1992) and Harari (1992). Very high doses are given, much higher than can be given when ultrashort schedules such as CHART (12 days) are used. Computer modelling has suggested that optimum overall times, to yield maximum cell kill in tumours ((α/β = 10 Gy) for a constant level of late complications (α/β = 3 Gy) would be X or X-1 weeks, where X is the doubling time of the tumour cells in days (Fowler 1990). For median doubling times of about 5 days, overall times of 4 or 5 weeks should be ideal. (U.K.)
Compartmental modelling of the pharmacokinetics of a breast cancer resistance protein.
Grandjean, Thomas R B; Chappell, Mike J; Yates, James T W; Jones, Kevin; Wood, Gemma; Coleman, Tanya
2011-11-01
A mathematical model for the pharmacokinetics of Hoechst 33342 following administration into a culture medium containing a population of transfected cells (HEK293 hBCRP) with a potent breast cancer resistance protein inhibitor, Fumitremorgin C (FTC), present is described. FTC is reported to almost completely annul resistance mediated by BCRP in vitro. This non-linear compartmental model has seven macroscopic sub-units, with 14 rate parameters. It describes the relationship between the concentration of Hoechst 33342 and FTC, initially spiked in the medium, and the observed change in fluorescence due to Hoechst 33342 binding to DNA. Structural identifiability analysis has been performed using two methods, one based on the similarity transformation/exhaustive modelling approach and the other based on the differential algebra approach. The analyses demonstrated that all models derived are uniquely identifiable for the experiments/observations available. A kinetic modelling software package, namely FACSIMILE (MPCA Software, UK), was used for parameter fitting and to obtain numerical solutions for the system equations. Model fits gave very good agreement with in vitro data provided by AstraZeneca across a variety of experimental scenarios. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.
International Nuclear Information System (INIS)
Smith, G.T.; Hubner, K.F.; Goodman, M.M.; Stubbs, J.B.
1992-01-01
Positron emission tomography (PET) has been used to measure tissue radiotracer concentration in vivo. Radiochemical distribution can be determined with compartmental model analysis. A two compartment model describes the kinetics of N-13 ammonia ( 13 NH 3 ) in the myocardium. The model consists of a vascular space, Q 1 and a space for 13 NH 3 bound within the tissue, Q 2 . Differential equations for the model can be written: X(t) = AX(t) + BU( t), Y(t)= CX(t)+ DU(t) (1) where X(t) is a column vector [Q 1 (t); Q 2 (t)], U(t) is the arterial input activity measured from the left ventricular blood pool, and Y(t) is the measured tissue activity using PET. Matrices A, B, C, and D are dependent on physiological parameters describing the kinetics of 13 NH 3 in the myocardium. Estimated parameter matrices in Equation 1 have been validated in dog experiments by measuring myocardial perfusion with dynamic PET scanning and intravenous injection of 13 NH 3 . Tracer concentrations for each compartment can be calculated by direct integration of Equation 1. If the cellular level distribution of each compartment is known, the concentration of tracer within the intracellular and extracellular space can be determined. Applications of this type of modeling include parameter estimation for measurement of physiological processes, organ level dosimetry, and determination of cellular radiotracer distribution
Energy Technology Data Exchange (ETDEWEB)
DeAngelis, D.L.; Yeh, G.T.; Huff, D.D.
1984-10-01
This report documents a model, FRACPORT, that simulates the transport of a solute through a fractured porous matrix. The model should be useful in analyzing the possible transport of radionuclides from shallow-land burial sites in humid environments. The use of the model is restricted to transport through saturated zones. The report first discusses the general modeling approach used, which is based on the Integrated Compartmental Method. The basic equations of solute transport are then presented. The model, which assumes a known water velocity field, solves these equations on two different time scales; one related to rapid transport of solute along fractures and the other related to slower transport through the porous matrix. FRACPORT is validated by application to a simple example of fractured porous medium transport that has previously been analyzed by other methods. Then its utility is demonstrated in analyzing more complex cases of pulses of solute into a fractured matrix. The report serves as a user's guide to FRACPORT. A detailed description of data input, along with a listing of input for a sample problem, is provided. 16 references, 18 figures, 3 tables.
Proposing a Compartmental Model for Leprosy and Parameterizing Using Regional Incidence in Brazil.
Smith, Rebecca Lee
2016-08-01
Hansen's disease (HD), or leprosy, is still considered a public health risk in much of Brazil. Understanding the dynamics of the infection at a regional level can aid in identification of targets to improve control. A compartmental continuous-time model for leprosy dynamics was designed based on understanding of the biology of the infection. The transmission coefficients for the model and the rate of detection were fit for each region using Approximate Bayesian Computation applied to paucibacillary and multibacillary incidence data over the period of 2000 to 2010, and model fit was validated on incidence data from 2011 to 2012. Regional variation was noted in detection rate, with cases in the Midwest estimated to be infectious for 10 years prior to detection compared to 5 years for most other regions. Posterior predictions for the model estimated that elimination of leprosy as a public health risk would require, on average, 44-45 years in the three regions with the highest prevalence. The model is easily adaptable to other settings, and can be studied to determine the efficacy of improved case finding on leprosy control.
Linear least squares compartmental-model-independent parameter identification in PET
International Nuclear Information System (INIS)
Thie, J.A.; Smith, G.T.; Hubner, K.F.
1997-01-01
A simplified approach involving linear-regression straight-line parameter fitting of dynamic scan data is developed for both specific and nonspecific models. Where compartmental-model topologies apply, the measured activity may be expressed in terms of: its integrals, plasma activity and plasma integrals -- all in a linear expression with macroparameters as coefficients. Multiple linear regression, as in spreadsheet software, determines parameters for best data fits. Positron emission tomography (PET)-acquired gray-matter images in a dynamic scan are analyzed: both by this method and by traditional iterative nonlinear least squares. Both patient and simulated data were used. Regression and traditional methods are in expected agreement. Monte-Carlo simulations evaluate parameter standard deviations, due to data noise, and much smaller noise-induced biases. Unique straight-line graphical displays permit visualizing data influences on various macroparameters as changes in slopes. Advantages of regression fitting are: simplicity, speed, ease of implementation in spreadsheet software, avoiding risks of convergence failures or false solutions in iterative least squares, and providing various visualizations of the uptake process by straight line graphical displays. Multiparameter model-independent analyses on lesser understood systems is also made possible
Retinol metabolism in rats with low vitamin A status: A compartmental model
International Nuclear Information System (INIS)
Lewis, K.C.; Green, M.H.; Green, J.B.; Zech, L.A.
1990-01-01
A compartmental model was developed to describe the metabolism of vitamin A in rats with low vitamin A status maintained by a low dietary intake of vitamin A (approximately 2 micrograms retinol equivalents/day). After the IV bolus injection of [3H]retinol in its physiological transport complex, tracer and trace data were obtained from plasma, organs (liver, kidneys, small intestine, eyes, adrenals, testes, lungs, carcass), and tracer data were obtained from urine and feces. The dietary protocol developed for this study resulted in animals having plasma vitamin A levels less than 10 micrograms retinol/dl and total liver vitamin A levels of approximately 1 microgram retinol equivalent. Four compartments were used to model the plasma: one to describe retinol, one to describe the nonphysiological portion of the dose, and two to simulate polar metabolites derived from retinol. The liver required two compartments and a delay, the carcass (small intestine, eyes, adrenals, testes, and lungs, plus remaining carcass) required three compartments, and the kidneys required two. The model predicted a vitamin A utilization rate of 1.65 micrograms retinol equivalents/day with the urine and feces accounting for most of the output. The plasma retinol turnover rate was approximately 20 micrograms retinol equivalents/day; this was 12 times greater than the utilization rate. This indicated that, of the large amount of retinol moving through the plasma each day, less than 10% of this was actually being irreversibly utilized. Similarly, as compared to the whole-body utilization rate, there was a relatively high turnover rate of retinol in the kidneys, carcass, and liver, coupled with a high degree of recycling of vitamin A through these tissues. Of the total vitamin A that entered the liver from all sources including the diet, approximately 86% was mobilized into the plasma
Linear regressive model structures for estimation and prediction of compartmental diffusive systems
Vries, D; Keesman, K.J.; Zwart, Heiko J.
In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state space
Linear regressive model structures for estimation and prediction of compartmental diffusive systems
Vries, D.; Keesman, K.J.; Zwart, H.
2006-01-01
Abstract In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state
Validation of Bayesian analysis of compartmental kinetic models in medical imaging.
Sitek, Arkadiusz; Li, Quanzheng; El Fakhri, Georges; Alpert, Nathaniel M
2016-10-01
Kinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated. The closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach. Posteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P>0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P<0.0001). The results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Compartmental study of biological systems
International Nuclear Information System (INIS)
Moretti, J.L.
1975-01-01
The compartmental analysis of biological system is dealt with on several chapters devoted successively to: terminology; a mathematical and symbolic account of a system at equilibrium; different compartment systems; analysis of the experimental results. For this it is pointed out that the application of compartmental systems to biological phenomena is not always without danger. Sometimes the compartmental system established in a reference subject fails to conform in the patient. The compartments can divide into two or join together, completely changing the aspect of the system so that parameters calculated with the old model become entirely false. The conclusion is that the setting up of a compartmental system to represent a biological phenomenon is a tricky undertaking and the results must be constantly criticized and questioned [fr
Computer Modeling of Sand Transport on Mars Using a Compart-Mentalized Fluids Algorithm (CFA)
Marshall, J.; Stratton, D.
1999-01-01
of sand comminution on Mars. A multiple-grain transport model using just the equations of grain motion describing lift and drag is impossible to develop owing to stochastic effects --the very effects we wish to model. Also, unless we were to employ supercomputing techniques and extremely complex computer codes that could deal with millions of grains simultaneously, it would also be difficult to model grain transport if we attempted to consider every grain in motion. No existing computer models were found that satisfactorily used the equations of motion to arrive at transport flux numbers for the different populations of saltation and reptation. Modeling all the grains in a transport system was an intractable problem within our resources, and thus we developed what we believe to be a new modeling approach to simulating grain transport. The CFA deals with grain populations, but considers them to belong to various compartmentalized fluid units in the boundary layer. In this way, the model circumvents the multigrain problem by dealing primarily with the consequences of grain transport --momentum transfer between air and grains, which is the physical essence of a dynamic grain-fluid mixture. We thus chose to model the aeolian transport process as a superposition of fluids. These fluids include the air as well as particle populations of various properties. The prime property distinguishing these fluids is upward and downward grain motion. In a normal saltation trajectory, a grain's downwind velocity increases with time, so a rising grain will have a smaller downwind velocity than a failing grain. Because of this disparity in rising and falling grain proper-ties, it seemed appropriate to track these as two separate grain populations within the same physical space. The air itself can be considered a separate fluid superimposed within and interacting with the various grain-cloud "fluids". Additional informaiton is contained in the original.
Energy Technology Data Exchange (ETDEWEB)
Slatt, R. [Colorado School of Mines, Golden, CO (United States); Jordan, D. [Arco International Oil and Gas Co., Plano, TX (United States); Stone, C. [Arkansas Geological Commission, Little Rock, AR (United States)] [and others
1995-08-01
Hollywood Quarry is a 600 x 375 x 150 ft. (200 x 125 x 50m) excavation which provides a window into lower Pennsylvanian Jackfork Formation turbidite stratal architecture along the crest of a faulted anticlinal fold. A variety of turbidite facies are present, including: (a) lenticular, channelized sandstones, pebbly sandstones, and conglomerates within shale, (b) laterally continuous, interbedded thin sandstones and shales, and (c) thicker, laterally continuous shales. The sandstone and shale layers we broken by several strike-slip and reverse faults, with vertical displacements of up to several feet. This combination of facies and structural elements has resulted in a highly compartmentalized stratigraphic interval, both horizontally and vertically, along the anticlinal flexure. The quarry can be considered analogous to a scaled-down turbidite reservoir. Outcrop gamma-ray logs, measured sections, a fault map, and cross sections provide a database which is analogous to what would be available for a subsurface reservoir. Thus, the quarry provides an ideal outdoor geologic and engineering {open_quote}workshop{close_quote} venue for visualizing the potential complexities of a combination structural-stratigraphic (turbidite) reservoir. Since all forms of compartmentalization are readily visible in the quarry, problems related to management of compartmentalized reservoirs can be discussed and analyzed first-hand while standing in the quarry, within this {open_quote}model reservoir{close_quotes}. These problems include: (a) the high degree of stratigraphic and structural complexity that may be encountered, even at close well spacings, (b) uncertainty in well log correlations and log-shape interpretations, (c) variations in volumetric calculations as a function of amount of data available, and (d) potential production problems associated with specific {open_quote}field{close_quote} development plans.
Application of compartmental metabolic models for determination of retention and excretion functions
International Nuclear Information System (INIS)
Rodrigues Junior, O.
1994-01-01
After an intake of radioactive material, its behaviour in the human body can be described by mathematical models, where organs, tissues or regions of the body are treated as a chain of linked compartments. The mathematical approach for such metabolic models is usually done through a system of differential equations of first order with constant coefficients. The solutions of this system of equations associates the radionuclide intake, with the fraction excreted or retained in the organ of interest. A computer program - called INCORP and for running in PC compatible microcomputers - was developed in order to find the solutions of such system of equations, using an analytical method based on expansion of series of exponential matrices. The metabolic model presented in the ICRP-30 publication was simulated using the INCORP program, in order to find the respective retention and excretion curves for selected radionuclides. (author)
A fractional model for dye removal
Directory of Open Access Journals (Sweden)
Ji-Huan He
2016-01-01
Full Text Available The adsorption process has a fractional property, and a fractional model is suggested to study a transport model of direct textile industry wastewater. An approximate solution of the concentration is obtained by the variational iteration method.
DEFF Research Database (Denmark)
Parlesak, Alexandr; Haller, D.; Brinz, S.
2004-01-01
To further investigate the interaction between human mononuclear leucocytes [peripheral blood mononuclear cells (PBMC)] and enterocytes, the effect of a confluent layer of differentiated CACO-2 cells on cytokine kinetics during challenge with bacteria in a compartmentalized coculture model...... cells when leucocytes were stimulated directly with bacteria. This suppression was not paralleled by changes in the production of IL-10, IL-6 and transforming growth factor (TGF)-beta. When the bacteria were applied apically to the CACO-2 cell layer, the production of TNF-alpha, IL-12, IL-1beta, IL-8......, IL-6, IL-10, TGF-beta and interferon-gamma was pronouncedly lower as compared to the bacterial stimulation of leucocytes beneath the CACO-2 cells. In the latter experiments, IL-6, IL-8 and TNF-alpha were the cytokines being mostly induced by apical addition of E. coli. Quantitative mRNA expression...
Moran, Nancy E; Cichon, Morgan J; Riedl, Kenneth M; Grainger, Elizabeth M; Schwartz, Steven J; Novotny, Janet A; Erdman, John W; Clinton, Steven K
2015-12-01
Lycopene, which is a red carotenoid in tomatoes, has been hypothesized to mediate disease-preventive effects associated with tomato consumption. Lycopene is consumed primarily as the all-trans geometric isomer in foods, whereas human plasma and tissues show greater proportions of cis isomers. With the use of compartmental modeling and stable isotope technology, we determined whether endogenous all-trans-to-cis-lycopene isomerization or isomeric-bioavailability differences underlie the greater proportion of lycopene cis isomers in human tissues than in tomato foods. Healthy men (n = 4) and women (n = 4) consumed (13)C-lycopene (10.2 mg; 82% all-trans and 18% cis), and plasma was collected over 28 d. Unlabeled and (13)C-labeled total lycopene and lycopene-isomer plasma concentrations, which were measured with the use of high-performance liquid chromatography-mass spectrometry, were fit to a 7-compartment model. Subjects absorbed a mean ± SEM of 23% ± 6% of the lycopene. The proportion of plasma cis-(13)C-lycopene isomers increased over time, and all-trans had a shorter half-life than that of cis isomers (5.3 ± 0.3 and 8.8 ± 0.6 d, respectively; P lycopene bioavailability and endogenous trans-to-cis-lycopene isomerization was predictive of plasma (13)C and unlabeled cis- and all-trans-lycopene concentrations. Although the bioavailability of cis (24.5% ± 6%) and all-trans (23.2% ± 8%) isomers did not differ, endogenous isomerization (0.97 ± 0.25 μmol/d in the fast-turnover tissue lycopene pool) drove tissue and plasma isomeric profiles. (13)C-Lycopene combined with physiologic compartmental modeling provides a strategy for following complex in vivo metabolic processes in humans and reveals that postabsorptive trans-to-cis-lycopene isomerization, and not the differential bioavailability of isomers, drives tissue and plasma enrichment of cis-lycopene. This trial was registered at clinicaltrials.gov as NCT01692340. © 2015 American Society for Nutrition.
Moran, Nancy E; Cichon, Morgan J; Riedl, Kenneth M; Grainger, Elizabeth M; Schwartz, Steven J; Novotny, Janet A; Erdman, John W; Clinton, Steven K
2015-01-01
Background: Lycopene, which is a red carotenoid in tomatoes, has been hypothesized to mediate disease-preventive effects associated with tomato consumption. Lycopene is consumed primarily as the all-trans geometric isomer in foods, whereas human plasma and tissues show greater proportions of cis isomers. Objective: With the use of compartmental modeling and stable isotope technology, we determined whether endogenous all-trans-to-cis-lycopene isomerization or isomeric-bioavailability differences underlie the greater proportion of lycopene cis isomers in human tissues than in tomato foods. Design: Healthy men (n = 4) and women (n = 4) consumed 13C-lycopene (10.2 mg; 82% all-trans and 18% cis), and plasma was collected over 28 d. Unlabeled and 13C-labeled total lycopene and lycopene-isomer plasma concentrations, which were measured with the use of high-performance liquid chromatography–mass spectrometry, were fit to a 7-compartment model. Results: Subjects absorbed a mean ± SEM of 23% ± 6% of the lycopene. The proportion of plasma cis-13C-lycopene isomers increased over time, and all-trans had a shorter half-life than that of cis isomers (5.3 ± 0.3 and 8.8 ± 0.6 d, respectively; P lycopene bioavailability and endogenous trans-to-cis-lycopene isomerization was predictive of plasma 13C and unlabeled cis- and all-trans-lycopene concentrations. Although the bioavailability of cis (24.5% ± 6%) and all-trans (23.2% ± 8%) isomers did not differ, endogenous isomerization (0.97 ± 0.25 μmol/d in the fast-turnover tissue lycopene pool) drove tissue and plasma isomeric profiles. Conclusion: 13C-Lycopene combined with physiologic compartmental modeling provides a strategy for following complex in vivo metabolic processes in humans and reveals that postabsorptive trans-to-cis-lycopene isomerization, and not the differential bioavailability of isomers, drives tissue and plasma enrichment of cis-lycopene. This trial was registered at clinicaltrials.gov as NCT01692340. PMID
Liu, Huolong; Li, Mingzhong
2014-11-20
In this work a two-compartmental population balance model (TCPBM) was proposed to model a pulsed top-spray fluidized bed granulation. The proposed TCPBM considered the spatially heterogeneous granulation mechanisms of the granule growth by dividing the granulator into two perfectly mixed zones of the wetting compartment and drying compartment, in which the aggregation mechanism was assumed in the wetting compartment and the breakage mechanism was considered in the drying compartment. The sizes of the wetting and drying compartments were constant in the TCPBM, in which 30% of the bed was the wetting compartment and 70% of the bed was the drying compartment. The exchange rate of particles between the wetting and drying compartments was determined by the details of the flow properties and distribution of particles predicted by the computational fluid dynamics (CFD) simulation. The experimental validation has shown that the proposed TCPBM can predict evolution of the granule size and distribution within the granulator under different binder spray operating conditions accurately. Copyright © 2014 Elsevier B.V. All rights reserved.
Wang, Kai; Riera, Jorge; Enjieu-Kadji, Herve; Kawashima, Ryuta
2013-07-01
With the rapid increase in the number of technologies aimed at observing electric activity inside the brain, scientists have felt the urge to create proper links between intracellular- and extracellular-based experimental approaches. Biophysical models at both physical scales have been formalized under assumptions that impede the creation of such links. In this work, we address this issue by proposing a multicompartment model that allows the introduction of complex extracellular and intracellular resistivity profiles. This model accounts for the geometrical and electrotonic properties of any type of neuron through the combination of four devices: the integrator, the propagator, the 3D connector, and the collector. In particular, we applied this framework to model the tufted pyramidal cells of layer 5 (PCL5) in the neocortex. Our model was able to reproduce the decay and delay curves of backpropagating action potentials (APs) in this type of cell with better agreement with experimental data. We used the voltage drops of the extracellular resistances at each compartment to approximate the local field potentials generated by a PCL5 located in close proximity to linear microelectrode arrays. Based on the voltage drops produced by backpropagating APs, we were able to estimate the current multipolar moments generated by a PCL5. By adding external current sources in parallel to the extracellular resistances, we were able to create a sensitivity profile of PCL5 to electric current injections from nearby microelectrodes. In our model for PCL5, the kinetics and spatial profile of each ionic current were determined based on a literature survey, and the geometrical properties of these cells were evaluated experimentally. We concluded that the inclusion of the extracellular space in the compartmental models of neurons as an extra electrotonic medium is crucial for the accurate simulation of both the propagation of the electric potentials along the neuronal dendrites and the
Kallehauge, Jesper F; Sourbron, Steven; Irving, Benjamin; Tanderup, Kari; Schnabel, Julia A; Chappell, Michael A
2017-06-01
Fitting tracer kinetic models using linear methods is much faster than using their nonlinear counterparts, although this comes often at the expense of reduced accuracy and precision. The aim of this study was to derive and compare the performance of the linear compartmental tissue uptake (CTU) model with its nonlinear version with respect to their percentage error and precision. The linear and nonlinear CTU models were initially compared using simulations with varying noise and temporal sampling. Subsequently, the clinical applicability of the linear model was demonstrated on 14 patients with locally advanced cervical cancer examined with dynamic contrast-enhanced magnetic resonance imaging. Simulations revealed equal percentage error and precision when noise was within clinical achievable ranges (contrast-to-noise ratio >10). The linear method was significantly faster than the nonlinear method, with a minimum speedup of around 230 across all tested sampling rates. Clinical analysis revealed that parameters estimated using the linear and nonlinear CTU model were highly correlated (ρ ≥ 0.95). The linear CTU model is computationally more efficient and more stable against temporal downsampling, whereas the nonlinear method is more robust to variations in noise. The two methods may be used interchangeably within clinical achievable ranges of temporal sampling and noise. Magn Reson Med 77:2414-2423, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.
Fractional Order Models of Industrial Pneumatic Controllers
Directory of Open Access Journals (Sweden)
Abolhassan Razminia
2014-01-01
Full Text Available This paper addresses a new approach for modeling of versatile controllers in industrial automation and process control systems such as pneumatic controllers. Some fractional order dynamical models are developed for pressure and pneumatic systems with bellows-nozzle-flapper configuration. In the light of fractional calculus, a fractional order derivative-derivative (FrDD controller and integral-derivative (FrID are remodeled. Numerical simulations illustrate the application of the obtained theoretical results in simple examples.
A Fractionally Integrated Wishart Stochastic Volatility Model
M. Asai (Manabu); M.J. McAleer (Michael)
2013-01-01
textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of
A framework for 2-stage global sensitivity analysis of GastroPlus™ compartmental models.
Scherholz, Megerle L; Forder, James; Androulakis, Ioannis P
2018-04-01
Parameter sensitivity and uncertainty analysis for physiologically based pharmacokinetic (PBPK) models are becoming an important consideration for regulatory submissions, requiring further evaluation to establish the need for global sensitivity analysis. To demonstrate the benefits of an extensive analysis, global sensitivity was implemented for the GastroPlus™ model, a well-known commercially available platform, using four example drugs: acetaminophen, risperidone, atenolol, and furosemide. The capabilities of GastroPlus were expanded by developing an integrated framework to automate the GastroPlus graphical user interface with AutoIt and for execution of the sensitivity analysis in MATLAB ® . Global sensitivity analysis was performed in two stages using the Morris method to screen over 50 parameters for significant factors followed by quantitative assessment of variability using Sobol's sensitivity analysis. The 2-staged approach significantly reduced computational cost for the larger model without sacrificing interpretation of model behavior, showing that the sensitivity results were well aligned with the biopharmaceutical classification system. Both methods detected nonlinearities and parameter interactions that would have otherwise been missed by local approaches. Future work includes further exploration of how the input domain influences the calculated global sensitivity measures as well as extending the framework to consider a whole-body PBPK model.
Directory of Open Access Journals (Sweden)
Vladimir E Bondarenko
Full Text Available The β1-adrenergic signaling system plays an important role in the functioning of cardiac cells. Experimental data shows that the activation of this system produces inotropy, lusitropy, and chronotropy in the heart, such as increased magnitude and relaxation rates of [Ca(2+]i transients and contraction force, and increased heart rhythm. However, excessive stimulation of β1-adrenergic receptors leads to heart dysfunction and heart failure. In this paper, a comprehensive, experimentally based mathematical model of the β1-adrenergic signaling system for mouse ventricular myocytes is developed, which includes major subcellular functional compartments (caveolae, extracaveolae, and cytosol. The model describes biochemical reactions that occur during stimulation of β1-adrenoceptors, changes in ionic currents, and modifications of Ca(2+ handling system. Simulations describe the dynamics of major signaling molecules, such as cyclic AMP and protein kinase A, in different subcellular compartments; the effects of inhibition of phosphodiesterases on cAMP production; kinetics and magnitudes of phosphorylation of ion channels, transporters, and Ca(2+ handling proteins; modifications of action potential shape and duration; magnitudes and relaxation rates of [Ca(2+]i transients; changes in intracellular and transmembrane Ca(2+ fluxes; and [Na(+]i fluxes and dynamics. The model elucidates complex interactions of ionic currents upon activation of β1-adrenoceptors at different stimulation frequencies, which ultimately lead to a relatively modest increase in action potential duration and significant increase in [Ca(2+]i transients. In particular, the model includes two subpopulations of the L-type Ca(2+ channels, in caveolae and extracaveolae compartments, and their effects on the action potential and [Ca(2+]i transients are investigated. The presented model can be used by researchers for the interpretation of experimental data and for the developments of
Compartmental model for tritium persistence in the soil-plant system
International Nuclear Information System (INIS)
Iyengar, T.S.; Sadarangani, S.H.; Vaze, P.K.; Soman, S.D.
1977-01-01
A three-component computer model for tritium persistence in the soil-plant system, on the basis of an exponential polynomial is attempted. A series of field experiments with four species of trees, viz. Cardia sebastina, Terminalia catappa, Aracaria bidwilli and Mangifera indica, were carried out to generate data for testing the model. It is observed that there are two short-term components and one long-term component for tritium mean residence time, corresponding to the three phases of tritium in the system, viz. Tissue-Free-Water-Tritium, labile component of Tissue-Bound-Tritium and non-labile component of Tissue-Bound-Tritium. (author)
Simulation of radon short lived decay daughters' inhalation using the lung compartmental model
International Nuclear Information System (INIS)
Tomulescu, Vlad C.
2002-01-01
Radon and its short-lived decay daughters are the main source of radiation on natural ways for population. The radon gas, released from soil, water or construction materials is producing by radioactive decay the following solid daughters: Po-218, Bi-214, Pb-214, and Po-214, which can attach to aerosols, and consequently penetrate the organism by inhalation. The human respiratory tract can be approximated by aid of a compartment model that takes into account the different anatomical structures exposed to contamination and irradiation, as well as the respective physiological processes. This model is associated to a mathematical equation system that describes the behavior of the radioactive material inside the body. The results represent the dose equivalent on different organs and tissues, as a function of subject and the activity performed in contaminating environment. (author)
Ott, Wayne R; Klepeis, Neil E; Switzer, Paul
2003-08-01
This paper derives the analytical solutions to multi-compartment indoor air quality models for predicting indoor air pollutant concentrations in the home and evaluates the solutions using experimental measurements in the rooms of a single-story residence. The model uses Laplace transform methods to solve the mass balance equations for two interconnected compartments, obtaining analytical solutions that can be applied without a computer. Environmental tobacco smoke (ETS) sources such as the cigarette typically emit pollutants for relatively short times (7-11 min) and are represented mathematically by a "rectangular" source emission time function, or approximated by a short-duration source called an "impulse" time function. Other time-varying indoor sources also can be represented by Laplace transforms. The two-compartment model is more complicated than the single-compartment model and has more parameters, including the cigarette or combustion source emission rate as a function of time, room volumes, compartmental air change rates, and interzonal air flow factors expressed as dimensionless ratios. This paper provides analytical solutions for the impulse, step (Heaviside), and rectangular source emission time functions. It evaluates the indoor model in an unoccupied two-bedroom home using cigars and cigarettes as sources with continuous measurements of carbon monoxide (CO), respirable suspended particles (RSP), and particulate polycyclic aromatic hydrocarbons (PPAH). Fine particle mass concentrations (RSP or PM3.5) are measured using real-time monitors. In our experiments, simultaneous measurements of concentrations at three heights in a bedroom confirm an important assumption of the model-spatial uniformity of mixing. The parameter values of the two-compartment model were obtained using a "grid search" optimization method, and the predicted solutions agreed well with the measured concentration time series in the rooms of the home. The door and window positions in
A Computational Model of Fraction Arithmetic
Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.
2017-01-01
Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…
International Nuclear Information System (INIS)
Smith, C.N.; Clarke, S.; McDonald, P.; Goshawk, J.A.; Jones, S.R.
2000-01-01
A mathematical model is presented that simulates the annually averaged transport of radionuclides, originating from the BNFL reprocessing plant at Sellafield, throughout the Irish Sea. The model, CUMBRIA77, represents the processes of radionuclide transport and dispersion in the marine environment and allows predictions of radionuclide concentration in various environmental media, including biota, to be made throughout the whole of the Irish Sea. In this paper we describe the use of the model to reconstruct the historical activity concentrations of 137Cs and 239+240Pu in a variety of environmental media in the western Irish Sea and along the Irish east coast back to 1950. This reconstruction exercise is of interest because only limited measurements of 137Cs and 239+240Pu activity are available prior to the 1980s. The predictions were compared to the available measured data to validate their accuracy. The results of the reconstruction indicate that activity concentrations of 137Cs in the western Irish Sea follow a similar, though slightly delayed and smoothed, profile to the discharges from the Sellafield site, with concentrations at the time of peak discharge (the mid-1970s) being around an order of magnitude higher than those measured in the 1980s and 1990s. By contrast, the concentrations of 239+240Pu at the time of peak discharges were similar to those presently measured. These differences reflect the distinct marine chemistries of the two nuclides, in particular the higher propensity of plutonium to bind to sediments leading to extended transport times. Despite these differences in behaviour the doses to Irish seafood consumers from 137Cs remain significantly higher than those from 239+240Pu
DEFF Research Database (Denmark)
Liu, Joanne K.; O’Brien, Edward J.; Lerman, Joshua A.
2014-01-01
Background: Membranes play a crucial role in cellular functions. Membranes provide a physical barrier, control the trafficking of substances entering and leaving the cell, and are a major determinant of cellular ultra-structure. In addition, components embedded within the membrane participate...... the computation of cellular phenotypes through an integrated computation of proteome composition, abundance, and activity in four cellular compartments (cytoplasm, periplasm, inner and outer membrane). Reconstruction and validation of the model has demonstrated that the iJL1678-ME is capable of capturing...
Comparative study of void fraction models
International Nuclear Information System (INIS)
Borges, R.C.; Freitas, R.L.
1985-01-01
Some models for the calculation of void fraction in water in sub-cooled boiling and saturated vertical upward flow with forced convection have been selected and compared with experimental results in the pressure range of 1 to 150 bar. In order to know the void fraction axial distribution it is necessary to determine the net generation of vapour and the fluid temperature distribution in the slightly sub-cooled boiling region. It was verified that the net generation of vapour was well represented by the Saha-Zuber model. The selected models for the void fraction calculation present adequate results but with a tendency to super-estimate the experimental results, in particular the homogeneous models. The drift flux model is recommended, followed by the Armand and Smith models. (F.E.) [pt
International Nuclear Information System (INIS)
Mutihac, R.; Mutihac, R.C.; Cicuttin, A.
2001-09-01
gradient-descent techniques are adequate if the parameter space is low-dimensional, relatively smooth, and has a few local minima (e.g., parameterizing single-neuron compartmental models). Only the fast algorithms and/or a decent (low) number of model parameters are candidates for automated parameter search because of practical reasons. Eventually, the size of the parameter space may be reduced and/or parallel supercomputers may be used. Data overfitting may negatively affect the generalization ability of the model. Bayesian methods include Occam's factor, which set the preference for simpler models. Proliferation of (neural) models raises the question of rigorous criteria for comparing the overall performance of various models designed to match the same type of data. Bayesian methods provide the best framework to assess the neural models quantitatively. Paradoxically, parameter-search methods may sometimes be more useful when they fail by discarding unrealistic mechanisms used in the model design, rather than fitting experimental data to an alleged model
Fractional diffusion models of nonlocal transport
International Nuclear Information System (INIS)
Castillo-Negrete, D. del
2006-01-01
A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ('memory') effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an α-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the 'effective' diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, τ, with the system's size, L, τ∼L α , of low-confinement mode plasma where 1<α<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments
A Network Thermodynamic Approach to Compartmental Analysis
Mikulecky, D. C.; Huf, E. G.; Thomas, S. R.
1979-01-01
We introduce a general network thermodynamic method for compartmental analysis which uses a compartmental model of sodium flows through frog skin as an illustrative example (Huf and Howell, 1974a). We use network thermodynamics (Mikulecky et al., 1977b) to formulate the problem, and a circuit simulation program (ASTEC 2, SPICE2, or PCAP) for computation. In this way, the compartment concentrations and net fluxes between compartments are readily obtained for a set of experimental conditions involving a square-wave pulse of labeled sodium at the outer surface of the skin. Qualitative features of the influx at the outer surface correlate very well with those observed for the short circuit current under another similar set of conditions by Morel and LeBlanc (1975). In related work, the compartmental model is used as a basis for simulation of the short circuit current and sodium flows simultaneously using a two-port network (Mikulecky et al., 1977a, and Mikulecky et al., A network thermodynamic model for short circuit current transients in frog skin. Manuscript in preparation; Gary-Bobo et al., 1978). The network approach lends itself to computation of classic compartmental problems in a simple manner using circuit simulation programs (Chua and Lin, 1975), and it further extends the compartmental models to more complicated situations involving coupled flows and non-linearities such as concentration dependencies, chemical reaction kinetics, etc. PMID:262387
Fractional virus epidemic model on financial networks
Directory of Open Access Journals (Sweden)
Balci Mehmet Ali
2016-01-01
Full Text Available In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.
Energy Technology Data Exchange (ETDEWEB)
Giraudeau, Celine; Leporq, Benjamin; Doblas, Sabrina [University Paris Diderot, Sorbonne Paris Cite, Hopital Beaujon, Laboratory of Imaging Biomarkers, UMR1149 Inserm, Clichy (France); Lagadec, Matthieu; Daire, Jean-Luc; Van Beers, Bernard E. [University Paris Diderot, Sorbonne Paris Cite, Hopital Beaujon, Laboratory of Imaging Biomarkers, UMR1149 Inserm, Clichy (France); Beaujon University Hospital Paris Nord, Department of Radiology, Clichy (France); Pastor, Catherine M. [University Paris Diderot, Sorbonne Paris Cite, Hopital Beaujon, Laboratory of Imaging Biomarkers, UMR1149 Inserm, Clichy (France); Hopitaux Universitaires de Geneve, Departement d' Imagerie et des Sciences de l' Information Medicale, Geneva (Switzerland)
2017-05-15
Changes in the expression of hepatocyte membrane transporters in advanced fibrosis decrease the hepatic transport function of organic anions. The aim of our study was to assess if these changes can be evaluated with pharmacokinetic analysis of the hepatobiliary transport of the MR contrast agent gadoxetate. Dynamic gadoxetate-enhanced MRI was performed in 17 rats with advanced fibrosis and 8 normal rats. After deconvolution, hepatocyte three-compartmental analysis was performed to calculate the hepatocyte influx, biliary efflux and sinusoidal backflux rates. The expression of Oatp1a1, Mrp2 and Mrp3 organic anion membrane transporters was assessed with reverse transcription polymerase chain reaction. In the rats with advanced fibrosis, the influx and efflux rates of gadoxetate decreased and the backflux rate increased significantly (p = 0.003, 0.041 and 0.010, respectively). Significant correlations were found between influx and Oatp1a1 expression (r = 0.78, p < 0.001), biliary efflux and Mrp2 (r = 0.50, p = 0.016) and sinusoidal backflux and Mrp3 (r = 0.61, p = 0.002). These results show that changes in the bidirectional organic anion hepatocyte transport function in rats with advanced liver fibrosis can be assessed with compartmental analysis of gadoxetate-enhanced MRI. (orig.)
International Nuclear Information System (INIS)
Giraudeau, Celine; Leporq, Benjamin; Doblas, Sabrina; Lagadec, Matthieu; Daire, Jean-Luc; Van Beers, Bernard E.; Pastor, Catherine M.
2017-01-01
Changes in the expression of hepatocyte membrane transporters in advanced fibrosis decrease the hepatic transport function of organic anions. The aim of our study was to assess if these changes can be evaluated with pharmacokinetic analysis of the hepatobiliary transport of the MR contrast agent gadoxetate. Dynamic gadoxetate-enhanced MRI was performed in 17 rats with advanced fibrosis and 8 normal rats. After deconvolution, hepatocyte three-compartmental analysis was performed to calculate the hepatocyte influx, biliary efflux and sinusoidal backflux rates. The expression of Oatp1a1, Mrp2 and Mrp3 organic anion membrane transporters was assessed with reverse transcription polymerase chain reaction. In the rats with advanced fibrosis, the influx and efflux rates of gadoxetate decreased and the backflux rate increased significantly (p = 0.003, 0.041 and 0.010, respectively). Significant correlations were found between influx and Oatp1a1 expression (r = 0.78, p < 0.001), biliary efflux and Mrp2 (r = 0.50, p = 0.016) and sinusoidal backflux and Mrp3 (r = 0.61, p = 0.002). These results show that changes in the bidirectional organic anion hepatocyte transport function in rats with advanced liver fibrosis can be assessed with compartmental analysis of gadoxetate-enhanced MRI. (orig.)
Popović, Jovan K.; Spasić, Dragan T.; Tošić, Jela; Kolarović, Jovanka L.; Malti, Rachid; Mitić, Igor M.; Pilipović, Stevan; Atanacković, Teodor M.
2015-05-01
The aim of this study is to promote a model based on the fractional differential calculus related to the pharmacokinetic individualization of high dose methotrexate treatment in children with acute lymphoblastic leukaemia, especially in high risk patients. We applied two-compartment fractional model on 8 selected cases with the largest number (4-19) of measured concentrations, among 43 pediatric patients received 24-h methotrexate 2-5 g/m2 infusions. The plasma concentrations were determined by fluorescence polarization immunoassay. Our mathematical procedure, designed by combining Post's and Newton's method, was coded in Mathematica 8.0 and performed on Fujicu Celsius M470-2 PC. Experimental data show that most of the measured values of methotrexate were in decreasing order. However, in certain treatments local maximums were detected. On the other hand, integer order compartmental models do not give values which fit well with the observed data. By the use of our model, we obtained better results, since it gives more accurate behavior of the transmission, as well as the local maximums which were recognized in methotrexate monitoring. It follows from our method that an additional test with a small methotrexate dose can be suggested for the fractional system parameter identification and the prediction of a possible pattern with a full dose in the case of high risk patients. A special feature of the fractional model is that it can also recognize and better fit an observed non-monotonic behavior. A new parameter determination procedure can be successfully used.
A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games
Institute of Scientific and Technical Information of China (English)
Kecai Cao; Yang Quan Chen; Daniel Stuart
2016-01-01
Modeling a crowd of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micromacro model for crowds of pedestrians are obtained in the end.Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model,respectively.
Fractional dynamical model for neurovascular coupling
Belkhatir, Zehor
2014-08-01
The neurovascular coupling is a key mechanism linking the neural activity to the hemodynamic behavior. Modeling of this coupling is very important to understand the brain function but it is at the same time very complex due to the complexity of the involved phenomena. Many studies have reported a time delay between the neural activity and the cerebral blood flow, which has been described by adding a delay parameter in some of the existing models. An alternative approach is proposed in this paper, where a fractional system is used to model the neurovascular coupling. Thanks to its nonlocal property, a fractional derivative is suitable for modeling the phenomena with delay. The proposed model is coupled with the first version of the well-known balloon model, which relates the cerebral blood flow to the Blood Oxygen Level Dependent (BOLD) signal measured using functional Magnetic Resonance Imaging (fMRI). Through some numerical simulations, the properties of the fractional model are explained and some preliminary comparisons to a real BOLD data set are provided. © 2014 IEEE.
Revised models of interstellar nitrogen isotopic fractionation
Wirström, E. S.; Charnley, S. B.
2018-03-01
Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom-molecular ion and ion-molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirström et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral-neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of >2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.
Dynamical models of happiness with fractional order
Song, Lei; Xu, Shiyun; Yang, Jianying
2010-03-01
This present study focuses on a dynamical model of happiness described through fractional-order differential equations. By categorizing people of different personality and different impact factor of memory (IFM) with different set of model parameters, it is demonstrated via numerical simulations that such fractional-order models could exhibit various behaviors with and without external circumstance. Moreover, control and synchronization problems of this model are discussed, which correspond to the control of emotion as well as emotion synchronization in real life. This study is an endeavor to combine the psychological knowledge with control problems and system theories, and some implications for psychotherapy as well as hints of a personal approach to life are both proposed.
Modeling electron fractionalization with unconventional Fock spaces.
Cobanera, Emilio
2017-08-02
It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality [Formula: see text] of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.
Energy Technology Data Exchange (ETDEWEB)
Zanzonico, Pat; O' Donoghue, Joseph A.; Humm, John L. [Memorial Sloan Kettering Cancer Center, Department of Medical Physics, New York, NY (United States); Carrasquillo, Jorge A.; Pandit-Taskar, Neeta; Ruan, Shutian; Larson, Steven M. [Memorial Sloan Kettering Cancer Center, Department of Radiology, New York, NY (United States); Smith-Jones, Peter [Memorial Sloan Kettering Cancer Center, Department of Radiology, New York, NY (United States); Stony Brook School of Medicine, Departments of Psychiatry and Radiology, Stony Brook, NY (United States); Divgi, Chaitanya [Columbia University Medical Center, New York, NY (United States); Scott, Andrew M. [La Trobe University, Olivia Newton-John Cancer Research Institute, Melbourne (Australia); Kemeny, Nancy E.; Wong, Douglas; Scheinberg, David [Memorial Sloan Kettering Cancer Center, Department of Medicine, New York, NY (United States); Fong, Yuman [Memorial Sloan Kettering Cancer Center, Department of Surgery, New York, NY (United States); City of Hope, Department of Surgery, Duarte, CA (United States); Ritter, Gerd; Jungbluth, Achem; Old, Lloyd J. [Memorial Sloan Kettering Cancer Center, Ludwig Institute for Cancer Research, New York, NY (United States)
2015-10-15
The molecular specificity of monoclonal antibodies (mAbs) directed against tumor antigens has proven effective for targeted therapy of human cancers, as shown by a growing list of successful antibody-based drug products. We describe a novel, nonlinear compartmental model using PET-derived data to determine the ''best-fit'' parameters and model-derived quantities for optimizing biodistribution of intravenously injected {sup 124}I-labeled antitumor antibodies. As an example of this paradigm, quantitative image and kinetic analyses of anti-A33 humanized mAb (also known as ''A33'') were performed in 11 colorectal cancer patients. Serial whole-body PET scans of {sup 124}I-labeled A33 and blood samples were acquired and the resulting tissue time-activity data for each patient were fit to a nonlinear compartmental model using the SAAM II computer code. Excellent agreement was observed between fitted and measured parameters of tumor uptake, ''off-target'' uptake in bowel mucosa, blood clearance, tumor antigen levels, and percent antigen occupancy. This approach should be generally applicable to antibody-antigen systems in human tumors for which the masses of antigen-expressing tumor and of normal tissues can be estimated and for which antibody kinetics can be measured with PET. Ultimately, based on each patient's resulting ''best-fit'' nonlinear model, a patient-specific optimum mAb dose (in micromoles, for example) may be derived. (orig.)
Parameter estimation in fractional diffusion models
Kubilius, Kęstutis; Ralchenko, Kostiantyn
2017-01-01
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides s...
International Nuclear Information System (INIS)
Gremare, A.; Amouroux, J.M.; Charles, F.
1991-01-01
The present study assesses the problem of recycling when using radiotracers to quantify ingestion and assimilation rates of particulate organic matter by benthic invertebrates. The rapid production of dissolved organic matter and its subsequent utilization by benthic invertebrates constitutes a major bias in this kind of study. However recycling processes may also concern POM through the production and reingestion of faeces. The present paper shows that compartmental analysis of the diffusion kinetics of the radiotracer between the different compartments of the system studied and the analog modelling of the exchanges of radioactivity between compartments may be used in order to determine ingestion and assimilation rates. This method is illustrated by the study of a system composed of the bacteria Lactobacillus sp. and the filter-feeding bivalve Venerupis decussata. The advantages and drawbacks of this approach relative to other existing methods are briefly discussed. (Author)
Fractional-moment Capital Asset Pricing model
International Nuclear Information System (INIS)
Li Hui; Wu Min; Wang Xiaotian
2009-01-01
In this paper, we introduce the definition of the 'α-covariance' and present the fractional-moment versions of Capital Asset Pricing Model,which can be used to price assets when asset return distributions are likely to be stable Levy (or Student-t) distribution during panics and stampedes in worldwide security markets in 2008. Furthermore, if asset returns are truly governed by the infinite-variance stable Levy distributions, life is fundamentally riskier than in a purely Gaussian world. Sudden price movements like the worldwide security market crash in 2008 turn into real-world possibilities.
Modeling of heat conduction via fractional derivatives
Fabrizio, Mauro; Giorgi, Claudio; Morro, Angelo
2017-09-01
The modeling of heat conduction is considered by letting the time derivative, in the Cattaneo-Maxwell equation, be replaced by a derivative of fractional order. The purpose of this new approach is to overcome some drawbacks of the Cattaneo-Maxwell equation, for instance possible fluctuations which violate the non-negativity of the absolute temperature. Consistency with thermodynamics is shown to hold for a suitable free energy potential, that is in fact a functional of the summed history of the heat flux, subject to a suitable restriction on the set of admissible histories. Compatibility with wave propagation at a finite speed is investigated in connection with temperature-rate waves. It follows that though, as expected, this is the case for the Cattaneo-Maxwell equation, the model involving the fractional derivative does not allow the propagation at a finite speed. Nevertheless, this new model provides a good description of wave-like profiles in thermal propagation phenomena, whereas Fourier's law does not.
Choiri, S.; Ainurofiq, A.
2018-03-01
Drug release from a montmorillonite (MMT) matrix is a complex mechanism controlled by swelling mechanism of MMT and an interaction of drug and MMT. The aim of this research was to explain a suitable model of the drug release mechanism from MMT and its binary mixture with a hydrophilic polymer in the controlled release formulation based on a compartmental modelling approach. Theophylline was used as a drug model and incorporated into MMT and a binary mixture with hydroxyl propyl methyl cellulose (HPMC) as a hydrophilic polymer, by a kneading method. The dissolution test was performed and the modelling of drug release was assisted by a WinSAAM software. A 2 model was purposed based on the swelling capability and basal spacing of MMT compartments. The model evaluation was carried out to goodness of fit and statistical parameters and models were validated by a cross-validation technique. The drug release from MMT matrix regulated by a burst release mechanism of unloaded drug, swelling ability, basal spacing of MMT compartment, and equilibrium between basal spacing and swelling compartments. Furthermore, the addition of HPMC in MMT system altered the presence of swelling compartment and equilibrium between swelling and basal spacing compartment systems. In addition, a hydrophilic polymer reduced the burst release mechanism of unloaded drug.
Ford, Jennifer Lynn; Green, Joanne Balmer; Lietz, Georg; Oxley, Anthony; Green, Michael H
2017-09-01
Background: Provitamin A carotenoids are an important source of dietary vitamin A for many populations. Thus, accurate and simple methods for estimating carotenoid bioefficacy are needed to evaluate the vitamin A value of test solutions and plant sources. β-Carotene bioefficacy is often estimated from the ratio of the areas under plasma isotope response curves after subjects ingest labeled β-carotene and a labeled retinyl acetate reference dose [isotope reference method (IRM)], but to our knowledge, the method has not yet been evaluated for accuracy. Objectives: Our objectives were to develop and test a physiologically based compartmental model that includes both absorptive and postabsorptive β-carotene bioconversion and to use the model to evaluate the accuracy of the IRM and a simple plasma retinol isotope ratio [(RIR), labeled β-carotene-derived retinol/labeled reference-dose-derived retinol in one plasma sample] for estimating relative bioefficacy. Methods: We used model-based compartmental analysis (Simulation, Analysis and Modeling software) to develop and apply a model that provided known values for β-carotene bioefficacy. Theoretical data for 10 subjects were generated by the model and used to determine bioefficacy by RIR and IRM; predictions were compared with known values. We also applied RIR and IRM to previously published data. Results: Plasma RIR accurately predicted β-carotene relative bioefficacy at 14 d or later. IRM also accurately predicted bioefficacy by 14 d, except that, when there was substantial postabsorptive bioconversion, IRM underestimated bioefficacy. Based on our model, 1-d predictions of relative bioefficacy include absorptive plus a portion of early postabsorptive conversion. Conclusion: The plasma RIR is a simple tracer method that accurately predicts β-carotene relative bioefficacy based on analysis of one blood sample obtained at ≥14 d after co-ingestion of labeled β-carotene and retinyl acetate. The method also provides
State-Space Modelling of Loudspeakers using Fractional Derivatives
DEFF Research Database (Denmark)
King, Alexander Weider; Agerkvist, Finn T.
2015-01-01
This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractio......This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data...
New method dynamically models hydrocarbon fractionation
Energy Technology Data Exchange (ETDEWEB)
Kesler, M.G.; Weissbrod, J.M.; Sheth, B.V. [Kesler Engineering, East Brunswick, NJ (United States)
1995-10-01
A new method for calculating distillation column dynamics can be used to model time-dependent effects of independent disturbances for a range of hydrocarbon fractionation. It can model crude atmospheric and vacuum columns, with relatively few equilibrium stages and a large number of components, to C{sub 3} splitters, with few components and up to 300 equilibrium stages. Simulation results are useful for operations analysis, process-control applications and closed-loop control in petroleum, petrochemical and gas processing plants. The method is based on an implicit approach, where the time-dependent variations of inventory, temperatures, liquid and vapor flows and compositions are superimposed at each time step on the steady-state solution. Newton-Raphson (N-R) techniques are then used to simultaneously solve the resulting finite-difference equations of material, equilibrium and enthalpy balances that characterize distillation dynamics. The important innovation is component-aggregation and tray-aggregation to contract the equations without compromising accuracy. This contraction increases the N-R calculations` stability. It also significantly increases calculational speed, which is particularly important in dynamic simulations. This method provides a sound basis for closed-loop, supervisory control of distillation--directly or via multivariable controllers--based on a rigorous, phenomenological column model.
International Nuclear Information System (INIS)
Araujo, Elaine Bortoleti de
1995-01-01
The present work reflects the clinical interest for labelling diamino dithiol compounds with technetium-99m. Both chosen compounds, L,L-Ethylene dicysteine (L,L-EC) and L,L-Ethylene dicysteine diethyl esther (L,L-ECD) were obtained with relative good yield and characterized by IR and NMR. The study of labelling conditions with technetium-99m showed the influence of the type and mass of reducing agent as well as the pH on the formation of complexes with desired biological characteristics. Radiochemical purity was determined by thin layer chromatography (TLC) and high performance liquid chromatography (HPLC). Lyophilised kits of L,L-EC and L,L-ECD for labelling with 99m Tc were obtained, with stability superior to 120 days, when stored under refrigeration, enabling the kits marketing. The ideal formulation of the kits as well as the use of liquid nitrogen in the freezing process, determined the lyophilization success. Distribution biological studies of the 99m Tc complexes were performed on mice by invasive method and on bigger animals by scintigraphic evaluation. Biological distribution studies of the complex 99m Tc-L,L-EC showed fast blood clearance, with the elimination of about 90% of the administered dose after 60 minutes, almost exclusively by the urinary system. The biological distribution results were adjusted to a three compartmental distribution model, as expected for a radiopharmaceutical designed to renal dynamic studies, with tubular elimination. The complex interaction with renal tubular receptors is related with structural characteristics of the compound, more specifically with the presence and location of polar groups. In comparison with 99m Tc-L,L-EC, biological studies of the complex 99m Tc -L,L-ECD showed different distribution aspects, despite some structural similarities. The presence of ethyl groups confers to the complex neutrality and lipophilicity. It cross the intact blood brain barrier and is retained in the brain for enough period
Katiyar, Prateek; Divine, Mathew R; Kohlhofer, Ursula; Quintanilla-Martinez, Leticia; Schölkopf, Bernhard; Pichler, Bernd J; Disselhorst, Jonathan A
2017-04-01
In this study, we described and validated an unsupervised segmentation algorithm for the assessment of tumor heterogeneity using dynamic 18 F-FDG PET. The aim of our study was to objectively evaluate the proposed method and make comparisons with compartmental modeling parametric maps and SUV segmentations using simulations of clinically relevant tumor tissue types. Methods: An irreversible 2-tissue-compartmental model was implemented to simulate clinical and preclinical 18 F-FDG PET time-activity curves using population-based arterial input functions (80 clinical and 12 preclinical) and the kinetic parameter values of 3 tumor tissue types. The simulated time-activity curves were corrupted with different levels of noise and used to calculate the tissue-type misclassification errors of spectral clustering (SC), parametric maps, and SUV segmentation. The utility of the inverse noise variance- and Laplacian score-derived frame weighting schemes before SC was also investigated. Finally, the SC scheme with the best results was tested on a dynamic 18 F-FDG measurement of a mouse bearing subcutaneous colon cancer and validated using histology. Results: In the preclinical setup, the inverse noise variance-weighted SC exhibited the lowest misclassification errors (8.09%-28.53%) at all noise levels in contrast to the Laplacian score-weighted SC (16.12%-31.23%), unweighted SC (25.73%-40.03%), parametric maps (28.02%-61.45%), and SUV (45.49%-45.63%) segmentation. The classification efficacy of both weighted SC schemes in the clinical case was comparable to the unweighted SC. When applied to the dynamic 18 F-FDG measurement of colon cancer, the proposed algorithm accurately identified densely vascularized regions from the rest of the tumor. In addition, the segmented regions and clusterwise average time-activity curves showed excellent correlation with the tumor histology. Conclusion: The promising results of SC mark its position as a robust tool for quantification of tumor
Analysis of Drude model using fractional derivatives without singular kernels
Directory of Open Access Journals (Sweden)
Jiménez Leonardo Martínez
2017-11-01
Full Text Available We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF, and fractional derivatives with a stretched Mittag-Leffler function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < γ ≤ 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when γ < 0.8.
International Nuclear Information System (INIS)
Araujo, E.B. de.
1990-01-01
Biologic distribution of p- [(bis-carboxymethylaminomethyl carboxyamino)] hippuric acid (PAHIDA) labeled with sup(99m)Tc in Wistar rats, showed a selective renal uptake among the other organs and tissues. The compound is predominantly eliminated by urinary tract, with small enterohepatic percent of excretion Chromatographic analysis of urine showed the product and possible metabolites. PAHIDA- sup(99m)Tc blood clearance is relatively rapid and a good percent is transported by plasmatic proteins. The percent binding to the erythrocytes is significant after one hour, this is due probably to hydrolysed technetium. The extrapolation of the plasmatic curve denoted the existence of three exponentials, suggesting a model with three compartments: central or intravascular and two peripherics or extravasculars - rapid and slow exchange (retention). Exponential's half life and the transfer constant (k) among the compartments were determined. The compound retention was reaffirmed by whole body determination. The decomposition of the curve in two exponentials allowed to assess the component's half-life. The compartmental model proposed in agreement with the experimental results, showed the complex retention that may be related the binding with the blood components, the possibility of renal metabolization or a structural impediment in the interaction with the tubular cells receptors. (author)
International Nuclear Information System (INIS)
Augusto Ciussani
2007-01-01
Complete test of publication follows. The successful application of radiopharmaceuticals requires a patient-specific optimization of the activity to be administered, in order to deliver the desired therapeutic dose to the target organ while saving the healthy tissues. For a therapy specifically tailored on the characteristics of the patient, the correct knowledge of the morphology of the regions of interest, of the fractional uptake and of the related kinetics is necessary. Compartmental modelling can represent a powerful and simple tool for deriving the information of interest. In this presentation, the potentiality of compartmental analysis will be illustrated and two applications presented. The first study was conducted in patients with the autonomous functioning thyroid nodule (AFTN) syndrome treated with 131 I at the Ospedale Maggiore Policlinico of Milano (Milano, Italy). In these patients, the great challenge is represented by the healthy lobe surrounding the malignant nodule. A model was developed, where nodule and lobe are considered as separate entities in order to provide distinct dose estimates for the two tissues. The model has been also used for the optimization of the sampling schedule and for interpretation of biokinetic discrepancies observed between the diagnostic tests and the therapeutic application. The second study, carried out at Ospedali Riuniti di Bergamo (Bergamo, Italy), dealt with the application of [ 186 Re]-HEDP (hydroxyethyliden-diphosphonate disodium salt) for palliation of pain due to bone metastases of primary carcinomas. On the basis of the biodistribution studies and of chromatographic measurements, a compartmental model was suggested, taking into account the possible dissociation of the compound after injection into the patient. Also in this case, the compartmental model represents a valuable tool for individual optimization of the therapeutic procedure and for a more precise evaluation of the radiation dose the organs.
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
Petráš, Ivo
2011-01-01
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...
Yamamoto, Yumi; Valitalo, Pyry A.; van den Berg, Dirk-Jan; Hartman, Robin; van den Brink, Willem; Wong, Yin Cheong; Huntjens, Dymphy R.; Proost, Johannes H.; Vermeulen, An; Krauwinkel, Walter; Bakshi, Suruchi; Aranzana-Climent, Vincent; Marchand, Sandrine; Dahyot-Fizelier, Claire; Couet, William; Danhof, Meindert; van Hasselt, Johan G. C.; de lange, Elizabeth C. M.
Purpose Predicting target site drug concentration in the brain is of key importance for the successful development of drugs acting on the central nervous system. We propose a generic mathematical model to describe the pharmacokinetics in brain compartments, and apply this model to predict human
Table-sized matrix model in fractional learning
Soebagyo, J.; Wahyudin; Mulyaning, E. C.
2018-05-01
This article provides an explanation of the fractional learning model i.e. a Table-Sized Matrix model in which fractional representation and its operations are symbolized by the matrix. The Table-Sized Matrix are employed to develop problem solving capabilities as well as the area model. The Table-Sized Matrix model referred to in this article is used to develop an understanding of the fractional concept to elementary school students which can then be generalized into procedural fluency (algorithm) in solving the fractional problem and its operation.
Oldick, B S; Firkins, J L; Kohn, R A
2000-09-01
Two- and three-compartment models were developed to describe N kinetics within the rumen using three Holstein heifers and one nonlactating Holstein cow fitted with ruminal and duodenal cannulas. A 4 x 4 Latin square design included a control diet containing no supplemental fat and diets containing 4.85% of diet dry matter as partially hydrogenated tallow (iodine value = 13), tallow (iodine value = 51), or animal-vegetable fat (iodine value = 110). Effects of fat on intraruminal N recycling and relationships between intraruminal N recycling and ruminal protozoa concentration or the efficiency of microbial protein synthesis were determined. A pulse dose of 15(NH4)2SO4 was introduced into the ruminal NH3 N pool, and samples were taken over time from the ruminal NH3 N and nonammonia N pools. For the three-compartment model, precipitates of nonammonia N after trichloroacetic acid and ethanol extraction were defined as slowly turning over nonammonia N; rapidly turning over nonammonia N was determined by difference. Curves of 15N enrichment were fit to models with two (NH3 N and nonammonia N) or three (NH3 N, rapidly turning over nonammonia N, and slowly turning over nonammonia N) compartments using the software SAAM II. Because the three-compartment model did not remove a small systematic bias or improve the fit of the data, the two-compartment model was used to provide measurements of intraruminal N recycling. Intraruminal NH3 N recycling (45% for control) decreased linearly as fat unsaturation increased (50.2, 43.0, and 41.7% for partially hydrogenated tallow, tallow, and animal-vegetable fat, respectively). Intraruminal nitrogen recycling was not correlated with efficiency of microbial protein synthesis or ruminal protozoa counts.
Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases
Directory of Open Access Journals (Sweden)
Fazal Haq
2017-01-01
Full Text Available The fractional order Susceptible-Infected-Recovered (SIR epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.
Spiking and bursting patterns of fractional-order Izhikevich model
Teka, Wondimu W.; Upadhyay, Ranjit Kumar; Mondal, Argha
2018-03-01
Bursting and spiking oscillations play major roles in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies have shown that models with fractional order can produce several types of history-dependent neuronal activities without the adjustment of several parameters. We studied the fractional-order Izhikevich model and analyzed different kinds of oscillations that emerge from the fractional dynamics. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phase of the burst increase when the fractional-order model further deviates from the classical model. For smaller fractional order, the model produces memory dependent spiking activity after the pulse signal turned off. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shifts from random to scale-free spiking. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.
Network thermodynamic approach compartmental analysis. Na+ transients in frog skin.
Mikulecky, D C; Huf, E G; Thomas, S R
1979-01-01
We introduce a general network thermodynamic method for compartmental analysis which uses a compartmental model of sodium flows through frog skin as an illustrative example (Huf and Howell, 1974a). We use network thermodynamics (Mikulecky et al., 1977b) to formulate the problem, and a circuit simulation program (ASTEC 2, SPICE2, or PCAP) for computation. In this way, the compartment concentrations and net fluxes between compartments are readily obtained for a set of experimental conditions involving a square-wave pulse of labeled sodium at the outer surface of the skin. Qualitative features of the influx at the outer surface correlate very well with those observed for the short circuit current under another similar set of conditions by Morel and LeBlanc (1975). In related work, the compartmental model is used as a basis for simulation of the short circuit current and sodium flows simultaneously using a two-port network (Mikulecky et al., 1977a, and Mikulecky et al., A network thermodynamic model for short circuit current transients in frog skin. Manuscript in preparation; Gary-Bobo et al., 1978). The network approach lends itself to computation of classic compartmental problems in a simple manner using circuit simulation programs (Chua and Lin, 1975), and it further extends the compartmental models to more complicated situations involving coupled flows and non-linearities such as concentration dependencies, chemical reaction kinetics, etc.
A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics
Lei, Dong; Liang, Yingjie; Xiao, Rui
2018-01-01
We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.
The fractional volatility model: An agent-based interpretation
Vilela Mendes, R.
2008-06-01
Based on the criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are reviewed and extended to account for leverage effects. Using agent-based models, one tries to find which agent strategies and (or) properties of the financial institutions might be responsible for the features of the fractional volatility model.
Large deflection of viscoelastic beams using fractional derivative model
International Nuclear Information System (INIS)
Bahranini, Seyed Masoud Sotoodeh; Eghtesad, Mohammad; Ghavanloo, Esmaeal; Farid, Mehrdad
2013-01-01
This paper deals with large deflection of viscoelastic beams using a fractional derivative model. For this purpose, a nonlinear finite element formulation of viscoelastic beams in conjunction with the fractional derivative constitutive equations has been developed. The four-parameter fractional derivative model has been used to describe the constitutive equations. The deflected configuration for a uniform beam with different boundary conditions and loads is presented. The effect of the order of fractional derivative on the large deflection of the cantilever viscoelastic beam, is investigated after 10, 100, and 1000 hours. The main contribution of this paper is finite element implementation for nonlinear analysis of viscoelastic fractional model using the storage of both strain and stress histories. The validity of the present analysis is confirmed by comparing the results with those found in the literature.
A void fraction model for annular two-phase flow
Energy Technology Data Exchange (ETDEWEB)
Tandon, T.N.; Gupta, C.P.; Varma, H.K.
1985-01-01
An analytical model has been developed for predicting void fraction in two-phase annular flow. In the analysis, the Lockhart-Martinelli method has been used to calculate two-phase frictional pressure drop and von Karman's universal velocity profile is used to represent the velocity distribution in the annular liquid film. Void fractions predicted by the proposed model are generally in good agreement with a available experimental data. This model appears to be as good as Smith's correlation and better than the Wallis and Zivi correlations for computing void fraction.
Fractional-order in a macroeconomic dynamic model
David, S. A.; Quintino, D. D.; Soliani, J.
2013-10-01
In this paper, we applied the Riemann-Liouville approach in order to realize the numerical simulations to a set of equations that represent a fractional-order macroeconomic dynamic model. It is a generalization of a dynamic model recently reported in the literature. The aforementioned equations have been simulated for several cases involving integer and non-integer order analysis, with some different values to fractional order. The time histories and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the macroeconomic dynamic model proposed here involves the public sector deficit equation, which renders the model more realistic and complete when compared with the ones encountered in the literature. The results reveal that the fractional-order macroeconomic model can exhibit a real reasonable behavior to macroeconomics systems and might offer greater insights towards the understanding of these complex dynamic systems.
Advanced compositional gradient and compartmentalization analysis
Energy Technology Data Exchange (ETDEWEB)
Canas, Jesus A.; Petti, Daniela; Mullins, Oliver [Schlumberger Servicos de Petroleo Ltda., Rio de Janeiro, RJ (Brazil)
2008-07-01
acting as compartmentalization elements. Using this method we present field DFA and pressure gradient data acquisitions and integrate into numerical simulation modeling to conceptually evaluate the impact of fluid composition / properties gradation and compartmentalization in the productivity of some reservoirs. (author)
Tempered fractional time series model for turbulence in geophysical flows
Meerschaert, Mark M.; Sabzikar, Farzad; Phanikumar, Mantha S.; Zeleke, Aklilu
2014-09-01
We propose a new time series model for velocity data in turbulent flows. The new model employs tempered fractional calculus to extend the classical 5/3 spectral model of Kolmogorov. Application to wind speed and water velocity in a large lake are presented, to demonstrate the practical utility of the model.
Tempered fractional time series model for turbulence in geophysical flows
International Nuclear Information System (INIS)
Meerschaert, Mark M; Sabzikar, Farzad; Phanikumar, Mantha S; Zeleke, Aklilu
2014-01-01
We propose a new time series model for velocity data in turbulent flows. The new model employs tempered fractional calculus to extend the classical 5/3 spectral model of Kolmogorov. Application to wind speed and water velocity in a large lake are presented, to demonstrate the practical utility of the model. (paper)
Application of Integer and Fractional Models in Electrochemical Systems
Directory of Open Access Journals (Sweden)
Isabel S. Jesus
2012-01-01
Full Text Available This paper describes the use of integer and fractional electrical elements, for modelling two electrochemical systems. A first type of system consists of botanical elements and a second type is implemented by electrolyte processes with fractal electrodes. Experimental results are analyzed in the frequency domain, and the pros and cons of adopting fractional-order electrical components for modelling these systems are compared.
Fractional dynamical model for neurovascular coupling
Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem
2014-01-01
The neurovascular coupling is a key mechanism linking the neural activity to the hemodynamic behavior. Modeling of this coupling is very important to understand the brain function but it is at the same time very complex due to the complexity
Drivers of compartmentalization in a Mediterranean pollination network
DEFF Research Database (Denmark)
Gonzalez, Ana M. Martin; Allesina, Stefano; Rodrigo, Anselm
2012-01-01
We study compartmentalization in a Mediterranean pollination network using three different analytical approaches: unipartite modularity (UM), bipartite modularity (BM) and the group model (GM). Our objectives are to compare compartments obtained with these three approaches and to explore the role...... of several species attributes related to pollination syndromes, species phenology, abundance and connectivity in structuring compartmentalization. BM could not identify compartments in our network. By contrast, UM revealed four modules composed of plants and pollinators, and GM four groups of plants and five...... of pollinators. Phenology had a major influence on compartmentalization, and compartments (both UM and GM) had distinct phenophases. Compartments were also strongly characterized by species degree (number of connections) and betweenness centrality. These two attributes were highly related to each other...
Fractional and multivariable calculus model building and optimization problems
Mathai, A M
2017-01-01
This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...
On an Estimation Method for an Alternative Fractionally Cointegrated Model
DEFF Research Database (Denmark)
Carlini, Federico; Łasak, Katarzyna
In this paper we consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than models proposed in Granger (1986) and Johansen (2008, 2009). We discuss the identification issues of the model of Avarucci (2007), following th...
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2010-01-01
This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data X1......,...,X_{T} given the initial values X_{-n}, n=0,1,..., as is usually done. The initial values are not modeled but assumed to be bounded. This represents a considerable generalization relative to all previous work where it is assumed that initial values are zero. For the statistical analysis we assume...... the conditional Gaussian likelihood and for the probability analysis we also condition on initial values but assume that the errors in the autoregressive model are i.i.d. with suitable moment conditions. We analyze the conditional likelihood and its derivatives as stochastic processes in the parameters, including...
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, Junior, O
1994-07-01
After an intake of radioactive material, its behaviour in the human body can be described by mathematical models, where organs, tissues or regions of the body are treated as a chain of linked compartments. The mathematical approach for such metabolic models is usually done through a system of differential equations of first order with constant coefficients. The solutions of this system of equations associates the radionuclide intake, with the fraction excreted or retained in the organ of interest. A computer program - called INCORP and for running in PC compatible microcomputers - was developed in order to find the solutions of such system of equations, using an analytical method based on expansion of series of exponential matrices. The metabolic model presented in the ICRP-30 publication was simulated using the INCORP program, in order to find the respective retention and excretion curves for selected radionuclides. (author)
An approximate fractional Gaussian noise model with computational cost
Sø rbye, Sigrunn H.; Myrvoll-Nilsen, Eirik; Rue, Haavard
2017-01-01
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2013-02-01
Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.
Fractional Heat Conduction Models and Thermal Diffusivity Determination
Directory of Open Access Journals (Sweden)
Monika Žecová
2015-01-01
Full Text Available The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.
Protocell design through modular compartmentalization.
Miller, David; Booth, Paula J; Seddon, John M; Templer, Richard H; Law, Robert V; Woscholski, Rudiger; Ces, Oscar; Barter, Laura M C
2013-10-06
De novo synthetic biological design has the potential to significantly impact upon applications such as energy generation and nanofabrication. Current designs for constructing organisms from component parts are typically limited in scope, as they utilize a cut-and-paste ideology to create simple stepwise engineered protein-signalling pathways. We propose the addition of a new design element that segregates components into lipid-bound 'proto-organelles', which are interfaced with response elements and housed within a synthetic protocell. This design is inspired by living cells, which utilize multiple types of signalling molecules to facilitate communication between isolated compartments. This paper presents our design and validation of the components required for a simple multi-compartment protocell machine, for coupling a light transducer to a gene expression system. This represents a general design concept for the compartmentalization of different types of artificial cellular machinery and the utilization of non-protein signal molecules for signal transduction.
Model for radial gas fraction profiles in vertical pipe flow
International Nuclear Information System (INIS)
Lucas, D.; Krepper, E.; Prasser, H.M.
2001-01-01
A one-dimensional model is presented, which predicts the radial volume fraction profiles from a given bubble size distribution. It bases on the assumption of an equilibrium of the forces acting on a bubble perpendicularly to the flow path (non drag forces). For the prediction of the flow pattern this model could be used within an procedure together with appropriate models for local bubble coalescence and break-up. (orig.)
Likelihood inference for a fractionally cointegrated vector autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2012-01-01
such that the process X_{t} is fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß'X_{t} is fractional of order d-b, and no other fractionality order is possible. We define the statistical model by 0inference when the true values satisfy b0¿1/2 and d0-b0......We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model with a restricted constant term, ¿, based on the Gaussian likelihood conditional on initial values. The model nests the I(d) VAR model. We give conditions on the parameters...... process in the parameters when errors are i.i.d. with suitable moment conditions and initial values are bounded. When the limit is deterministic this implies uniform convergence in probability of the conditional likelihood function. If the true value b0>1/2, we prove that the limit distribution of (ß...
Inter-fraction variations in respiratory motion models
Energy Technology Data Exchange (ETDEWEB)
McClelland, J R; Modat, M; Ourselin, S; Hawkes, D J [Centre for Medical Image Computing, University College London (United Kingdom); Hughes, S; Qureshi, A; Ahmad, S; Landau, D B, E-mail: j.mcclelland@cs.ucl.ac.uk [Department of Oncology, Guy' s and St Thomas' s Hospitals NHS Trust, London (United Kingdom)
2011-01-07
Respiratory motion can vary dramatically between the planning stage and the different fractions of radiotherapy treatment. Motion predictions used when constructing the radiotherapy plan may be unsuitable for later fractions of treatment. This paper presents a methodology for constructing patient-specific respiratory motion models and uses these models to evaluate and analyse the inter-fraction variations in the respiratory motion. The internal respiratory motion is determined from the deformable registration of Cine CT data and related to a respiratory surrogate signal derived from 3D skin surface data. Three different models for relating the internal motion to the surrogate signal have been investigated in this work. Data were acquired from six lung cancer patients. Two full datasets were acquired for each patient, one before the course of radiotherapy treatment and one at the end (approximately 6 weeks later). Separate models were built for each dataset. All models could accurately predict the respiratory motion in the same dataset, but had large errors when predicting the motion in the other dataset. Analysis of the inter-fraction variations revealed that most variations were spatially varying base-line shifts, but changes to the anatomy and the motion trajectories were also observed.
Fractional calculus model of electrical impedance applied to human skin.
Vosika, Zoran B; Lazovic, Goran M; Misevic, Gradimir N; Simic-Krstic, Jovana B
2013-01-01
Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1) Weyl fractional derivative operator, 2) Cole equation, and 3) Constant Phase Element (CPE). These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
Fractional calculus model of electrical impedance applied to human skin.
Directory of Open Access Journals (Sweden)
Zoran B Vosika
Full Text Available Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1 Weyl fractional derivative operator, 2 Cole equation, and 3 Constant Phase Element (CPE. These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
Discrete random walk models for space-time fractional diffusion
International Nuclear Information System (INIS)
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-01-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order α is part of (0,2] and skewness θ (moduleθ≤{α,2-α}), and the first-order time derivative with a Caputo derivative of order β is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation
Fractional calculus phenomenology in two-dimensional plasma models
Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill
2006-10-01
Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).
Statistical properties of several models of fractional random point processes
Bendjaballah, C.
2011-08-01
Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
S. Peiris (Shelton); M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility
Modelling nematode movement using time-fractional dynamics.
Hapca, Simona; Crawford, John W; MacMillan, Keith; Wilson, Mike J; Young, Iain M
2007-09-07
We use a correlated random walk model in two dimensions to simulate the movement of the slug parasitic nematode Phasmarhabditis hermaphrodita in homogeneous environments. The model incorporates the observed statistical distributions of turning angle and speed derived from time-lapse studies of individual nematode trails. We identify strong temporal correlations between the turning angles and speed that preclude the case of a simple random walk in which successive steps are independent. These correlated random walks are appropriately modelled using an anomalous diffusion model, more precisely using a fractional sub-diffusion model for which the associated stochastic process is characterised by strong memory effects in the probability density function.
Leaky-box approximation to the fractional diffusion model
International Nuclear Information System (INIS)
Uchaikin, V V; Sibatov, R T; Saenko, V V
2013-01-01
Two models based on fractional differential equations for galactic cosmic ray diffusion are applied to the leaky-box approximation. One of them (Lagutin-Uchaikin, 2000) assumes a finite mean free path of cosmic ray particles, another one (Lagutin-Tyumentsev, 2004) uses distribution with infinite mean distance between collision with magnetic clouds, when the trajectories have form close to ballistic. Calculations demonstrate that involving boundary conditions is incompatible with spatial distributions given by the second model.
Kinetic compartmental analysis of carnitine metabolism in the dog
International Nuclear Information System (INIS)
Rebouche, C.J.; Engel, A.G.
1983-01-01
This study was undertaken to quantitate the dynamic parameters of carnitine metabolism in the dog. Six mongrel dogs were given intravenous injections of L-[methyl-3H]carnitine and the specific radioactivity of carnitine was followed in plasma and urine for 19-28 days. The data were analyzed by kinetic compartmental analysis. A three-compartment, open-system model [(a) extracellular fluid, (b) cardiac and skeletal muscle, (c) other tissues, particularly liver and kidney] was adopted and kinetic parameters (carnitine flux, pool sizes, kinetic constants) were derived. In four of six dogs the size of the muscle carnitine pool obtained by kinetic compartmental analysis agreed (+/- 5%) with estimates based on measurement of carnitine concentrations in different muscles. In three of six dogs carnitine excretion rates derived from kinetic compartmental analysis agreed (+/- 9%) with experimentally measured values, but in three dogs the rates by kinetic compartmental analysis were significantly higher than the corresponding rates measured directly. Appropriate chromatographic analyses revealed no radioactive metabolites in muscle or urine of any of the dogs. Turnover times for carnitine were (mean +/- SEM): 0.44 +/- 0.05 h for extracellular fluid, 232 +/- 22 h for muscle, and 7.9 +/- 1.1 h for other tissues. The estimated flux of carnitine in muscle was 210 pmol/min/g of tissue. Whole-body turnover time for carnitine was 62.9 +/- 5.6 days (mean +/- SEM). Estimated carnitine biosynthesis ranged from 2.9 to 28 mumol/kg body wt/day. Results of this study indicate that kinetic compartmental analysis may be applicable to study of human carnitine metabolism
Modeling and analysis of fractional order DC-DC converter.
Radwan, Ahmed G; Emira, Ahmed A; AbdelAty, Amr M; Azar, Ahmad Taher
2017-07-11
Due to the non-idealities of commercial inductors, the demand for a better model that accurately describe their dynamic response is elevated. So, the fractional order models of Buck, Boost and Buck-Boost DC-DC converters are presented in this paper. The detailed analysis is made for the two most common modes of converter operation: Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). Closed form time domain expressions are derived for inductor currents, voltage gain, average current, conduction time and power efficiency where the effect of the fractional order inductor is found to be strongly present. For example, the peak inductor current at steady state increases with decreasing the inductor order. Advanced Design Systems (ADS) circuit simulations are used to verify the derived formulas, where the fractional order inductor is simulated using Valsa Constant Phase Element (CPE) approximation and Generalized Impedance Converter (GIC). Different simulation results are introduced with good matching to the theoretical formulas for the three DC-DC converter topologies under different fractional orders. A comprehensive comparison with the recently published literature is presented to show the advantages and disadvantages of each approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Compartmental analysis to predict biodistribution in radiopharmaceutical design studies
Energy Technology Data Exchange (ETDEWEB)
Lima, Marina F.; Pujatti, Priscilla B.; Araujo, Elaine B.; Mesquita, Carlos H. [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)], e-mail: mflima@ipen.br
2009-07-01
The use of compartmental analysis allows the mathematical separation of tissues and organs to determinate the concentration of activity in each fraction of interest. Although the radiochemical purity must observe Pharmacopoeia specification (values upper 95%), very lower contains of free radionuclides could contribute significantly as dose in the neighborhood organs and make tumor up take studies not viable in case of radiopharmaceutical on the basis of labeled peptides. Animal studies with a product of Lutetium-177 labeled Bombesin derivative ({sup 177}Lu-BBNP) developed in IPEN-CNEN/SP and free Lutetium-177 developed in CNEA/EZEIZA was used to show how subtract free {sup 177}Lu contribution over {sup 177}Lu-BBNP to estimate the radiopharmaceutical potential as diagnosis or therapy agent. The first approach of the studies included the knowledge of chemical kinetics and mimetism of the Lutetium and the possible targets of the diagnosis/therapy to choose the possible models to apply over the sampling standard methods used in experimental works. A model with only one physical compartment (whole body) and one chemical compartment ({sup 177}Lu-BBNP) generated with the compartmental analysis protocol ANACOMP showed high differences between experimental and theoretical values over 2.5 hours, in spite of the concentration of activity had been in a good statistics rang of measurement. The values used in this work were residence time from three different kinds of study with free {sup 177}Lu: whole body, average excretion and maximum excretion as a chemical compartment. Activity concentration values as time function in measurements of total whole body and activity measurement in samples of blood with projection to total circulating blood volume with {sup 177}Lu-BBNP. Considering the two sources of data in the same modeling a better consistence was obtained. The next step was the statistic treatment of biodistribution and dosimetry in mice (Balb C) considering three chemical
A Novel Method for Performance Analysis of Compartmentalized Reservoirs
Directory of Open Access Journals (Sweden)
Shahamat Mohammad Sadeq
2016-05-01
Full Text Available This paper presents a simple analytical model for performance analysis of compartmentalized reservoirs producing under Constant Terminal Rate (CTR and Constant Terminal Pressure (CTP. The model is based on the well-known material balance and boundary dominated flow equations and is written in terms of capacitance and resistance of a production and a support compartment. These capacitance and resistance terms account for a combination of reservoir parameters which enable the developed model to be used for characterizing such systems. In addition to considering the properties contrast between the two reservoir compartments, the model takes into account existence of transmissibility barriers with the use of resistance terms. The model is used to analyze production performance of unconventional reservoirs, where the multistage fracturing of horizontal wells effectively creates a Stimulated Reservoir Volume (SRV with an enhanced permeability surrounded by a non-stimulated region. It can also be used for analysis of compartmentalized conventional reservoirs. The analytical solutions provide type curves through which the controlling reservoirs parameters of a compartmentalized system can be estimated. The contribution of the supporting compartment is modeled based on a boundary dominated flow assumption. The transient behaviour of the support compartment is captured by application of “distance of investigation” concept. The model shows that depletion of the production and support compartments exhibit two unit slopes on a log-log plot of pressure versus time for CTR. For CTP, however, the depletions display two exponential declines. The depletion signatures are separated by transition periods, which depend on the contribution of the support compartment (i.e. transient or boundary dominated flow. The developed equations can be implemented easily in a spreadsheet application, and are corroborated with the use of a numerical simulation. The study
Mathematical modeling of fish burger baking using fractional calculus
Directory of Open Access Journals (Sweden)
Bainy Eduarda M.
2017-01-01
Full Text Available Tilapia (Oreochromis sp. is the most important and abundant fish species in Brazil due to its adaptability to different environments. The development of tilapia-based products could be an alternative in order to aggregate value and increase fish meat consumption. However, there is little information available on fishburger freezing and cooking in the literature. In this work, the mathematical modeling of the fish burger baking was studied. Previously to the baking process, the fishburgers were assembled in cylindrical shape of height equal to 8mm and diameter 100mm and then baked in an electrical oven with forced heat convection at 150ºC. A T-type thermocouple was inserted in the burger to obtain its temperature profile at the central position. In order to describe the temperature of the burger during the baking process, lumped-parameter models of integer and fractional order and also a nonlinear model due to heat capacity temperature dependence were considered. The burger physical properties were obtained from the literature. After proper parameter estimation tasks and statistical validation, the fractional order model could better describe the experimental temperature behavior, a value of 0.91±0.02 was obtained for the fractional order of the system with correlation coefficient of 0.99. Therefore, with the better temperature prediction, process control and economic optimization studies of the baking process can be conducted.
Non-exponential extinction of radiation by fractional calculus modelling
International Nuclear Information System (INIS)
Casasanta, G.; Ciani, D.; Garra, R.
2012-01-01
Possible deviations from exponential attenuation of radiation in a random medium have been recently studied in several works. These deviations from the classical Beer-Lambert law were justified from a stochastic point of view by Kostinski (2001) . In his model he introduced the spatial correlation among the random variables, i.e. a space memory. In this note we introduce a different approach, including a memory formalism in the classical Beer-Lambert law through fractional calculus modelling. We find a generalized Beer-Lambert law in which the exponential memoryless extinction is only a special case of non-exponential extinction solutions described by Mittag-Leffler functions. We also justify this result from a stochastic point of view, using the space fractional Poisson process. Moreover, we discuss some concrete advantages of this approach from an experimental point of view, giving an estimate of the deviation from exponential extinction law, varying the optical depth. This is also an interesting model to understand the meaning of fractional derivative as an instrument to transmit randomness of microscopic dynamics to the macroscopic scale.
Compartmentation of glycogen metabolism revealed from 13C isotopologue distributions
Directory of Open Access Journals (Sweden)
Marin de Mas Igor
2011-10-01
Full Text Available Abstract Background Stable isotope tracers are used to assess metabolic flux profiles in living cells. The existing methods of measurement average out the isotopic isomer distribution in metabolites throughout the cell, whereas the knowledge of compartmental organization of analyzed pathways is crucial for the evaluation of true fluxes. That is why we accepted a challenge to create a software tool that allows deciphering the compartmentation of metabolites based on the analysis of average isotopic isomer distribution. Results The software Isodyn, which simulates the dynamics of isotopic isomer distribution in central metabolic pathways, was supplemented by algorithms facilitating the transition between various analyzed metabolic schemes, and by the tools for model discrimination. It simulated 13C isotope distributions in glucose, lactate, glutamate and glycogen, measured by mass spectrometry after incubation of hepatocytes in the presence of only labeled glucose or glucose and lactate together (with label either in glucose or lactate. The simulations assumed either a single intracellular hexose phosphate pool, or also channeling of hexose phosphates resulting in a different isotopic composition of glycogen. Model discrimination test was applied to check the consistency of both models with experimental data. Metabolic flux profiles, evaluated with the accepted model that assumes channeling, revealed the range of changes in metabolic fluxes in liver cells. Conclusions The analysis of compartmentation of metabolic networks based on the measured 13C distribution was included in Isodyn as a routine procedure. The advantage of this implementation is that, being a part of evaluation of metabolic fluxes, it does not require additional experiments to study metabolic compartmentation. The analysis of experimental data revealed that the distribution of measured 13C-labeled glucose metabolites is inconsistent with the idea of perfect mixing of hexose
A holographic model for the fractional quantum Hall effect
Energy Technology Data Exchange (ETDEWEB)
Lippert, Matthew [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, 1090GL Amsterdam (Netherlands); Meyer, René [Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo,Kashiwa, Chiba 277-8568 (Japan); Taliotis, Anastasios [Theoretische Natuurkunde, Vrije Universiteit Brussel andThe International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium)
2015-01-08
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ{sub 0}(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an SL(2,ℤ)-invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the SL(2,ℤ) action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.
A holographic model for the fractional quantum Hall effect
Lippert, Matthew; Meyer, René; Taliotis, Anastasios
2015-01-01
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ0(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an -invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.
Transient heat conduction in a pebble fuel applying fractional model
International Nuclear Information System (INIS)
Gomez A, R.; Espinosa P, G.
2009-10-01
In this paper we presents the equation of thermal diffusion of temporary-fractional order in the one-dimensional space in spherical coordinates, with the objective to analyze the heat transference between the fuel and coolant in a fuel element of a Pebble Bed Modular Reactor. The pebble fuel is the heterogeneous system made by microsphere constitutes by U O, pyrolytic carbon and silicon carbide mixed with graphite. To describe the heat transfer phenomena in the pebble fuel we applied a constitutive law fractional (Non-Fourier) in order to analyze the behaviour transient of the temperature distribution in the pebble fuel with anomalous thermal diffusion effects a numerical model is developed. (Author)
Phase Diagram of a Simple Model for Fractional Topological Insulator
Chen, Hua; Yang, Kun
2012-02-01
We study a simple model of two species of (or spin-1/2) fermions with short-range intra-species repulsion in the presence of opposite (effetive) magnetic field, each at filling factor 1/3. In the absence of inter-species interaction, the ground state is simply two copies of the 1/3 Laughlin state, with opposite chirality. Due to the overall time-reversal symmetry, this is a fractional topological insulator. We show this phase is stable against moderate inter-species interactions. However strong enough inter-species repulsion leads to phase separation, while strong enough inter-species attraction drives the system into a superfluid phase. We obtain the phase diagram through exact diagonalization caluclations. Nature of the fractional topological insluator-superfluid phase transition is discussed using an appropriate Chern-Simons-Ginsburg-Landau effective field theory.
Deformed Calogero-Sutherland model and fractional quantum Hall effect
Atai, Farrokh; Langmann, Edwin
2017-01-01
The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.
Beaumelle, Léa; Hedde, Mickaël; Vandenbulcke, Franck; Lamy, Isabelle
2017-05-01
Partitioning tissue metal concentration into subcellular compartments reflecting toxicologically available pools may provide good descriptors of the toxicological effects of metals on organisms. Here we investigated the relationships between internal compartmentalization of Cd, Pb and Zn and biomarker responses in a model soil organism: the earthworm. The aim of this study was to identify metal fractions reflecting the toxic pressure in an endogeic, naturally occurring earthworm species (Aporrectodea caliginosa) exposed to realistic field-contaminated soils. After a 21 days exposure experiment to 31 field-contaminated soils, Cd, Pb and Zn concentrations in earthworms and in three subcellular fractions (cytosol, debris and granules) were quantified. Different biomarkers were measured: the expression of a metallothionein gene (mt), the activity of catalase (CAT) and of glutathione-s-transferase (GST), and the protein, lipid and glycogen reserves. Biomarkers were further combined into an integrated biomarker index (IBR). The subcellular fractionation provided better predictors of biomarkers than the total internal contents hence supporting its use when assessing toxicological bioavailability of metals to earthworms. The most soluble internal pools of metals were not always the best predictors of biomarker responses. metallothionein expression responded to increasing concentrations of Cd in the insoluble fraction (debris + granules). Protein and glycogen contents were also mainly related to Cd and Pb in the insoluble fraction. On the other hand, GST activity was better explained by Pb in the cytosolic fraction. CAT activity and lipid contents variations were not related to metal subcellular distribution. The IBR was best explained by both soluble and insoluble fractions of Pb and Cd. This study further extends the scope of mt expression as a robust and specific biomarker in an ecologically representative earthworm species exposed to field-contaminated soils. The
Influence of the void fraction in the linear reactivity model
International Nuclear Information System (INIS)
Castillo, J.A.; Ramirez, J.R.; Alonso, G.
2003-01-01
The linear reactivity model allows the multicycle analysis in pressurized water reactors in a simple and quick way. In the case of the Boiling water reactors the void fraction it varies axially from 0% of voids in the inferior part of the fuel assemblies until approximately 70% of voids to the exit of the same ones. Due to this it is very important the determination of the average void fraction during different stages of the reactor operation to predict the burnt one appropriately of the same ones to inclination of the pattern of linear reactivity. In this work a pursuit is made of the profile of power for different steps of burnt of a typical operation cycle of a Boiling water reactor. Starting from these profiles it builds an algorithm that allows to determine the voids profile and this way to obtain the average value of the same one. The results are compared against those reported by the CM-PRESTO code that uses another method to carry out this calculation. Finally, the range in which is the average value of the void fraction during a typical cycle is determined and an estimate of the impact that it would have the use of this value in the prediction of the reactivity produced by the fuel assemblies is made. (Author)
Modeling discrete and continuous entities with fractions and decimals.
Rapp, Monica; Bassok, Miriam; DeWolf, Melissa; Holyoak, Keith J
2015-03-01
When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric "contain" relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/vases). Here we investigate the possibility that semantic alignment is also involved in the comprehension and use of rational numbers (fractions and decimals). A textbook analysis and results from two experiments revealed that both mathematic educators and college students tend to align the discreteness versus continuity of the entities in word problems (e.g., marbles vs. distance) with distinct symbolic representations of rational numbers--fractions versus decimals, respectively. In addition, fractions and decimals tend to be used with nonmetric units and metric units, respectively. We discuss the importance of the ontological distinction between continuous and discrete entities to mathematical cognition, the role of symbolic notations, and possible implications of our findings for the teaching of rational numbers. PsycINFO Database Record (c) 2015 APA, all rights reserved.
Fractional diffusion models of transport in magnetically confined plasmas
International Nuclear Information System (INIS)
Castillo-Negrete, D. del; Carreras, B. A.; Lynch, V. E.
2005-01-01
Experimental and theoretical evidence suggests that transport in magnetically confined fusion plasmas deviates from the standard diffusion paradigm. Some examples include the confinement time scaling in L-mode plasmas, rapid pulse propagation phenomena, and inward transport in off-axis fueling experiments. The limitations of the diffusion paradigm can be traced back to the restrictive assumptions in which it is based. In particular, Fick's law, one of the cornerstones of diffusive transport, assumes that the fluxes only depend on local quantities, i. e. the spatial gradient of the field (s). another key issue is the Markovian assumption that neglects memory effects. Also, at a microscopic level, standard diffusion assumes and underlying Gaussian, uncorrelated stochastic process (i. e. a Brownian random walk) with well defined characteristic spatio-temporal scales. Motivated by the need to develop models of non-diffusive transport, we discuss here a class of transport models base on the use of fractional derivative operators. The models incorporates in a unified way non-Fickian transport, non-Markovian processes or memory effects, and non-diffusive scaling. At a microscopic level, the models describe an underlying stochastic process without characteristic spatio-temporal scales that generalizes the Brownian random walk. As a concrete case study to motivate and test the model, we consider transport of tracers in three-dimensional, pressure-gradient-driven turbulence. We show that in this system transport is non-diffusive and cannot be described in the context of the standard diffusion parading. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit super-diffusive scaling. there is quantitative agreement between the turbulence transport calculations and the proposed fractional diffusion model. In particular, the model
A Stochastic Fractional Dynamics Model of Rainfall Statistics
Kundu, Prasun; Travis, James
2013-04-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.
Energy Technology Data Exchange (ETDEWEB)
Llaurado, J. G. [Biomedical Engineering Group, Marquette University (United States); Marquette School of Medicine, Milwaukee (United States); Nuclear Medicine Service of Veterans Administration Center, Wood, WI (United States)
1971-02-15
A method commonly used for the study of the distribution of a substance among the different spaces ol a biological tissue is the continuous washout (outflow) and isotope counting of fragments of tissue previously incubated with a tracer. A first order kinetics compartmental system can be postulated and characterized by the transport rates (k) at which the substance of interest moves across its different compartments. Direct solution from the outflow data requires knowledge of the initial conditions for, or to have access for measurements in, each compartment. This cannot be fulfilled in most biological problems. In the course of studying {sup 22}Na distribution in segments of arteries a digital computer simulation approach was developed to solve the system. In the belief that the approach transcends this particular application, its mathematical basis is herein presented: the movement of radioactive tracer obeys Divides dq/d Divides = - Divides k Divides Divides q Divides + Divides r Divides (1) where |q| is a vector of response functions for each compartment, |k] is a square matrix of transport rate constants and |r| is a vector of input rates to the system. Solution of Eq. 1 is Divides q Divides = e{sup - Divides k Divides t} {integral}{sub 0}{sup t} e{sup Divides k Divides t} Divides r Divides dt + e{sup - Divides k Divides t} Divides q{sub 0} Divides (2) (i) For an inflow experiment, with 0 initial conditions and a constant unit input rate |r{sub u}| Divides q Divides = ( Divides I Divides - e{sup - Divides k Divides t}) Divides k Divides {sup -1} Divides r{sub u} Divides (3) as t --> {infinity}, Divides q{sub {infinity}} Divides = Divides k Divides {sup -1} Divides r{sub u} Divides , which replaced in Eq. 3, Divides q Divides = Divides q{sub {infinity}} Divides -e{sup - Divides k Divides t} Divides q{sub {infinity}} Divides (4) (ii) For an outflow experiment Divides r Divides = 0 and Eq. 2 becomes Divides q Divides = e{sup - Divides k Divides t} Divides q{sub 0
Murine Models of Heart Failure With Preserved Ejection Fraction
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Maria Valero-Muñoz, PhD
2017-12-01
Full Text Available Heart failure with preserved ejection fraction (HFpEF is characterized by signs and symptoms of heart failure in the presence of a normal left ventricular ejection fraction. Despite accounting for up to 50% of all clinical presentations of heart failure, the mechanisms implicated in HFpEF are poorly understood, thus precluding effective therapy. The pathophysiological heterogeneity in the HFpEF phenotype also contributes to this disease and likely to the absence of evidence-based therapies. Limited access to human samples and imperfect animal models that completely recapitulate the human HFpEF phenotype have impeded our understanding of the mechanistic underpinnings that exist in this disease. Aging and comorbidities such as atrial fibrillation, hypertension, diabetes and obesity, pulmonary hypertension, and renal dysfunction are highly associated with HFpEF, yet the relationship and contribution between them remains ill-defined. This review discusses some of the distinctive clinical features of HFpEF in association with these comorbidities and highlights the advantages and disadvantage of commonly used murine models used to study the HFpEF phenotype.
Compartmentalized storage tank for electrochemical cell system
Piecuch, Benjamin Michael (Inventor); Dalton, Luke Thomas (Inventor)
2010-01-01
A compartmentalized storage tank is disclosed. The compartmentalized storage tank includes a housing, a first fluid storage section disposed within the housing, a second fluid storage section disposed within the housing, the first and second fluid storage sections being separated by a movable divider, and a constant force spring. The constant force spring is disposed between the housing and the movable divider to exert a constant force on the movable divider to cause a pressure P1 in the first fluid storage section to be greater than a pressure P2 in the second fluid storage section, thereby defining a pressure differential.
Particle Based Modeling of Electrical Field Flow Fractionation Systems
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Tonguc O. Tasci
2015-10-01
Full Text Available Electrical Field Flow Fractionation (ElFFF is a sub method in the field flow fractionation (FFF family that relies on an applied voltage on the channel walls to effect a separation. ElFFF has fallen behind some of the other FFF methods because of the optimization complexity of its experimental parameters. To enable better optimization, a particle based model of the ElFFF systems has been developed and is presented in this work that allows the optimization of the main separation parameters, such as electric field magnitude, frequency, duty cycle, offset, flow rate and channel dimensions. The developed code allows visualization of individual particles inside the separation channel, generation of realistic fractograms, and observation of the effects of the various parameters on the behavior of the particle cloud. ElFFF fractograms have been generated via simulations and compared with experiments for both normal and cyclical ElFFF. The particle visualizations have been used to verify that high duty cycle voltages are essential to achieve long retention times and high resolution separations. Furthermore, by simulating the particle motions at the channel outlet, it has been demonstrated that the top channel wall should be selected as the accumulation wall for cyclical ElFFF to reduce band broadening and achieve high efficiency separations. While the generated particle based model is a powerful tool to estimate the outcomes of the ElFFF experiments and visualize particle motions, it can also be used to design systems with new geometries which may lead to the design of higher efficiency ElFFF systems. Furthermore, this model can be extended to other FFF techniques by replacing the electrical field component of the model with the fields used in the other FFF techniques.
Fractional Gaussian noise: Prior specification and model comparison
Sø rbye, Sigrunn Holbek; Rue, Haavard
2017-01-01
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
Fractional Gaussian noise: Prior specification and model comparison
Sørbye, Sigrunn Holbek
2017-07-07
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
International Nuclear Information System (INIS)
Lim, S C; Teo, L P
2009-01-01
Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion
An approximate fractional Gaussian noise model with computational cost
Sørbye, Sigrunn H.
2017-09-18
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.
Fractional Calculus in Hydrologic Modeling: A Numerical Perspective
Energy Technology Data Exchange (ETDEWEB)
David A. Benson; Mark M. Meerschaert; Jordan Revielle
2012-01-01
Fractional derivatives can be viewed either as a handy extension of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Levy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Levy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.
Tunable polymeric sorbent materials for fractionation of model naphthenates.
Mohamed, Mohamed H; Wilson, Lee D; Headley, John V
2013-04-04
The sorption properties are reported for several examples of single-component carboxylic acids representing naphthenic acids (NAs) with β-cyclodextrin (β-CD) based polyurethane sorbents. Seven single-component examples of NAs were chosen with variable z values, carbon number, and chemical structure as follows: 2-hexyldecanoic acid (z = 0 and C = 16; S1), n-caprylic acid (z = 0 and C = 8; S2), trans-4-pentylcyclohexanecarboxylic acid (z = -2 and C = 12; S3), 4-methylcyclohexanecarboxylic acid (z = -2 and C = 8; S4), dicyclohexylacetic acid (z = -4; C = 14; S5), 4-pentylbicyclo[2.2.2]octane-1-carboxylic acid (z = -4; C = 14; S6), and lithocholic acid (z = -6; C = 24; S7). The copolymer sorbents were synthesized at three relative β-CD:diisocyanate mole ratios (i.e., 1:1, 1:2, and 1:3) using 4,4'-dicyclohexylmethane diisocyanate (CDI) and 4,4'-diphenylmethane diisocyanate (MDI). The sorption properties of the copolymer sorbents were characterized using equilibrium sorption isotherms in aqueous solution at pH 9.00 with electrospray ionization mass spectrometry. The equilibrium fraction of the unbound carboxylate anions was monitored in the aqueous phase. The sorption properties of the copolymer sorbents (i.e., Qm) were obtained from the Sips isotherm model. The Qm values generally decrease as the number of accessible β-CD inclusion sites in the copolymer framework decreases. The chemical structure of the adsorbates played an important role in their relative uptake, as evidenced by the adsorbate lipophilic surface area (LSA) and the involvement of hydrophobic effects. The copolymers exhibit molecular selective sorption of the single-component carboxylates in mixtures which suggests their application as sorbents for fractionation of mixtures of NAs. By comparison, granular activated carbon (GAC) and chitosan sorbents did not exhibit any significant molecular selective sorption relative to the copolymer materials; however, evidence of variable sorption capacity was
Fractional model for heat conduction in polar bear hairs
Directory of Open Access Journals (Sweden)
Wang Qing-Li
2012-01-01
Full Text Available Time-fractional differential equations can accurately describe heat conduction in fractal media, such as wool fibers, goose down and polar bear hair. The fractional complex transform is used to convert time-fractional heat conduction equations with the modified Riemann-Liouville derivative into ordinary differential equations, and exact solutions can be easily obtained. The solution process is straightforward and concise.
Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions
Shahbari, Juhaina Awawdeh; Peled, Irit
2017-01-01
This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…
A fractional motion diffusion model for grading pediatric brain tumors.
Karaman, M Muge; Wang, He; Sui, Yi; Engelhard, Herbert H; Li, Yuhua; Zhou, Xiaohong Joe
2016-01-01
To demonstrate the feasibility of a novel fractional motion (FM) diffusion model for distinguishing low- versus high-grade pediatric brain tumors; and to investigate its possible advantage over apparent diffusion coefficient (ADC) and/or a previously reported continuous-time random-walk (CTRW) diffusion model. With approval from the institutional review board and written informed consents from the legal guardians of all participating patients, this study involved 70 children with histopathologically-proven brain tumors (30 low-grade and 40 high-grade). Multi- b -value diffusion images were acquired and analyzed using the FM, CTRW, and mono-exponential diffusion models. The FM parameters, D fm , φ , ψ (non-Gaussian diffusion statistical measures), and the CTRW parameters, D m , α , β (non-Gaussian temporal and spatial diffusion heterogeneity measures) were compared between the low- and high-grade tumor groups by using a Mann-Whitney-Wilcoxon U test. The performance of the FM model for differentiating between low- and high-grade tumors was evaluated and compared with that of the CTRW and the mono-exponential models using a receiver operating characteristic (ROC) analysis. The FM parameters were significantly lower ( p < 0.0001) in the high-grade ( D fm : 0.81 ± 0.26, φ : 1.40 ± 0.10, ψ : 0.42 ± 0.11) than in the low-grade ( D fm : 1.52 ± 0.52, φ : 1.64 ± 0.13, ψ : 0.67 ± 0.13) tumor groups. The ROC analysis showed that the FM parameters offered better specificity (88% versus 73%), sensitivity (90% versus 82%), accuracy (88% versus 78%), and area under the curve (AUC, 93% versus 80%) in discriminating tumor malignancy compared to the conventional ADC. The performance of the FM model was similar to that of the CTRW model. Similar to the CTRW model, the FM model can improve differentiation between low- and high-grade pediatric brain tumors over ADC.
Directory of Open Access Journals (Sweden)
Joanne M. Wells
2002-07-01
Full Text Available 2-[11C]Thymidine (TdR, a PET tracer for cellular proliferation, may be advantageous for monitoring brain tumor progression and response to therapy. We previously described and validated a five-compartment model for thymidine incorporation into DNA in somatic tissues, but the effect of the blood–brain barrier on the transport of TdR and its metabolites necessitated further validation before it could be applied to brain tumors. Methods: We investigated the behavior of the model under conditions experienced in the normal brain and brain tumors, performed sensitivity and identifiability analysis to determine the ability of the model to estimate the model parameters, and conducted simulations to determine whether it can distinguish between thymidine transport and retention. Results: Sensitivity and identifiability analysis suggested that the non-CO2 metabolite parameters could be fixed without significantly affecting thymidine parameter estimation. Simulations showed that K1t and KTdR could be estimated accurately (r = .97 and .98 for estimated vs. true parameters with standard errors < 15%. The model was able to separate increased transport from increased retention associated with tumor proliferation. Conclusion: Our model adequately describes normal brain and brain tumor kinetics for thymidine and its metabolites, and it can provide an estimate of the rate of cellular proliferation in brain tumors.
Lopez-Teros, Veronica; Ford, Jennifer Lynn; Green, Michael H; Tang, Guangwen; Grusak, Michael A; Quihui-Cota, Luis; Muzhingi, Tawanda; Paz-Cassini, Mariela; Astiazaran-Garcia, Humberto
2017-12-01
Background: Worldwide, an estimated 250 million children children. Methods: β-Carotene was intrinsically labeled by growing MO plants in a 2 H 2 O nutrient solution. Fifteen well-nourished children (17-35 mo old) consumed puréed MO leaves (1 mg β-carotene) and a reference dose of [ 13 C 10 ]retinyl acetate (1 mg) in oil. Blood (2 samples/child) was collected 10 times (2 or 3 children each time) over 35 d. The bioefficacy of MO leaves was calculated from areas under the composite "super-child" plasma isotope response curves, and MO VA equivalence was estimated through the use of these values; a compartmental model was developed to predict VA TBS and retinol kinetics through the use of composite plasma [ 13 C 10 ]retinol data. TBS were also estimated with isotope dilution. Results: The relative bioefficacy of β-carotene retinol activity equivalents from MO was 28%; VA equivalence was 3.3:1 by weight (0.56 μmol retinol:1 μmol β-carotene). Kinetics of plasma retinol indicate more rapid plasma appearance and turnover and more extensive recycling in these children than are observed in adults. Model-predicted mean TBS (823 μmol) was similar to values predicted using a retinol isotope dilution equation applied to data from 3 to 6 d after dosing (mean ± SD: 832 ± 176 μmol; n = 7). Conclusions: The super-child approach can be used to estimate population carotenoid bioefficacy and VA equivalence, VA status, and parameters of retinol metabolism from a composite data set. Our results provide initial estimates of retinol kinetics in well-nourished young children with adequate VA stores and demonstrate that MO leaves may be an important source of VA. © 2017 American Society for Nutrition.
Thin stillage fractionation using ultrafiltration: resistance in series model.
Arora, Amit; Dien, Bruce S; Belyea, Ronald L; Wang, Ping; Singh, Vijay; Tumbleson, M E; Rausch, Kent D
2009-02-01
The corn based dry grind process is the most widely used method in the US for fuel ethanol production. Fermentation of corn to ethanol produces whole stillage after ethanol is removed by distillation. It is centrifuged to separate thin stillage from wet grains. Thin stillage contains 5-10% solids. To concentrate solids of thin stillage, it requires evaporation of large amounts of water and maintenance of evaporators. Evaporator maintenance requires excess evaporator capacity at the facility, increasing capital expenses, requiring plant slowdowns or shut downs and results in revenue losses. Membrane filtration is one method that could lead to improved value of thin stillage and may offer an alternative to evaporation. Fractionation of thin stillage using ultrafiltration was conducted to evaluate membranes as an alternative to evaporators in the ethanol industry. Two regenerated cellulose membranes with molecular weight cut offs of 10 and 100 kDa were evaluated. Total solids (suspended and soluble) contents recovered through membrane separation process were similar to those from commercial evaporators. Permeate flux decline of thin stillage using a resistance in series model was determined. Each of the four components of total resistance was evaluated experimentally. Effects of operating variables such as transmembrane pressure and temperature on permeate flux rate and resistances were determined and optimum conditions for maximum flux rates were evaluated. Model equations were developed to evaluate the resistance components that are responsible for fouling and to predict total flux decline with respect to time. Modeling results were in agreement with experimental results (R(2) > 0.98).
Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord
International Nuclear Information System (INIS)
Shun Wong, C.; Toronto University; Minkin, S.; Hill, R.P.; Toronto University
1993-01-01
The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. Experiments are described in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spine cord. The first group of rats was given doses in 1, 2, 4, 8 and 40 fractions/day. The second group received 3 initial 'top-up'doses of 9 Gy given once daily, representing 3/4 tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 fractions/day. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 fractions/day (25.0-1.98 Gy/fraction) indicated consistency with the LQ model yielding an α/β value of 2.41 Gy. Analysis of data from experiments in which the 3 'top-up' doses were followed by up to 10 fractions (10.0-1.64 Gy/fraction) gave an α/β value of 3.41 Gy. However, data from 'top-up' experiments with 20, 30 and 40 fractions (1.60-0.55 Gy/fraction) were inconsistent with LQ model and gave a very small α/β of 0.48 Gy. It is concluded that LQ model based on data from large doses/fraction underestimates the sparing effect of small doses/fraction, provided sufficient time is allowed between each fraction for repair of sublethal damage. (author). 28 refs., 5 figs., 1 tab
Tcp and NTCP radiobiological models: conventional and hypo fractionated treatments in radiotherapy
Energy Technology Data Exchange (ETDEWEB)
Astudillo V, A.; Paredes G, L. [ININ, Carretera Mexico-Toluca s/n, Ocoyoacac 52750, Estado de Mexico (Mexico); Resendiz G, G.; Posadas V, A. [Hospital Angeles Lomas, Av. Vialidad de la Barranca s/n, Col. Valle de las Palmas, 52763 Huixquilucan de Degallado, Estado de Mexico (Mexico); Mitsoura, E. [Universidad Autonoma del Estado de Mexico, Facultad de Medicina, Paseo Tollocan, Esq. Jesus Carranza s/n, Col. Moderna de la Cruz, 50180 Toluca, Estado de Mexico (Mexico); Rodriguez L, A.; Flores C, J. M., E-mail: armando.astudillo@inin.gob.mx [Hospital Medica Sur, Puente de Piedra 150, Col. Toriello Guerra, 14050 Tlalpan, Mexico D. F. (Mexico)
2015-10-15
The hypo and conventional fractionated schedules performance were compared in terms of the tumor control and the normal tissue complications. From the records of ten patients, treated for adenocarcinoma and without mastectomy, the dose-volume histogram was used. Using radiobiological models the probabilities for tumor control and normal tissue complications were calculated. For both schedules the tumor control was approximately the same. However, the damage in the normal tissue was larger in conventional fractionated schedule. This is important because patients assistance time to their fractions (15 fractions/25 fractions) can be optimized. Thus, the hypo fractionated schedule has suitable characteristics to be implemented. (Author)
Tcp and NTCP radiobiological models: conventional and hypo fractionated treatments in radiotherapy
International Nuclear Information System (INIS)
Astudillo V, A.; Paredes G, L.; Resendiz G, G.; Posadas V, A.; Mitsoura, E.; Rodriguez L, A.; Flores C, J. M.
2015-10-01
The hypo and conventional fractionated schedules performance were compared in terms of the tumor control and the normal tissue complications. From the records of ten patients, treated for adenocarcinoma and without mastectomy, the dose-volume histogram was used. Using radiobiological models the probabilities for tumor control and normal tissue complications were calculated. For both schedules the tumor control was approximately the same. However, the damage in the normal tissue was larger in conventional fractionated schedule. This is important because patients assistance time to their fractions (15 fractions/25 fractions) can be optimized. Thus, the hypo fractionated schedule has suitable characteristics to be implemented. (Author)
A fractional Fokker-Planck model for anomalous diffusion
Energy Technology Data Exchange (ETDEWEB)
Anderson, Johan, E-mail: anderson.johan@gmail.com [Department of Earth and Space Sciences, Chalmers University of Technology, SE-412 96 Göteborg (Sweden); Kim, Eun-jin [Department of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Moradi, Sara [Ecole Polytechnique, CNRS UMR7648, LPP, F-91128 Palaiseau (France)
2014-12-15
In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.
Mittag-Leffler function for discrete fractional modelling
Directory of Open Access Journals (Sweden)
Guo-Cheng Wu
2016-01-01
Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.
Beam shaping for conformal fractionated stereotactic radiotherapy: a modeling study
International Nuclear Information System (INIS)
Hacker, Fred L.; Kooy, Hanne M.; Bellerive, Marc R.; Killoran, Joseph H.; Leber, Zachary H.; Shrieve, Dennis C.; Tarbell, Nancy J.; Loeffler, Jay S.
1997-01-01
Purpose: The patient population treated with fractionated stereotactic radiotherapy (SRT) is significantly different than that treated with stereotactic radiosurgery (SRS). Generally, lesions treated with SRT are larger, less spherical, and located within critical regions of the central nervous system; hence, they offer new challenges to the treatment planner. Here a simple, cost effective, beam shaping system has been evaluated relative to both circular collimators and an ideal dynamically conforming system for effectiveness in providing conformal therapy for these lesions. Methods and Materials: We have modeled a simple system for conformal arc therapy using four independent jaws. The jaw positions and collimator angle are changed between arcs but held fixed for the duration of each arc. Eleven previously treated SRT cases have been replanned using this system. The rectangular jaw plans were then compared to the original treatment plans which used circular collimators. The plans were evaluated with respect to tissue sparing at 100%, 80%, 50%, and 20% of the prescription dose. A plan was also done for each tumor in which the beam aperture was continuously conformed to the beams eye view projection of the tumor. This was used as an ideal standard for conformal therapy in the absence of fluence modulation. Results: For tumors with a maximum extent of over 3.5 cm the rectangular jaw plans reduced the mean volume of healthy tissue involved at the prescription dose by 57% relative to the circular collimator plans. The ideal conformal plans offered no significant further improvement at the prescription dose. The relative advantage of the rectangular jaw plans decreased at lower isodoses so that at 20% of the prescription dose tissue involvement for the rectangular jaw plans was equivalent to that for the circular collimator plans. At these isodoses the ideal conformal plans gave substantially better tissue sparing. Conclusion: A simple and economical field shaping
Effective-field-theory model for the fractional quantum Hall effect
International Nuclear Information System (INIS)
Zhang, S.C.; Hansson, T.H.; Kivelson, S.
1989-01-01
Starting directly from the microscopic Hamiltonian, we derive a field-theory model for the fractional quantum hall effect. By considering an approximate coarse-grained version of the same model, we construct a Landau-Ginzburg theory similar to that of Girvin. The partition function of the model exhibits cusps as a function of density and the Hall conductance is quantized at filling factors ν = (2k-1)/sup -1/ with k an arbitrary integer. At these fractions the ground state is incompressible, and the quasiparticles and quasiholes have fractional charge and obey fractional statistics. Finally, we show that the collective density fluctuations are massive
A representation theory for a class of vector autoregressive models for fractional processes
DEFF Research Database (Denmark)
Johansen, Søren
2008-01-01
Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a un...... root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors ß so that ß'X(t) is fractional of order d-b, 0...
LPV model for PV cell and fractional control of DC/DC converter for photovoltaic systems
Martínez González, Rubén; Bolea Monte, Yolanda; Grau Saldes, Antoni; Martínez García, Herminio
2011-01-01
This paper deals with the fractional modelling of a DC-DC converter, suitable in solar-powered electrical generation systems, and the design of a fractional controller for the aforementioned switching converter. A new model for PV cells is proposed in order to obtain a linear equation for V-I characteristic via scheduling dependence of temperature and irradiance. Due to the fractional nature of the ultracapacitors this kind of controller gives a suitable and good performance. Peer Reviewed
LPV model for PV cells and fractional control of DC/DC converter for photovoltaic systems
Martínez González, Rubén; Bolea Monte, Yolanda; Grau Saldes, Antoni; Martínez García, Herminio
2011-01-01
This paper deals with the fractional modelling of a DC-DC converter, suitable in solar-powered electrical generation systems, and the design of a fractional controller for the aforementioned switching converter. A new model for PV cells is proposed in order to obtain a linear equation for VI characteristic via scheduling dependence of temperature and irradiance. Due to the fractional nature of the ultracapacitors this kind of controller gives a suitable and good performance. Peer Rev...
International Nuclear Information System (INIS)
Brossard, N.; Croset, M.; Lecerf, J.; Lagarde, M.; Pachiaudi, C.; Normand, S.; Riou, J.P.; Chirouze, V.; Tayot, J.L.
1994-01-01
In order to study the compartmental metabolism of the 22:6n-3 fatty acid, and particularly the role of the transport plasmatic forms for the tissue uptake (especially brain), a technique is developed using carbon 13 stable isotope and an isotopic mass spectrometry coupled to gaseous chromatography technique. This method has been validated in rat with docosahexaenoic acid enriched in 13 C and esterified in triglycerides. The compartmental metabolism is monitored by measuring the variation of 22:6n-3 isotopic enrichment in the various lipoprotein lipidic fractions, in blood globules and in the brain. 1 fig., 1 tab., 12 refs
An Investigation of Fraction Models in Early Elementary Grades: A Mixed-Methods Approach
Wilkerson, Trena L.; Cooper, Susan; Gupta, Dittika; Montgomery, Mark; Mechell, Sara; Arterbury, Kristin; Moore, Sherrie; Baker, Betty Ruth; Sharp, Pat T.
2015-01-01
This study examines the effect varying models have on student understanding of fractions. The study addressed the question of what students know and understand about fractional concepts through the use of discrete and continuous models. A sample of 54 students in kindergarten and 3rd grade were given an interview pretest, participated in…
SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES
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S.ZIBAEI
2016-12-01
Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.
Compartmentation of redox metabolism in malaria parasites.
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Sebastian Kehr
Full Text Available Malaria, caused by the apicomplexan parasite Plasmodium, still represents a major threat to human health and welfare and leads to about one million human deaths annually. Plasmodium is a rapidly multiplying unicellular organism undergoing a complex developmental cycle in man and mosquito - a life style that requires rapid adaptation to various environments. In order to deal with high fluxes of reactive oxygen species and maintain redox regulatory processes and pathogenicity, Plasmodium depends upon an adequate redox balance. By systematically studying the subcellular localization of the major antioxidant and redox regulatory proteins, we obtained the first complete map of redox compartmentation in Plasmodium falciparum. We demonstrate the targeting of two plasmodial peroxiredoxins and a putative glyoxalase system to the apicoplast, a non-photosynthetic plastid. We furthermore obtained a complete picture of the compartmentation of thioredoxin- and glutaredoxin-like proteins. Notably, for the two major antioxidant redox-enzymes--glutathione reductase and thioredoxin reductase--Plasmodium makes use of alternative-translation-initiation (ATI to achieve differential targeting. Dual localization of proteins effected by ATI is likely to occur also in other Apicomplexa and might open new avenues for therapeutic intervention.
Generalized modeling of the fractional-order memcapacitor and its character analysis
Guo, Zhang; Si, Gangquan; Diao, Lijie; Jia, Lixin; Zhang, Yanbin
2018-06-01
Memcapacitor is a new type of memory device generalized from the memristor. This paper proposes a generalized fractional-order memcapacitor model by introducing the fractional calculus into the model. The generalized formulas are studied and the two fractional-order parameter α, β are introduced where α mostly affects the fractional calculus value of charge q within the generalized Ohm's law and β generalizes the state equation which simulates the physical mechanism of a memcapacitor into the fractional sense. This model will be reduced to the conventional memcapacitor as α = 1 , β = 0 and to the conventional memristor as α = 0 , β = 1 . Then the numerical analysis of the fractional-order memcapacitor is studied. And the characteristics and output behaviors of the fractional-order memcapacitor applied with sinusoidal charge are derived. The analysis results have shown that there are four basic v - q and v - i curve patterns when the fractional order α, β respectively equal to 0 or 1, moreover all v - q and v - i curves of the other fractional-order models are transition curves between the four basic patterns.
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
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Zhenhua Hu
2013-01-01
Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.
2012-11-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.; Radwan, Ahmed G.; Salama, Khaled N.; Momani, Shaher M.; Hashim, Ishak
2012-01-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
Universal block diagram based modeling and simulation schemes for fractional-order control systems.
Bai, Lu; Xue, Dingyü
2017-05-08
Universal block diagram based schemes are proposed for modeling and simulating the fractional-order control systems in this paper. A fractional operator block in Simulink is designed to evaluate the fractional-order derivative and integral. Based on the block, the fractional-order control systems with zero initial conditions can be modeled conveniently. For modeling the system with nonzero initial conditions, the auxiliary signal is constructed in the compensation scheme. Since the compensation scheme is very complicated, therefore the integrator chain scheme is further proposed to simplify the modeling procedures. The accuracy and effectiveness of the schemes are assessed in the examples, the computation results testify the block diagram scheme is efficient for all Caputo fractional-order ordinary differential equations (FODEs) of any complexity, including the implicit Caputo FODEs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Schnell, Gretja; Spudich, Serena; Harrington, Patrick; Price, Richard W; Swanstrom, Ronald
2009-04-01
Human immunodeficiency virus type 1 (HIV-1) invades the central nervous system (CNS) shortly after systemic infection and can result in the subsequent development of HIV-1-associated dementia (HAD) in a subset of infected individuals. Genetically compartmentalized virus in the CNS is associated with HAD, suggesting autonomous viral replication as a factor in the disease process. We examined the source of compartmentalized HIV-1 in the CNS of subjects with HIV-1-associated neurological disease and in asymptomatic subjects who were initiating antiretroviral therapy. The heteroduplex tracking assay (HTA), targeting the variable regions of env, was used to determine which HIV-1 genetic variants in the cerebrospinal fluid (CSF) were compartmentalized and which variants were shared with the blood plasma. We then measured the viral decay kinetics of individual variants after the initiation of antiretroviral therapy. Compartmentalized HIV-1 variants in the CSF of asymptomatic subjects decayed rapidly after the initiation of antiretroviral therapy, with a mean half-life of 1.57 days. Rapid viral decay was also measured for CSF-compartmentalized variants in four HAD subjects (t(1/2) mean = 2.27 days). However, slow viral decay was measured for CSF-compartmentalized variants from an additional four subjects with neurological disease (t(1/2) range = 9.85 days to no initial decay). The slow decay detected for CSF-compartmentalized variants was not associated with poor CNS drug penetration, drug resistant virus in the CSF, or the presence of X4 virus genotypes. We found that the slow decay measured for CSF-compartmentalized variants in subjects with neurological disease was correlated with low peripheral CD4 cell count and reduced CSF pleocytosis. We propose a model in which infiltrating macrophages replace CD4(+) T cells as the primary source of productive viral replication in the CNS to maintain high viral loads in the CSF in a substantial subset of subjects with HAD.
Directory of Open Access Journals (Sweden)
Gretja Schnell
2009-04-01
Full Text Available Human immunodeficiency virus type 1 (HIV-1 invades the central nervous system (CNS shortly after systemic infection and can result in the subsequent development of HIV-1-associated dementia (HAD in a subset of infected individuals. Genetically compartmentalized virus in the CNS is associated with HAD, suggesting autonomous viral replication as a factor in the disease process. We examined the source of compartmentalized HIV-1 in the CNS of subjects with HIV-1-associated neurological disease and in asymptomatic subjects who were initiating antiretroviral therapy. The heteroduplex tracking assay (HTA, targeting the variable regions of env, was used to determine which HIV-1 genetic variants in the cerebrospinal fluid (CSF were compartmentalized and which variants were shared with the blood plasma. We then measured the viral decay kinetics of individual variants after the initiation of antiretroviral therapy. Compartmentalized HIV-1 variants in the CSF of asymptomatic subjects decayed rapidly after the initiation of antiretroviral therapy, with a mean half-life of 1.57 days. Rapid viral decay was also measured for CSF-compartmentalized variants in four HAD subjects (t(1/2 mean = 2.27 days. However, slow viral decay was measured for CSF-compartmentalized variants from an additional four subjects with neurological disease (t(1/2 range = 9.85 days to no initial decay. The slow decay detected for CSF-compartmentalized variants was not associated with poor CNS drug penetration, drug resistant virus in the CSF, or the presence of X4 virus genotypes. We found that the slow decay measured for CSF-compartmentalized variants in subjects with neurological disease was correlated with low peripheral CD4 cell count and reduced CSF pleocytosis. We propose a model in which infiltrating macrophages replace CD4(+ T cells as the primary source of productive viral replication in the CNS to maintain high viral loads in the CSF in a substantial subset of subjects with HAD.
Amato, Ernesto; Italiano, Antonio; Baldari, Sergio
2014-01-01
We developed a general model for the calculation of absorbed fractions in ellipsoidal volumes of soft tissue uniformly filled with alpha, beta and gamma emitting radionuclides. The approach exploited Monte Carlo simulations with the Geant4 code to determine absorbed fractions in ellipsoids characterized by a wide range of dimensions and ellipticities, for monoenergetic emissions of each radiation type. The so-obtained absorbed fractions were put in an analytical relationship with the 'general...
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Yang Xiao-Jun
2017-01-01
Full Text Available In this paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from mathematical view of point. The comparative results of the anomalous relaxation among the various fractional derivatives are also given. They are very efficient in description of the complex phenomenon arising in heat transfer.
N'Doye, Ibrahima
2015-05-25
In this paper, a dynamical fractional viscoelastic fluids convection model in porous media is proposed and its chaotic behavior is studied. A preformed equilibrium points analysis indicates the conditions where chaotic dynamics can be observed, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate orders of a fractional viscoelastic fluids system, which exhibits chaos, are presented as well.
Three-compartmental analysis of effects of D-propranolol on thyroid hormone kinetics
International Nuclear Information System (INIS)
Van Der Heijden, J.T.M.; Krenning, E.P.; Van Toor, H.; Hennemann, G.; Docter, R.
1988-01-01
Tracer thyroxine (T 4 ), 3,3',5-triiodothyronine (T 3 ), and 3,3',5'-triiodothyronine (rT 3 ) kinetic studies were performed in normal T 4 substituted subjects before and during oral D-propranolol treatment to determine whether changes in thyroid hormone metabolism in a propranolol-induced low-T 3 syndrome result from inhibition of 5'-deiodination or inhibition of transport of iodothyronines into tissues. Data were analyzed according to a three-compartmental model of distribution and metabolism. No changes were observed in size of the three T 4 compartments or in fractional and mass transfer rates of T 4 from plasma to the rapidly (REP) and slowly (SEP) equilibrating pools. Serum T 3 , free T 3 , T 3 plasma pool, T 3 mass transfer rate to REP and SEP, and the T 3 pool masses were all significantly decreased during propranolol to a similar extent as the T 3 plasma production rate (PR). It is concluded that the D-propranolol-induced changes in thyroid hormone metabolism, resulting in a low-T 3 syndrome, are due to inhibition of thyroid hormone deiodination. This is in contrast to the low-T 3 syndrome during caloric deprivation, which results from inhibition of transport of iodothyronines into the liver
Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
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Nowak Tomasz Karol
2014-06-01
Full Text Available This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.
Fractional statistics in 2+1 dimensions through the Gaussian model
International Nuclear Information System (INIS)
Murthy, G.
1986-01-01
The free massless field in 2+1 dimensions is written as an ''integral'' over free massless fields in 1+1 dimensions. Taking the operators with fractional dimension in the Gaussian model as a springboard we construct operators with fractional statistics in the former theory
On the identification of fractionally cointegrated VAR models with the F(d) condition
DEFF Research Database (Denmark)
Carlini, Federico; Santucci de Magistris, Paolo
with different fractional integration and cointegration parameters. The properties of these multiple non-identified sub-models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d). The assessment of the F(d...
Directory of Open Access Journals (Sweden)
Yang Xiao-Jun
2016-01-01
Full Text Available In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also obtained by means of the Laplace transform.
SU-E-T-70: A Radiobiological Model of Reoxygenation and Fractionation Effects
Energy Technology Data Exchange (ETDEWEB)
Guerrero, M [University of Maryland School of Medicine, Baltimore, MD (United States); Carlson, DJ [Yale Univ. School of Medicine, New Haven, CT (United States)
2015-06-15
Purpose: To develop a simple reoxygenation model that fulfills the following goals:1-Quantify the reoxygenation effect in biologically effective dose (BED) and compare it to the repopulation effect.2-Model the hypoxic fraction in tumors as a function of the number of fractions.3-Develop a simple analytical expression for a reoxygenation term in BED calculations. Methods: The model considers tumor cells in two compartments: one normoxic population of cells and one hypoxic compartment including cells under a range of reduced oxygen concentrations. The surviving fraction is predicted using the linear-quadratic (LQ) model. A hypoxia reduction factor (HRF) is used to quantify reductions in radiosensitivity parameters α-A and β-A as cellular oxygen concentration decreases. The HRF is defined as the ratio of the dose at a specific level of hypoxia to the dose under fully aerobic conditions to achieve equal cell killing. The model assumes that a fraction of the hypoxic cells ( ) moves from the hypoxic to the aerobic compartment after each daily fraction. As an example, we consider standard fractionation for NSCLC (d=2Gy,n=33) versus a SBRT (n=5, d=10Gy) fractionation and compare the loss in reoxygenation biological effect with the gain in repopulation biological effect. Results: An analytic expression for the surviving fraction after n daily treatments is derived and the reoxygenation term in the biological effect is calculated. Reoxygenation and repopulation effects are the same order of magnitude for potential doubling time Td values of 2 to 5 days. The hypoxic fraction increases or decreases with n depending on the reoxygenation rate Δ. For certain combinations of parameters, the biological effect of reoxygenation goes as -(n-1)*ln(1-Δ) providing a simple expression that can be introduced in BED calculations. Conclusion: A novel radiobiological model was developed that can be used to evaluate the effect of reoxygenation in fractionated radiotherapy.
A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation
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Rongwu Lu
2017-01-01
Full Text Available Considering the popular use of a certain kind of supervision management problem in many fields, we firstly build an ordinary supervision game model of multiple stakeholders. Secondly, a fractional supervision game model is set up and solved based on the theory of fractional calculus and a predictor-corrector numerical approach. Thirdly, the methods of phase diagram and time series graph were applied to simulate and analyse the dynamic process of the fractional order game model. Results of numerical solutions are given to illustrate our conclusions and referred to the practice.
Passive Noise Filtering by Cellular Compartmentalization.
Stoeger, Thomas; Battich, Nico; Pelkmans, Lucas
2016-03-10
Chemical reactions contain an inherent element of randomness, which presents itself as noise that interferes with cellular processes and communication. Here we discuss the ability of the spatial partitioning of molecular systems to filter and, thus, remove noise, while preserving regulated and predictable differences between single living cells. In contrast to active noise filtering by network motifs, cellular compartmentalization is highly effective and easily scales to numerous systems without requiring a substantial usage of cellular energy. We will use passive noise filtering by the eukaryotic cell nucleus as an example of how this increases predictability of transcriptional output, with possible implications for the evolution of complex multicellularity. Copyright © 2016 Elsevier Inc. All rights reserved.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
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Shelton Peiris
2017-12-01
Full Text Available This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV components in order to develop the General Long Memory SV (GLMSV model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications.
Hydrogen solubility measurements of analyzed tall oil fractions and a solubility model
International Nuclear Information System (INIS)
Uusi-Kyyny, Petri; Pakkanen, Minna; Linnekoski, Juha; Alopaeus, Ville
2017-01-01
Highlights: • Hydrogen solubility was measured in four tall oil fractions between 373 and 597 K. • Continuous flow synthetic isothermal and isobaric method was used. • A Henry’s law model was developed for the distilled tall oil fractions. • The complex composition of the samples was analyzed and is presented. - Abstract: Knowledge of hydrogen solubility in tall oil fractions is important for designing hydrotreatment processes of these complex nonedible biobased materials. Unfortunately measurements of hydrogen solubility into these fractions are missing in the literature. This work reports hydrogen solubility measured in four tall oil fractions between 373 and 597 K and at pressures from 5 to 10 MPa. Three of the fractions were distilled tall oil fractions their resin acids contents are respectively 2, 20 and 23 in mass-%. Additionally one fraction was a crude tall oil (CTO) sample containing sterols as the main neutral fraction. Measurements were performed using a continuous flow synthetic isothermal and isobaric method based on the visual observation of the bubble point. Composition of the flow was changed step-wise for the bubble point composition determination. We assume that the tall oil fractions did not react during measurements, based on the composition analysis performed before and after the measurements. Additionally the densities of the fractions were measured at atmospheric pressure from 293.15 to 323.15 K. A Henry’s law model was developed for the distilled tall oil fractions describing the solubility with an absolute average deviation of 2.1%. Inputs of the solubility model are temperature, total pressure and the density of the oil at 323.15 K. The solubility of hydrogen in the CTO sample can be described with the developed model with an absolute average deviation of 3.4%. The solubility of hydrogen increases both with increasing pressure and/or increasing temperature. The more dense fractions of the tall oil exhibit lower hydrogen
Underprediction of human skin erythema at low doses per fraction by the linear quadratic model
International Nuclear Information System (INIS)
Hamilton, Christopher S.; Denham, James W.; O'Brien, Maree; Ostwald, Patricia; Kron, Tomas; Wright, Suzanne; Doerr, Wolfgang
1996-01-01
Background and purpose. The erythematous response of human skin to radiotherapy has proven useful for testing the predictions of the linear quadratic (LQ) model in terms of fractionation sensitivity and repair half time. No formal investigation of the response of human skin to doses less than 2 Gy per fraction has occurred. This study aims to test the validity of the LQ model for human skin at doses ranging from 0.4 to 5.2 Gy per fraction. Materials and methods. Complete erythema reaction profiles were obtained using reflectance spectrophotometry in two patient populations: 65 patients treated palliatively with 5, 10, 12 and 20 daily treatment fractions (varying thicknesses of bolus, various body sites) and 52 patients undergoing prostatic irradiation for localised carcinoma of the prostate (no bolus, 30-32 fractions). Results and conclusions. Gender, age, site and prior sun exposure influence pre- and post-treatment erythema values independently of dose administered. Out-of-field effects were also noted. The linear quadratic model significantly underpredicted peak erythema values at doses less than 1.5 Gy per fraction. This suggests that either the conventional linear quadratic model does not apply for low doses per fraction in human skin or that erythema is not exclusively initiated by radiation damage to the basal layer. The data are potentially explained by an induced repair model
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Taro Furubayashi
2018-01-01
Full Text Available The emergence and dominance of parasitic replicators are among the major hurdles for the proliferation of primitive replicators. Compartmentalization of replicators is proposed to relieve the parasite dominance; however, it remains unclear under what conditions simple compartmentalization uncoupled with internal reaction secures the long-term survival of a population of primitive replicators against incessant parasite emergence. Here, we investigate the sustainability of a compartmentalized host-parasite replicator (CHPR system undergoing periodic washout-mixing cycles, by constructing a mathematical model and performing extensive simulations. We describe sustainable landscapes of the CHPR system in the parameter space and elucidate the mechanism of phase transitions between sustainable and extinct regions. Our findings revealed that a large population size of compartments, a high mixing intensity, and a modest amount of nutrients are important factors for the robust survival of replicators. We also found two distinctive sustainable phases with different mixing intensities. These results suggest that a population of simple host–parasite replicators assumed before the origin of life can be sustained by a simple compartmentalization with periodic washout-mixing processes.
Modelling of diffuse solar fraction with multiple predictors
Energy Technology Data Exchange (ETDEWEB)
Ridley, Barbara; Boland, John [Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095 (Australia); Lauret, Philippe [Laboratoire de Physique du Batiment et des Systemes, University of La Reunion, Reunion (France)
2010-02-15
For some locations both global and diffuse solar radiation are measured. However, for many locations, only global radiation is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from direct on some other plane using trigonometry, we need to have diffuse radiation on the horizontal plane available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia. Boland et al. developed a validated model for Australian conditions. Boland et al. detailed our recent advances in developing the theoretical framework for the use of the logistic function instead of piecewise linear or simple nonlinear functions and was the first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors. We have developed a multiple predictor model, which is much simpler than previous models, and uses hourly clearness index, daily clearness index, solar altitude, apparent solar time and a measure of persistence of global radiation level as predictors. This model performs marginally better than currently used models for locations in the Northern Hemisphere and substantially better for Southern Hemisphere locations. We suggest it can be used as a universal model. (author)
Inositol lipid turnover and compartmentation in canine trachealis smooth muscle
International Nuclear Information System (INIS)
Baron, C.B.; Pring, M.; Coburn, R.F.
1989-01-01
We established conditions for the study of metabolism and compartmentation of inositol phospholipids in canine trachealis muscle. Unstimulated muscle was incubated with myo-[3H]inositol for 30 min at 37 degrees C which resulted in labeling of the tissue free myo-inositol pool, whereas only a small amount of radioactivity was incorporated into inositol phospholipids or inositol phosphates. After addition of 5.5 microM carbachol, phosphatidylinositol (PI), phosphatidylinositol-4-phosphate (PIP), and phosphatidylinositol-4,5-bisphosphate (PIP2), specific radioactivities increased exponentially, reaching apparent constant values in 180-240 min. Initial rates of increases in PI, PIP, and PIP2 specific radioactivities were 39, 32, and 66 times that measured in unstimulated muscle. Metabolic flux rates (nmol.100 nmol total lipid Pi-1.min-1) during development of force averaged 0.42 +/- 0.09 and during force maintenance averaged 0.14 +/- 0.01. Fractions of total PI, PIP, and PIP2 pools that were linked to muscarinic cholinergic activation were estimated to be 0.97, 0.85, and 0.65, respectively. Initial rates of increase in specific radioactivities and specific radioactivities during carbachol activation were similar in PI, PIP, and PIP2 fast active compartments, suggesting metabolic flux from PI to PIP to PIP2 was in near chemical equilibrium. Turnover times for PI, PIP, and PIP2 fast active compartments were estimated to be 21, 1.6, and 4.0 min, respectively
International Nuclear Information System (INIS)
Sasaki, Takehito; Kamata, Rikisaburo; Urahashi, Shingo; Yamaguchi, Tetsuji.
1993-01-01
One hundred and sixty-nine cervical lymph node-metastases from head and neck squamous cell carcinomas treated with either even fractionation or uneven fractionation regimens were analyzed in the present investigation. Logistic multivariate regression analysis indicated that: type of fractionation (even vs uneven), size of metastases, T value of primary tumors, and total dose are independent variables out of 18 variables that significantly influenced the rate of tumor clearance. The data, with statistical bias corrected by the regression equation, indicated that the uneven fractionation scheme significantly improved the rate of tumor clearance for the same size of metastases, total dose, and overall time compared to the even fractionation scheme. Further analysis by a linear-quadratic cell survival model indicated that the clinical improvement by uneven fractionation might not be explained entirely by a larger dose per fraction. It is suggested that tumor cells irradiated with an uneven fractionation regimen might repopulate more slowly, or they might be either less hypoxic or redistributed in a more radiosensitive phase in the cell cycle than those irradiated with even fractionation. This conclusion is clearly not definite, but it is suitable, pending the results of further investigation. (author)
Cusimano, N.; Gerardo-Giorda, L.
2018-06-01
Classical models of electrophysiology do not typically account for the effects of high structural heterogeneity in the spatio-temporal description of excitation waves propagation. We consider a modification of the Monodomain model obtained by replacing the diffusive term of the classical formulation with a fractional power of the operator, defined in the spectral sense. The resulting nonlocal model describes different levels of tissue heterogeneity as the fractional exponent is varied. The numerical method for the solution of the fractional Monodomain relies on an integral representation of the nonlocal operator combined with a finite element discretisation in space, allowing to handle in a natural way bounded domains in more than one spatial dimension. Numerical tests in two spatial dimensions illustrate the features of the model. Activation times, action potential duration and its dispersion throughout the domain are studied as a function of the fractional parameter: the expected peculiar behaviour driven by tissue heterogeneities is recovered.
Compartmental analysis, imaging techniques and population pharmacokinetic. Experiences at CENTIS
International Nuclear Information System (INIS)
Hernández, Ignacio; León, Mariela; Leyva, Rene; Castro, Yusniel; Ayra, Fernando E.
2016-01-01
Introduction: In pharmacokinetic evaluation small rodents are used in a large extend. Traditional pharmacokinetic evaluations by the two steps approach can be replaced by the sparse data design which may also represent a complicated situation to evaluate satisfactorily from the statistical point of view. In this presentation different situations of sparse data sampling are analyzed based on practical consideration. Non linear mixed effect model was selected in order to estimate pharmacokinetic parameters in simulated data from real experimental results using blood sampling and imaging procedures. Materials and methods: Different scenarios representing several experimental designs of incomplete individual profiles were evaluated. Data sets were simulated based on real data from previous experiments. In all cases three to five blood samples were considered per time point. A combination of compartmental analysis with tumor uptake obtained by gammagraphy of radiolabeled drugs is also evaluated.All pharmacokinetic profiles were analyzed by means of MONOLIX software version 4.2.3. Results: All sampling schedules yield the same results when computed using the MONOLIX software and the SAEM algorithm. Population and individual pharmacokinetic parameters were accurately estimated with three or five determination per sampling point. According with the used methodology and software tool, it can be an expected result, but demonstrating the method performance in such situations, allow us to select a more flexible design using a very small number of animals in preclinical research. The combination with imaging procedures also allows us to construct a completely structured compartmental analysis. Results of real experiments are presented demonstrating the versatility of used methodology in different evaluations. The same sampling approach can be considered in phase I or II clinical trials. (author)
A Semianalytical Solution of the Fractional Derivative Model and Its Application in Financial Market
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Lina Song
2018-01-01
Full Text Available Fractional differential equation has been introduced to the financial theory, which presents new ideas and tools for the theoretical researches and the practical applications. In the work, an approximate semianalytical solution of the time-fractional European option pricing model is derived using the method of combining the enhanced technique of Adomian decomposition method with the finite difference method. And then the result is introduced in China’s financial market. The work makes every effort to test the feasibility of the fractional derivative model in the actual financial market.
On the identification of fractionally cointegrated VAR models with the F(d) condition
DEFF Research Database (Denmark)
Carlini, Federico; Santucci de Magistris, Paolo
for any choice of the lag length, also when the true cointegration rank is known. The properties of these multiple non-identified models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d......) and it is a generalization to the fractional case of the I(1) condition in the VECM model. The assessment of the F(d) condition in the empirical analysis is relevant for the determination of the fractional parameters as well as the number of lags. The paper also illustrates the indeterminacy between the cointegration rank...
On the identification of fractionally cointegrated VAR models with the F(d) condition
DEFF Research Database (Denmark)
Santucci de Magistris, Paolo; Carlini, Federico
for any choice of the lag-length when the true cointegration rank is known. The properties of these multiple non-identified models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d......). This is a generalization of the well-known I(1) condition to the fractional case. Imposing a proper restriction on the fractional integration parameter, d, is sufficient to guarantee identification of all model parameters and the validity of the F(d) condition. The paper also illustrates the indeterminacy between...
Use of Angle Model to Understand Addition and Subtraction of Fractions
Directory of Open Access Journals (Sweden)
Muzwangowenyu Mukwambo
2018-02-01
Full Text Available Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and learning (TMATL of operations of fraction. With the hope of engaging the reformed mathematical approach of teaching and learning (RMATL this study investigated the following: How can trainee teachers use the angle model in RMATL operations of fractions? What are the perceptions of trainee teachers in the use of the angle model which engages RMATL to teach the operations of fractions? With the goal to fill the mentioned gap in which learners struggle to perform operations involving fractions, we observed and analysed worksheets on operation with fractions students wrote. Observations and interviews with trainee teachers of lower primary revealed poor performance in problems related to operations with fractions. Observed patterns supported by cognitivism revealed that invented methods or strategies on which RMATL is anchored are suitable enough to engage learner–centred teaching and learning which can prevent the abstractness of the concept of operations with fractions.
On conservation laws for models in discrete, noncommutative and fractional differential calculus
International Nuclear Information System (INIS)
Klimek, M.
2001-01-01
We present the general method of derivation the explicit form of conserved currents for equations built within the framework of discrete, noncommutative or fractional differential calculus. The procedure applies to linear models with variable coefficients including also nonlinear potential part. As an example an equation on quantum plane, nonlinear Toda lattice model and homogeneous equation of fractional diffusion in 1+1 dimensions are studied
Neutron fraction and neutrino mean free path predictions in relativistic mean field models
International Nuclear Information System (INIS)
Hutauruk, P.T.P.; Williams, C.K.; Sulaksono, A.; Mart, T.
2004-01-01
The equation of state (EOS) of dense matter and neutrino mean free path (NMFP) in a neutron star have been studied by using relativistic mean field models motivated by effective field theory. It is found that the models predict too large proton fractions, although one of the models (G2) predicts an acceptable EOS. This is caused by the isovector terms. Except G2, the other two models predict anomalous NMFP's. In order to minimize the anomaly, besides an acceptable EOS, a large M* is favorable. A model with large M* retains the regularity in the NMFP even for a small neutron fraction
Stochastic fractional differential equations: Modeling, method and analysis
International Nuclear Information System (INIS)
Pedjeu, Jean-C.; Ladde, Gangaram S.
2012-01-01
By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.
Field Testing of Compartmentalization Methods for Multifamily Construction
Energy Technology Data Exchange (ETDEWEB)
Ueno, K. [Building Science Corporation, Westford, MA (United States); Lstiburek, J. W. [Building Science Corporation, Westford, MA (United States)
2015-03-01
The 2012 International Energy Conservation Code (IECC) has an airtightness requirement of 3 air changes per hour at 50 Pascals test pressure (3 ACH50) for single-family and multifamily construction (in climate zones 3–8). The Leadership in Energy & Environmental Design certification program and ASHRAE Standard 189 have comparable compartmentalization requirements. ASHRAE Standard 62.2 will soon be responsible for all multifamily ventilation requirements (low rise and high rise); it has an exceptionally stringent compartmentalization requirement. These code and program requirements are driving the need for easier and more effective methods of compartmentalization in multifamily buildings.
Model-order reduction of lumped parameter systems via fractional calculus
Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio
2018-04-01
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.
A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2016-12-01
Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions. Copyright © 2016 Elsevier Inc. All rights reserved.
No-arbitrage, leverage and completeness in a fractional volatility model
Vilela Mendes, R.; Oliveira, M. J.; Rodrigues, A. M.
2015-02-01
When the volatility process is driven by fractional noise one obtains a model which is consistent with the empirical market data. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behaviors. Here, the no-arbitrage and completeness properties of the models are rigorously studied.
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses...... the multivariate non-cointegrated fractional ARIMA model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probablity, thus making...
Fractional single-phase-lagging heat conduction model for describing anomalous diffusion
Directory of Open Access Journals (Sweden)
T.N. Mishra
2016-03-01
Full Text Available The fractional single-phase-lagging (FSPL heat conduction model is obtained by combining scalar time fractional conservation equation to the single-phase-lagging (SPL heat conduction model. Based on the FSPL heat conduction model, anomalous diffusion within a finite thin film is investigated. The effect of different parameters on solution has been observed and studied the asymptotic behavior of the FSPL model. The analytical solution is obtained using Laplace transform method. The whole analysis is presented in dimensionless form. Numerical examples of particular interest have been studied and discussed in details.
Directory of Open Access Journals (Sweden)
HASHEM SABERI NAJAFI
2016-07-01
Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.
Langlands, T A M; Henry, B I; Wearne, S L
2009-12-01
We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.
Gómez-Aguilar, J. F.
2018-03-01
In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.
A model to accumulate fractionated dose in a deforming organ
International Nuclear Information System (INIS)
Yan Di; Jaffray, D.A.; Wong, J.W.
1999-01-01
Purpose: Measurements of internal organ motion have demonstrated that daily organ deformation exists throughout the course of radiation treatment. However, a method of constructing the resultant dose delivered to the organ volume remains a difficult challenge. In this study, a model to quantify internal organ motion and a method to construct a cumulative dose in a deforming organ are introduced. Methods and Materials: A biomechanical model of an elastic body is used to quantify patient organ motion in the process of radiation therapy. Intertreatment displacements of volume elements in an organ of interest is calculated by applying an finite element method with boundary conditions, obtained from multiple daily computed tomography (CT) measurements. Therefore, by incorporating also the measurements of daily setup error, daily dose delivered to a deforming organ can be accumulated by tracking the position of volume elements in the organ. Furthermore, distribution of patient-specific organ motion is also predicted during the early phase of treatment delivery using the daily measurements, and the cumulative dose distribution in the organ can then be estimated. This dose distribution will be updated whenever a new measurement becomes available, and used to reoptimize the ongoing treatment. Results: An integrated process to accumulate dosage in a daily deforming organ was implemented. In this process, intertreatment organ motion and setup error were systematically quantified, and incorporated in the calculation of the cumulative dose. An example of the rectal wall motion in a prostate treatment was applied to test the model. The displacements of volume elements in the rectal wall, as well as the resultant doses, were calculated. Conclusion: This study is intended to provide a systematic framework to incorporate daily patient-specific organ motion and setup error in the reconstruction of the cumulative dose distribution in an organ of interest. The realistic dose
Compartmentalization of Aquaporins in the Human Intestine
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Rajendram V. Rajnarayanan
2008-06-01
Full Text Available Improper localization of water channel proteins called aquaporins (AQP induce mucosal injury which is implicated in CrohnÃ¢Â€Â™s disease and ulcerative colitis. The amino acid sequences of AQP3 and AQP10 are 79% similar and belong to the mammalian aquaglyceroporin subfamily. AQP10 is localized on the apical compartment of the intestinal epithelium called the glycocalyx while AQP3 is selectively targeted to the basolateral membrane. Despite the high sequence similarity and evolutionary relatedness, the molecular mechanism involved in the polarity, selective targeting and function of AQP3 and AQP10 in the intestine is largely unknown. Our hypothesis is that the differential polarity and selective targeting of AQP3 and AQP10 in the intestinal epithelial cells is influenced by amino acid signal motifs. We performed sequence and structural alignments to determine differences in signals for localization and posttranslational glycosylation. The basolateral sorting motif Ã¢Â€ÂœYRLLÃ¢Â€Â is present in AQP3 but absent in AQP10; while Nglycosylation signals are present in AQP10 but absent in AQP3. Furthermore, the C-terminal region of AQP3 is longer compared to AQP10. The sequence and structural differences between AQP3 and AQP10 provide insights into the differential compartmentalization and function of these two aquaporins commonly expressed in human intestines.
Compartmentalization and Transport in Synthetic Vesicles
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Christine eSchmitt
2016-02-01
Full Text Available Nano-scale vesicles have become a popular tool in life sciences. Besides liposomes that are generated from phospholipids of natural origin, polymersomes fabricated of synthetic block copolymers enjoy increasing popularity, as they represent more versatile membrane building blocks that can be selected based on their specific physicochemical properties, like permeability, stability or chemical reactivity.In this review, we focus on the application of simple and nested artificial vesicles in synthetic biology. First, we provide an introduction into the utilization of multi-compartmented vesosomes as compartmentalized nano-scale bioreactors. In the bottom-up development of protocells from vesicular nano-reactors, the specific exchange of pathway intermediates across compartment boundaries represents a bottleneck for future studies. To date, most compartmented bioreactors rely on unspecific exchange of substrates and products. This is either based on changes in permeability of the coblock polymer shell by physicochemical triggers or by the incorporation of unspecific porin proteins into the vesicle membrane. Since the incorporation of membrane transport proteins into simple and nested artificial vesicles offers the potential for specific exchange of substances between subcompartments, it opens new vistas in the design of protocells. Therefore we devote the main part of the review to summarize the technical advances in the use of phospholipids and block copolymers for the reconstitution of membrane proteins.
International Nuclear Information System (INIS)
Dale, R.G.
1986-01-01
By extending a previously developed mathematical model based on the linear-quadratic dose-effect relationship, it is possible to examine the consequences of performing fractionated treatments for which there is insufficient time between fractions to allow complete damage repair. Equations are derived which give the relative effectiveness of such treatments in terms of tissue-repair constants (μ values) and α/β ratios, and these are then applied to some examples of treatments involving multiple fractions per day. The interplay of the various mechanisms involved (including repopulation effects) and their possible influence on treatments involving closely spaced fractions are examined. If current indications of the differences in recovery rates between early- and late-reacting normal tissues are representative, then it is shown that such differences may limit the clinical potential of accelerated fractionation regimes, where several fractions per day are given in a relatively short overall time. (author)
A Semianalytical Solution of the Fractional Derivative Model and Its Application in Financial Market
Song, Lina
2018-01-01
Fractional differential equation has been introduced to the financial theory, which presents new ideas and tools for the theoretical researches and the practical applications. In the work, an approximate semianalytical solution of the time-fractional European option pricing model is derived using the method of combining the enhanced technique of Adomian decomposition method with the finite difference method. And then the result is introduced in China’s financial market. The work makes every e...
Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling
International Nuclear Information System (INIS)
Burnecki, Krzysztof; Weron, Aleksander
2014-01-01
In this survey paper we present a systematic methodology which demonstrates how to identify the origins of fractional dynamics. We consider three mechanisms which lead to it, namely fractional Brownian motion, fractional Lévy stable motion and an autoregressive fractionally integrated moving average (ARFIMA) process but we concentrate on the ARFIMA modelling. The methodology is based on statistical tools for identification and validation of the fractional dynamics, in particular on an ARFIMA parameter estimator, an ergodicity test, a self-similarity index estimator based on sample p-variation and a memory parameter estimator based on sample mean-squared displacement. A complete list of algorithms needed for this is provided in appendices A–F. Finally, we illustrate the methodology on various empirical data and show that ARFIMA can be considered as a universal model for fractional dynamics. Thus, we provide a practical guide for experimentalists on how to efficiently use ARFIMA modelling for a large class of anomalous diffusion data. (paper)
Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem
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V. Charles
2011-01-01
Full Text Available In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP problem approach is proposed, which strikes the balance between previous models available in the literature.
López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin
2017-09-01
Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.
Directory of Open Access Journals (Sweden)
Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
Modeling ramp-hold indentation measurements based on Kelvin-Voigt fractional derivative model
Zhang, Hongmei; zhe Zhang, Qing; Ruan, Litao; Duan, Junbo; Wan, Mingxi; Insana, Michael F.
2018-03-01
Interpretation of experimental data from micro- and nano-scale indentation testing is highly dependent on the constitutive model selected to relate measurements to mechanical properties. The Kelvin-Voigt fractional derivative model (KVFD) offers a compact set of viscoelastic features appropriate for characterizing soft biological materials. This paper provides a set of KVFD solutions for converting indentation testing data acquired for different geometries and scales into viscoelastic properties of soft materials. These solutions, which are mostly in closed-form, apply to ramp-hold relaxation, load-unload and ramp-load creep-testing protocols. We report on applications of these model solutions to macro- and nano-indentation testing of hydrogels, gastric cancer cells and ex vivo breast tissue samples using an atomic force microscope (AFM). We also applied KVFD models to clinical ultrasonic breast data using a compression plate as required for elasticity imaging. Together the results show that KVFD models fit a broad range of experimental data with a correlation coefficient typically R 2 > 0.99. For hydrogel samples, estimation of KVFD model parameters from test data using spherical indentation versus plate compression as well as ramp relaxation versus load-unload compression all agree within one standard deviation. Results from measurements made using macro- and nano-scale indentation agree in trend. For gastric cell and ex vivo breast tissue measurements, KVFD moduli are, respectively, 1/3-1/2 and 1/6 of the elasticity modulus found from the Sneddon model. In vivo breast tissue measurements yield model parameters consistent with literature results. The consistency of results found for a broad range of experimental parameters suggest the KVFD model is a reliable tool for exploring intrinsic features of the cell/tissue microenvironments.
International Nuclear Information System (INIS)
Dong, Jianping
2011-01-01
The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theorems in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics. -- Highlights: → Thomas-Fermi model under the framework of fractional quantum mechanics is studied. → We show the validity of the HK theorems in the space fractional quantum mechanics. → The density functional theory is generalized to the fractional quantum mechanics.
International Nuclear Information System (INIS)
Gerweck, Leo E.; Dubois, Willum; Baumann, Michael; Suit, Herman D.
1995-01-01
, the rank-order correlation coefficient between the single dose hypoxic versus fractionated dose TCD50s under hypoxic or aerobic conditions was 1.0. For all 5 tumors examined, a trend for rank correlation was observed between the single dose and the fractionated dose TCD50s performed under normal or clamp hypoxic conditions (r=0.7, p=0.16 in both cases). The linear correlation coefficients were 0.83, p=0.08 and 0.72, p=0.17, respectively. Failure to attain a rank correlation of 1.0 was due to one tumor exhibiting an insignificant fractionation effect. The rank correlation between the TCD50s for fractionated treatments under normal versus the extrapolated TCD50s under clamp hypoxic conditions was 1.00; the linear correlation coefficient was 0.97 (p=0.01). Conclusions: In the tumor models examined, factors controlling the single fraction tumor control dose, also impact the response to fractionated treatments. These results suggest that laboratory estimates of intrinsic radiosensitivity and tumor clonogen number at the onset of treatment, will be of use in predicting radiocurability for fractionated treatments, as has been observed for single dose treatments
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
2015-01-01
the multivariate non-cointegrated fractional autoregressive integrated moving average (ARIMA) model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge...
Fractional order creep model for dam concrete considering degree of hydration
Huang, Yaoying; Xiao, Lei; Bao, Tengfei; Liu, Yu
2018-05-01
Concrete is a material that is an intermediate between an ideal solid and an ideal fluid. The creep of concrete is related not only to the loading age and duration, but also to its temperature and temperature history. Fractional order calculus is a powerful tool for solving physical mechanics modeling problems. Using a software element based on the generalized Kelvin model, a fractional order creep model of concrete considering the loading age and duration is established. Then, the hydration rate of cement is considered in terms of the degree of hydration, and the fractional order creep model of concrete considering the degree of hydration is established. Moreover, uniaxial tensile creep tests of dam concrete under different curing temperatures were conducted, and the results were combined with the creep test data and complex optimization method to optimize the parameters of a new creep model. The results show that the fractional tensile creep model based on hydration degree can better describe the tensile creep properties of concrete, and this model involves fewer parameters than the 8-parameter model.
Forecasting daily political opinion polls using the fractionally cointegrated VAR model
DEFF Research Database (Denmark)
Nielsen, Morten Ørregaard; Shibaev, Sergei S.
We examine forecasting performance of the recent fractionally cointegrated vector autoregressive (FCVAR) model. We use daily polling data of political support in the United Kingdom for 2010-2015 and compare with popular competing models at several forecast horizons. Our findings show that the four...... trend from the model follows the vote share of the UKIP very closely, and we thus interpret it as a measure of Euro-skepticism in public opinion rather than an indicator of the more traditional left-right political spectrum. In terms of prediction of vote shares in the election, forecasts generated...... variants of the FCVAR model considered are generally ranked as the top four models in terms of forecast accuracy, and the FCVAR model significantly outperforms both univariate fractional models and the standard cointegrated VAR (CVAR) model at all forecast horizons. The relative forecast improvement...
Energy Technology Data Exchange (ETDEWEB)
Mavroidis, Panayiotis, E-mail: mavroidis@uthscsa.edu [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Department of Medical Radiation Physics, Karolinska Institutet and Stockholm University, Stockholm (Sweden); Milickovic, Natasa [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Cruz, Wilbert F. [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Tselis, Nikolaos [Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Karabis, Andreas [Pi-Medical Ltd., Athens (Greece); Stathakis, Sotirios; Papanikolaou, Nikos [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Zamboglou, Nikolaos [Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Baltas, Dimos [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Nuclear and Particle Physics Section, Physics Department, University of Athens, Athens (Greece)
2014-01-01
Purpose: The aim of the present study was the investigation of different fractionation schemes to estimate their clinical impact. For this purpose, widely applied radiobiological models and dosimetric measures were used to associate their results with clinical findings. Methods and Materials: The dose distributions of 12 clinical high-dose-rate brachytherapy implants for prostate were evaluated in relation to different fractionation schemes. The fractionation schemes compared were: (1) 1 fraction of 20 Gy; (2) 2 fractions of 14 Gy; (3) 3 fractions of 11 Gy; and (4) 4 fractions of 9.5 Gy. The clinical effectiveness of the different fractionation schemes was estimated through the complication-free tumor control probability (P{sub +}), the biologically effective uniform dose, and the generalized equivalent uniform dose index. Results: For the different fractionation schemes, the tumor control probabilities were 98.5% in 1 × 20 Gy, 98.6% in 2 × 14 Gy, 97.5% in 3 × 11 Gy, and 97.8% in 4 × 9.5 Gy. The corresponding P{sub +} values were 88.8% in 1 × 20 Gy, 83.9% in 2 × 14 Gy, 86.0% in 3 × 11 Gy, and 82.3% in 4 × 9.5 Gy. With use of the fractionation scheme 4 × 9.5 Gy as reference, the isoeffective schemes regarding tumor control for 1, 2, and 3 fractions were 1 × 19.68 Gy, 2 × 13.75 Gy, and 3 × 11.05 Gy. The optimum fractionation schemes for 1, 2, 3, and 4 fractions were 1 × 19.16 Gy with a P{sub +} of 91.8%, 2 × 13.2 Gy with a P{sub +} of 89.6%, 3 × 10.6 Gy with a P{sub +} of 88.4%, and 4 × 9.02 Gy with a P{sub +} of 86.9%. Conclusions: Among the fractionation schemes 1 × 20 Gy, 2 × 14 Gy, 3 × 11 Gy, and 4 × 9.5 Gy, the first scheme was more effective in terms of P{sub +}. After performance of a radiobiological optimization, it was shown that a single fraction of 19.2 to 19.7 Gy (average 19.5 Gy) should produce at least the same benefit as that given by the 4 × 9.5 Gy scheme, and it should reduce the expected total complication probability by
Determination of bone mineral volume fraction using impedance analysis and Bruggeman model
Energy Technology Data Exchange (ETDEWEB)
Ciuchi, Ioana Veronica; Olariu, Cristina Stefania, E-mail: oocristina@yahoo.com; Mitoseriu, Liliana, E-mail: lmtsr@uaic.ro
2013-11-20
Highlights: • Mineral volume fraction of a bone sample was determined. • Dielectric properties for bone sample and for the collagen type I were determined by impedance spectroscopy. • Bruggeman effective medium approximation was applied in order to evaluate mineral volume fraction of the sample. • The computed values were compared with ones derived from a histogram test performed on SEM micrographs. -- Abstract: Measurements by impedance spectroscopy and Bruggeman effective medium approximation model were employed in order to determine the mineral volume fraction of dry bone. This approach assumes that two or more phases are present into the composite: the matrix (environment) and the other ones are inclusion phases. A fragment of femur diaphysis dense bone from a young pig was investigated in its dehydrated state. Measuring the dielectric properties of bone and its main components (hydroxyapatite and collagen) and using the Bruggeman approach, the mineral volume filling factor was determined. The computed volume fraction of the mineral volume fraction was confirmed by a histogram test analysis based on the SEM microstructures. In spite of its simplicity, the method provides a good approximation for the bone mineral volume fraction. The method which uses impedance spectroscopy and EMA modeling can be further developed by considering the conductive components of the bone tissue as a non-invasive in situ impedance technique for bone composition evaluation and monitoring.
Determination of bone mineral volume fraction using impedance analysis and Bruggeman model
International Nuclear Information System (INIS)
Ciuchi, Ioana Veronica; Olariu, Cristina Stefania; Mitoseriu, Liliana
2013-01-01
Highlights: • Mineral volume fraction of a bone sample was determined. • Dielectric properties for bone sample and for the collagen type I were determined by impedance spectroscopy. • Bruggeman effective medium approximation was applied in order to evaluate mineral volume fraction of the sample. • The computed values were compared with ones derived from a histogram test performed on SEM micrographs. -- Abstract: Measurements by impedance spectroscopy and Bruggeman effective medium approximation model were employed in order to determine the mineral volume fraction of dry bone. This approach assumes that two or more phases are present into the composite: the matrix (environment) and the other ones are inclusion phases. A fragment of femur diaphysis dense bone from a young pig was investigated in its dehydrated state. Measuring the dielectric properties of bone and its main components (hydroxyapatite and collagen) and using the Bruggeman approach, the mineral volume filling factor was determined. The computed volume fraction of the mineral volume fraction was confirmed by a histogram test analysis based on the SEM microstructures. In spite of its simplicity, the method provides a good approximation for the bone mineral volume fraction. The method which uses impedance spectroscopy and EMA modeling can be further developed by considering the conductive components of the bone tissue as a non-invasive in situ impedance technique for bone composition evaluation and monitoring
Fractionations of rare earth elements in plants and their conceptive model.
Ding, ShiMing; Liang, Tao; Yan, JunCai; Zhang, ZiLi; Huang, ZeChun; Xie, YaNing
2007-02-01
Fractionations of rare earth elements (REEs) and their mechanisms in soybean were studied through application of exogenous mixed REEs under hydroponic conditions. Significant enrichment of middle REEs (MREEs) and heavy REEs (HREEs) was observed in plant roots and leaves respectively, with slight fractionation between light REEs (LREEs) and HREEs in stems. Moreover, the tetrad effect was observed in these organs. Investigations into REE speciation in roots and in the xylem sap using X-ray absorption spectroscopy (XAS) and nanometer-sized TiO2 adsorption techniques, associated with other controlled experiments, demonstrated that REE fractionations should be dominated by fixation mechanism in roots caused by cell wall absorption and phosphate precipitation, and by the combined effects of fixation mechanism and transport mechanism in aboveground parts caused by solution complexation by intrinsic organic ligands. A conceptive model was established for REE fractionations in plants based on the above studies.
Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate
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Adnane Boukhouima
2017-01-01
Full Text Available We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.
Directory of Open Access Journals (Sweden)
Salman IJAZ
2018-05-01
Full Text Available In this paper, a methodology has been developed to address the issue of force fighting and to achieve precise position tracking of control surface driven by two dissimilar actuators. The nonlinear dynamics of both actuators are first approximated as fractional order models. Based on the identified models, three fractional order controllers are proposed for the whole system. Two Fractional Order PID (FOPID controllers are dedicated to improving transient response and are designed in a position feedback configuration. In order to synchronize the actuator dynamics, a third fractional order PI controller is designed, which feeds the force compensation signal in position feedback loop of both actuators. Nelder-Mead (N-M optimization technique is employed in order to optimally tune controller parameters based on the proposed performance criteria. To test the proposed controllers according to real flight condition, an external disturbance of higher amplitude that acts as airload is applied directly on the control surface. In addition, a disturbance signal function of system states is applied to check the robustness of proposed controller. Simulation results on nonlinear system model validated the performance of the proposed scheme as compared to optimal PID and high gain PID controllers. Keywords: Aerospace, Fractional order control, Model identification, Nelder-Mead optimization, Robustness
Modelling size-fractionated primary production in the Atlantic Ocean from remote sensing
Brewin, Robert J. W.; Tilstone, Gavin H.; Jackson, Thomas; Cain, Terry; Miller, Peter I.; Lange, Priscila K.; Misra, Ankita; Airs, Ruth L.
2017-11-01
Marine primary production influences the transfer of carbon dioxide between the ocean and atmosphere, and the availability of energy for the pelagic food web. Both the rate and the fate of organic carbon from primary production are dependent on phytoplankton size. A key aim of the Atlantic Meridional Transect (AMT) programme has been to quantify biological carbon cycling in the Atlantic Ocean and measurements of total primary production have been routinely made on AMT cruises, as well as additional measurements of size-fractionated primary production on some cruises. Measurements of total primary production collected on the AMT have been used to evaluate remote-sensing techniques capable of producing basin-scale estimates of primary production. Though models exist to estimate size-fractionated primary production from satellite data, these have not been well validated in the Atlantic Ocean, and have been parameterised using measurements of phytoplankton pigments rather than direct measurements of phytoplankton size structure. Here, we re-tune a remote-sensing primary production model to estimate production in three size fractions of phytoplankton (10 μm) in the Atlantic Ocean, using measurements of size-fractionated chlorophyll and size-fractionated photosynthesis-irradiance experiments conducted on AMT 22 and 23 using sequential filtration-based methods. The performance of the remote-sensing technique was evaluated using: (i) independent estimates of size-fractionated primary production collected on a number of AMT cruises using 14C on-deck incubation experiments and (ii) Monte Carlo simulations. Considering uncertainty in the satellite inputs and model parameters, we estimate an average model error of between 0.27 and 0.63 for log10-transformed size-fractionated production, with lower errors for the small size class (10 μm), and errors generally higher in oligotrophic waters. Application to satellite data in 2007 suggests the contribution of cells 2 μm to total
Compartmentalization of prostaglandins in the canine kidney
International Nuclear Information System (INIS)
Morgan-Boyd, R.L.
1986-01-01
The kidney has been shown to synthesize all of the naturally occurring major prostaglandins which may be restricted to a discrete part of the kidney where their actions are physiologically important, such as the vascular compartment and the tubular compartment. In order to examine this concept of compartmentalization, the authors conducted a series of experiments to determine whether PGl 2 , measured as 6-keto-pGF/sub 1α/, produced in the kidney is restricted to the renal vascular compartment or whether it also has access to the tubular compartment. Experiments were performed in the pentobarbital-anesthetized dog. Increasing pre-glomerular levels of 6-keto-PFG/sub 1α/ caused marked increases in both the urinary excretion and the renal venous outflow to 6-keto-PGF/sub 1α/. When 3 H-6-keto-PGF/sub 1α/ was co-infused with inulin into the renal artery, 33% of the radioactivity and 23% of the inulin was recovered on first pass. With infusion of 3 H-PGl 2 and inulin, 20% of the radioactivity and 28% of the inulin reached the urine on first pass. Radioactive PGl 2 appeared to be less filterable at the glomeruli than either 3 H-6-keto-PGF/sub 1α/ or inulin. In the final set of experiments, in which dogs were prepared for a ureteral stopped-flow study, the PGE 2 /U/P/sub In/ ratio a peak was observed proximal to the Na + plateau but distal to the Na+ nadir. In light of the results from the stopped-flow study and the intrarenal infusion studies, they conclude that PGE 2 synthesized in the kidney enters both the renal and tubular compartments. In contrast, they find that 6-keto-PGF/sub 1α/ of renal origin enters only the renal origin enters only the renal vascular compartment and not the tubular compartment
Directory of Open Access Journals (Sweden)
José Francisco Gómez Aguilar
2012-07-01
Full Text Available Using the fractional calculus approach, we present the Laplace analysis of an equivalent electrical circuit for a multilayered system, which includes distributed elements of the Cole model type. The Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. A numerical Laplace transform is used with respect to the simulation of the fractional differential equations. From the results shown in the analysis, we obtain the formula for the equivalent electrical circuit of a simple spectrum, such as that generated by a real sample of blood tissue, and the corresponding Nyquist diagrams. In addition to maintaining consistency in adjusted electrical parameters, the advantage of using fractional differential equations in the study of the impedance spectra is made clear in the analysis used to determine a compact formula for the equivalent electrical circuit, which includes the Cole model and a simple RC model as special cases.
On a business cycle model with fractional derivative under narrow-band random excitation
International Nuclear Information System (INIS)
Lin, Zifei; Li, Jiaorui; Li, Shuang
2016-01-01
This paper analyzes the dynamics of a business cycle model with fractional derivative of order α (0 < α < 1) subject to narrow-band random excitation, in which fractional derivative describes the memory property of the economic variables. Stochastic dynamical system concepts are integrated into the business cycle model for understanding the economic fluctuation. Firstly, the method of multiple scales is applied to derive the model to obtain the approximate analytical solution. Secondly, the effect of economic policy with fractional derivative on the amplitude of the economic fluctuation and the effect on stationary probability density are studied. The results show macroeconomic regulation and control can lower the stable amplitude of economic fluctuation. While in the process of equilibrium state, the amplitude is magnified. Also, the macroeconomic regulation and control improves the stability of the equilibrium state. Thirdly, how externally stochastic perturbation affects the dynamics of the economy system is investigated.
Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms.
Chen, Duan
2017-11-01
In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.
A new visco-elasto-plastic model via time-space fractional derivative
Hei, X.; Chen, W.; Pang, G.; Xiao, R.; Zhang, C.
2018-02-01
To characterize the visco-elasto-plastic behavior of metals and alloys we propose a new constitutive equation based on a time-space fractional derivative. The rheological representative of the model can be analogous to that of the Bingham-Maxwell model, while the dashpot element and sliding friction element are replaced by the corresponding fractional elements. The model is applied to describe the constant strain rate, stress relaxation and creep tests of different metals and alloys. The results suggest that the proposed simple model can describe the main characteristics of the experimental observations. More importantly, the model can also provide more accurate predictions than the classic Bingham-Maxwell model and the Bingham-Norton model.
Energy Technology Data Exchange (ETDEWEB)
Ali, Farhad, E-mail: farhadaliecomaths@yahoo.com [Department of Mathematics, City University of Science and Information Technology, Peshawar 25000 (Pakistan); Sheikh, Nadeem Ahmad [Department of Mathematics, City University of Science and Information Technology, Peshawar 25000 (Pakistan); Khan, Ilyas [Basic Engineering Sciences Department, College of Engineering Majmaah University, Majmaah 11952 (Saudi Arabia); Saqib, Muhammad [Department of Mathematics, City University of Science and Information Technology, Peshawar 25000 (Pakistan)
2017-02-01
The effects of magnetohydrodynamics on the blood flow when blood is represented as a Casson fluid, along with magnetic particles in a horizontal cylinder is studied. The flow is due to an oscillating pressure gradient. The Laplace and finite Hankel transforms are used to obtain the closed form solutions of the fractional partial differential equations. Effects of various parameters on the flow of both blood and magnetic particles are shown graphically. The analysis shows that, the model with fractional order derivatives bring a remarkable changes as compared to the ordinary model. The study highlights that applied magnetic field reduces the velocities of both the blood and magnetic particles.
International Nuclear Information System (INIS)
Ali, Farhad; Sheikh, Nadeem Ahmad; Khan, Ilyas; Saqib, Muhammad
2017-01-01
The effects of magnetohydrodynamics on the blood flow when blood is represented as a Casson fluid, along with magnetic particles in a horizontal cylinder is studied. The flow is due to an oscillating pressure gradient. The Laplace and finite Hankel transforms are used to obtain the closed form solutions of the fractional partial differential equations. Effects of various parameters on the flow of both blood and magnetic particles are shown graphically. The analysis shows that, the model with fractional order derivatives bring a remarkable changes as compared to the ordinary model. The study highlights that applied magnetic field reduces the velocities of both the blood and magnetic particles.
The role of initial values in nonstationary fractional time series models
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider the nonstationary fractional model $\\Delta^{d}X_{t}=\\varepsilon _{t}$ with $\\varepsilon_{t}$ i.i.d.$(0,\\sigma^{2})$ and $d>1/2$. We derive an analytical expression for the main term of the asymptotic bias of the maximum likelihood estimator of $d$ conditional on initial values, and we...... discuss the role of the initial values for the bias. The results are partially extended to other fractional models, and three different applications of the theoretical results are given....
A mathematical model of the nine-month pregnant woman for calculating specific absorbed fractions
International Nuclear Information System (INIS)
Watson, E.E.; Stabin, M.G.
1987-01-01
Existing models which allow calculation of internal doses from radionuclide intakes by both men and women are based on a mathematical model of Reference Man. No attempt has been made to allow for the changing geometric relationships that occur during pregnancy which would affect the doses to the mother's organs and to the fetus. As pregnancy progresses, many of the mother's abdominal organs are repositioned, and their shapes may be somewhat changed. Estimation of specific absorbed fractions requires that existing mathematical models be modified to accommodate these changes. Specific absorbed fractions for Reference Woman at three, six and nine months of pregnancy should be sufficient for estimating the doses to the pregnant woman and the fetus. This report describes a model for the pregnant woman at nine months. An enlarged uterus was incorporated into a model for Reference Woman. Several abdominal organs as well as the exterior of the trunk were modified to accommodate the new uterus. This model will allow calculation of specific absorbed fractions for the fetus from photon emitters in maternal organs. Specific absorbed fractions for the repositioned maternal organs from other organs can also be calculated. 14 refs.; 2 figs
A mathematical model of the nine-month pregnant woman for calculating specific absorbed fractions
International Nuclear Information System (INIS)
Watson, E.E.; Stabin, M.G.
1986-01-01
Existing models that allow calculation of internal doses from radionuclide intakes by both men and women are based on a mathematical model of Reference Man. No attempt has been made to allow for the changing geometric relationships that occur during pregnancy which would affect the doses to the mother's organs and to the fetus. As pregnancy progresses, many of the mother's abdominal organs are repositioned, and their shapes may be somewhat changed. Estimation of specific absorbed fractions requires that existing mathematical models be modified to accommodate these changes. Specific absorbed fractions for Reference Woman at three, six, and nine months of pregnancy should be sufficient for estimating the doses to the pregnant woman and the fetus. This report describes a model for the pregnant woman at nine months. An enlarged uterus was incorporated into a model for Reference Woman. Several abdominal organs as well as the exterior of the trunk were modified to accommodate the new uterus. This model will allow calculation of specific absorbed fractions for the fetus from photon emitters in maternal organs. Specific absorbed fractions for the repositioned maternal organs from other organs can also be calculated. 14 refs., 2 figs
Two-Part Models for Fractional Responses Defined as Ratios of Integers
Directory of Open Access Journals (Sweden)
Harald Oberhofer
2014-09-01
Full Text Available This paper discusses two alternative two-part models for fractional response variables that are defined as ratios of integers. The first two-part model assumes a Binomial distribution and known group size. It nests the one-part fractional response model proposed by Papke and Wooldridge (1996 and, thus, allows one to apply Wald, LM and/or LR tests in order to discriminate between the two models. The second model extends the first one by allowing for overdispersion in the data. We demonstrate the usefulness of the proposed two-part models for data on the 401(k pension plan participation rates used in Papke and Wooldridge (1996.
Model for the isotopic fractionation of water in the Amazon basin
International Nuclear Information System (INIS)
Dall'Olio, A.; Azevedo, C.T. de
1979-01-01
Two models on the isotopic fractionation of water are presented. In the first model. It is assumed that the only source of water vapour for the Amazon region is the Atlantic Ocean, introduced by the predominant easterly winds. The second model contains the assumption that the forest also serves as a source of water vapour contributing an equal volume of water to the regional rains as the vapour of oceanic origin. (Author) [pt
Adaptive and neuroadaptive control for nonnegative and compartmental dynamical systems
Volyanskyy, Kostyantyn Y.
Neural networks have been extensively used for adaptive system identification as well as adaptive and neuroadaptive control of highly uncertain systems. The goal of adaptive and neuroadaptive control is to achieve system performance without excessive reliance on system models. To improve robustness and the speed of adaptation of adaptive and neuroadaptive controllers several controller architectures have been proposed in the literature. In this dissertation, we develop a new neuroadaptive control architecture for nonlinear uncertain dynamical systems. The proposed framework involves a novel controller architecture with additional terms in the update laws that are constructed using a moving window of the integrated system uncertainty. These terms can be used to identify the ideal system weights of the neural network as well as effectively suppress system uncertainty. Linear and nonlinear parameterizations of the system uncertainty are considered and state and output feedback neuroadaptive controllers are developed. Furthermore, we extend the developed framework to discrete-time dynamical systems. To illustrate the efficacy of the proposed approach we apply our results to an aircraft model with wing rock dynamics, a spacecraft model with unknown moment of inertia, and an unmanned combat aerial vehicle undergoing actuator failures, and compare our results with standard neuroadaptive control methods. Nonnegative systems are essential in capturing the behavior of a wide range of dynamical systems involving dynamic states whose values are nonnegative. A sub-class of nonnegative dynamical systems are compartmental systems. These systems are derived from mass and energy balance considerations and are comprised of homogeneous interconnected microscopic subsystems or compartments which exchange variable quantities of material via intercompartmental flow laws. In this dissertation, we develop direct adaptive and neuroadaptive control framework for stabilization, disturbance
Fractional-order mathematical model of an irrigation main canal pool
Directory of Open Access Journals (Sweden)
Shlomi N. Calderon-Valdez
2015-09-01
Full Text Available In this paper a fractional order model for an irrigation main canal is proposed. It is based on the experiments developed in a laboratory prototype of a hydraulic canal and the application of a direct system identification methodology. The hydraulic processes that take place in this canal are equivalent to those that occur in real main irrigation canals and the results obtained here can therefore be easily extended to real canals. The accuracy of the proposed fractional order model is compared by deriving two other integer-order models of the canal of a complexity similar to that proposed here. The parameters of these three mathematical models have been identified by minimizing the Integral Square Error (ISE performance index existing between the models and the real-time experimental data obtained from the canal prototype. A comparison of the performances of these three models shows that the fractional-order model has the lowest error and therefore the higher accuracy. Experiments showed that our model outperformed the accuracy of the integer-order models by about 25%, which is a significant improvement as regards to capturing the canal dynamics.
An in vitro lung model to assess true shunt fraction by multiple inert gas elimination.
Directory of Open Access Journals (Sweden)
Balamurugan Varadarajan
Full Text Available The Multiple Inert Gas Elimination Technique, based on Micropore Membrane Inlet Mass Spectrometry, (MMIMS-MIGET has been designed as a rapid and direct method to assess the full range of ventilation-to-perfusion (V/Q ratios. MMIMS-MIGET distributions have not been assessed in an experimental setup with predefined V/Q-distributions. We aimed (I to construct a novel in vitro lung model (IVLM for the simulation of predefined V/Q distributions with five gas exchange compartments and (II to correlate shunt fractions derived from MMIMS-MIGET with preset reference shunt values of the IVLM. Five hollow-fiber membrane oxygenators switched in parallel within a closed extracorporeal oxygenation circuit were ventilated with sweep gas (V and perfused with human red cell suspension or saline (Q. Inert gas solution was infused into the perfusion circuit of the gas exchange assembly. Sweep gas flow (V was kept constant and reference shunt fractions (IVLM-S were established by bypassing one or more oxygenators with perfusate flow (Q. The derived shunt fractions (MM-S were determined using MIGET by MMIMS from the retention data. Shunt derived by MMIMS-MIGET correlated well with preset reference shunt fractions. The in vitro lung model is a convenient system for the setup of predefined true shunt fractions in validation of MMIMS-MIGET.
Fractional Modeling of the AC Large-Signal Frequency Response in Magnetoresistive Current Sensors
Directory of Open Access Journals (Sweden)
Sergio Iván Ravelo Arias
2013-12-01
Full Text Available Fractional calculus is considered when derivatives and integrals of non-integer order are applied over a specific function. In the electrical and electronic domain, the transfer function dependence of a fractional filter not only by the filter order n, but additionally, of the fractional order α is an example of a great number of systems where its input-output behavior could be more exactly modeled by a fractional behavior. Following this aim, the present work shows the experimental ac large-signal frequency response of a family of electrical current sensors based in different spintronic conduction mechanisms. Using an ac characterization set-up the sensor transimpedance function is obtained considering it as the relationship between sensor output voltage and input sensing current,[PLEASE CHECK FORMULA IN THE PDF]. The study has been extended to various magnetoresistance sensors based in different technologies like anisotropic magnetoresistance (AMR, giant magnetoresistance (GMR, spin-valve (GMR-SV and tunnel magnetoresistance (TMR. The resulting modeling shows two predominant behaviors, the low-pass and the inverse low-pass with fractional index different from the classical integer response. The TMR technology with internal magnetization offers the best dynamic and sensitivity properties opening the way to develop actual industrial applications.
Monbouquette, H G
1987-06-01
Intrinsic models, which take into account biomass volume fraction, must be formulated for adequate simulation of high-biomass-density fermentations with cell recycle. Through comparison of corresponding intrinsic and non-intrinsic models in dimensionless form, constraints for non-intrinsic model usage in terms of biokinetic and fermenter operating parameters can be identified a priori. Analysis of a simple product-inhibition model indicates that the non-intrinsic approach is suitable only when the attainable biomass volume fraction in the fermentation broth is less than about 0.10. Inappropriate application of a non-intrinsic model can lead to gross errors in calculated substrate and product concentrations, substrate conversion, and volumetric productivity.
Models for high cell density bioreactors must consider biomass volume fraction: cell recycle example
Energy Technology Data Exchange (ETDEWEB)
Monbouquette, H.G.
1987-06-01
Intrinsic models, which take into account biomass volume fraction, must be formulated for adequate simulation of high-biomass-density fermentations with cell recycle. Through comparison of corresponding intrinsic and non-intrinsic models in dimensionless form, constraints for non-intrinsic model usage in terms of biokinetic and fermenter operating parameters can be identified a priori. Analysis of a simple product-inhibition model indicates that the non-intrinsic approach is suitable only when the attainable biomass volume fraction in the fermentation broth is less than about 0.10. Inappropriate application of a non-intrinsic model can lead to gross errors in calculated substrate and product concentrations, substrate conversion, and volumetric productivity. (Refs. 14).
Directory of Open Access Journals (Sweden)
Rafał Stanisławski
2016-01-01
Full Text Available This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples.
Fractional poisson--a simple dose-response model for human norovirus.
Messner, Michael J; Berger, Philip; Nappier, Sharon P
2014-10-01
This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures. © 2014 Society for Risk Analysis Published 2014. This article is a U.S. Government work and is in the public domain for the U.S.A.
DEFF Research Database (Denmark)
Nielsen, Kræn Vodder; Blanke, Mogens; Eriksson, Lars
2016-01-01
the behavior of the scavenge oxygen fraction well over the entire envelope of load and blower speed range that are relevant for EGR. The simplicity of the new model makes it suitable for observer and control design, which are essential steps to meet the emission requirements for marine diesel engines that take...
Wang, Xiao-Tian; Wu, Min; Zhou, Ze-Min; Jing, Wei-Shu
2012-02-01
This paper deals with the problem of discrete time option pricing using the fractional long memory stochastic volatility model with transaction costs. Through the 'anchoring and adjustment' argument in a discrete time setting, a European call option pricing formula is obtained.
Using Semiotic Resources to Build Images When Teaching the Part-Whole Model of Fractions
Mildenhall, Paula
2013-01-01
This paper reports an exploration into the use of a combination of semiotic resources when teaching the part-whole model of fractions. The study involved a single case study of one class teacher and six students in an Australian primary classroom. Using video as the predominate research tool it was possible to describe how gesture and language…
Hopf bifurcations in a fractional reaction–diffusion model for the ...
African Journals Online (AJOL)
The phenomenon of hopf bifurcation has been well-studied and applied to many physical situations to explain behaviour of solutions resulting from differential and partial differential equations. This phenomenon is applied to a fractional reaction diffusion model for tumor invasion and development. The result suggests that ...
Modelling of stable isotope fractionation by methane oxidation and diffusion in landfill cover soils
International Nuclear Information System (INIS)
Mahieu, Koenraad; De Visscher, Alex; Vanrolleghem, Peter A.; Van Cleemput, Oswald
2008-01-01
A technique to measure biological methane oxidation in landfill cover soils that is gaining increased interest is the measurement of stable isotope fractionation in the methane. Usually to quantify methane oxidation, only fractionation by oxidation is taken into account. Recently it was shown that neglecting the isotope fractionation by diffusion results in underestimation of the methane oxidation. In this study a simulation model was developed that describes gas transport and methane oxidation in landfill cover soils. The model distinguishes between 12 CH 4 , 13 CH 4 , and 12 CH 3 D explicitly, and includes isotope fractionation by diffusion and oxidation. To evaluate the model, the simulations were compared with column experiments from previous studies. The predicted concentration profiles and isotopic profiles match the measured ones very well, with a root mean square deviation (RMSD) of 1.7 vol% in the concentration and a RMSD of 0.8 per mille in the δ 13 C value, with δ 13 C the relative 13 C abundance as compared to an international standard. Overall, the comparison shows that a model-based isotope approach for the determination of methane oxidation efficiencies is feasible and superior to existing isotope methods
Sharp, Emily; Shih Dennis, Minyi
2017-01-01
This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…
Fractional dosing of yellow fever vaccine to extend supply: a modelling study.
Wu, Joseph T; Peak, Corey M; Leung, Gabriel M; Lipsitch, Marc
2016-12-10
The ongoing yellow fever epidemic in Angola strains the global vaccine supply, prompting WHO to adopt dose sparing for its vaccination campaign in Kinshasa, Democratic Republic of the Congo, in July-August, 2016. Although a 5-fold fractional-dose vaccine is similar to standard-dose vaccine in safety and immunogenicity, efficacy is untested. There is an urgent need to ensure the robustness of fractional-dose vaccination by elucidation of the conditions under which dose fractionation would reduce transmission. We estimate the effective reproductive number for yellow fever in Angola using disease natural history and case report data. With simple mathematical models of yellow fever transmission, we calculate the infection attack rate (the proportion of population infected over the course of an epidemic) with various levels of transmissibility and 5-fold fractional-dose vaccine efficacy for two vaccination scenarios, ie, random vaccination in a hypothetical population that is completely susceptible, and the Kinshasa vaccination campaign in July-August, 2016, with different age cutoff for fractional-dose vaccines. We estimate the effective reproductive number early in the Angola outbreak was between 5·2 and 7·1. If vaccine action is all-or-nothing (ie, a proportion of vaccine recipients receive complete protection [VE] and the remainder receive no protection), n-fold fractionation can greatly reduce infection attack rate as long as VE exceeds 1/n. This benefit threshold becomes more stringent if vaccine action is leaky (ie, the susceptibility of each vaccine recipient is reduced by a factor that is equal to the vaccine efficacy). The age cutoff for fractional-dose vaccines chosen by WHO for the Kinshasa vaccination campaign (2 years) provides the largest reduction in infection attack rate if the efficacy of 5-fold fractional-dose vaccines exceeds 20%. Dose fractionation is an effective strategy for reduction of the infection attack rate that would be robust with a
Fractional Dosing of Yellow Fever Vaccine to Extend Supply: A Modeling Study
Peak, Corey M.; Leung, Gabriel M.
2016-01-01
Background The ongoing yellow fever (YF) epidemic in Angola strains the global vaccine supply, prompting WHO to adopt dose sparing for its vaccination campaign in Kinshasa in July–August 2016. Although a 5-fold fractional-dose vaccine is similar to standard-dose vaccine in safety and immunogenicity, efficacy is untested. There is an urgent need to ensure the robustness of fractional-dose vaccination by elucidating the conditions under which dose fractionation would reduce transmission. Methods We estimate the effective reproductive number for YF in Angola using disease natural history and case report data. With simple mathematical models of YF transmission, we calculate the infection attack rate (IAR, the proportion of population infected over the course of an epidemic) under varying levels of transmissibility and five-fold fractional-dose vaccine efficacy for two vaccination scenarios: (i) random vaccination in a hypothetical population that is completely susceptible; (ii) the Kinshasa vaccination campaign in July–August 2016 with different age cutoff for fractional-dose vaccines. Findings We estimate the effective reproductive number early in the Angola outbreak was between 5·2 and 7·1. If vaccine action is all-or-nothing (i.e. a proportion VE of vaccinees receives complete and the remainder receive no protection), n-fold fractionation can dramatically reduce IAR as long as efficacy VE exceeds 1/n. This benefit threshold becomes more stringent if vaccine action is leaky (i.e. the susceptibility of each vaccinee is reduced by a factor that is equal to the vaccine efficacy VE). The age cutoff for fractional-dose vaccines chosen by the WHO for the Kinshasa vaccination campaign (namely, 2 years) provides the largest reduction in IAR if the efficacy of five-fold fractional-dose vaccines exceeds 20%. Interpretation Dose fractionation is a very effective strategy for reducing infection attack rate that would be robust with a large margin for error in case
Directory of Open Access Journals (Sweden)
Petráš Ivo
2011-01-01
Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.
Computing diffuse fraction of global horizontal solar radiation: A model comparison.
Dervishi, Sokol; Mahdavi, Ardeshir
2012-06-01
For simulation-based prediction of buildings' energy use or expected gains from building-integrated solar energy systems, information on both direct and diffuse component of solar radiation is necessary. Available measured data are, however, typically restricted to global horizontal irradiance. There have been thus many efforts in the past to develop algorithms for the derivation of the diffuse fraction of solar irradiance. In this context, the present paper compares eight models for estimating diffuse fraction of irradiance based on a database of measured irradiance from Vienna, Austria. These models generally involve mathematical formulations with multiple coefficients whose values are typically valid for a specific location. Subsequent to a first comparison of these eight models, three better performing models were selected for a more detailed analysis. Thereby, the coefficients of the models were modified to account for Vienna data. The results suggest that some models can provide relatively reliable estimations of the diffuse fractions of the global irradiance. The calibration procedure could only slightly improve the models' performance.
Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators
Koca, Ilknur
2018-03-01
The model of Ebola spread within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced by Atangana and Baleanu. It is expected that the proposed model will show better approximation than the models established before. The existence and uniqueness of solutions for the spread of Ebola disease model is given via the Picard-Lindelof method. Finally, numerical solutions for the model are given by using different parameter values.
Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.
2011-01-01
We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095
Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process
Directory of Open Access Journals (Sweden)
Hidetoshi Konno
2018-01-01
Full Text Available In neural spike counting experiments, it is known that there are two main features: (i the counting number has a fractional power-law growth with time and (ii the waiting time (i.e., the inter-spike-interval distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii can be modeled by the method of SSPPs. Namely, the first one (i associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP.
Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process
Konno, Hidetoshi; Tamura, Yoshiyasu
2018-01-01
In neural spike counting experiments, it is known that there are two main features: (i) the counting number has a fractional power-law growth with time and (ii) the waiting time (i.e., the inter-spike-interval) distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs) is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii) can be modeled by the method of SSPPs. Namely, the first one (i) associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP).
Eluru, Naveen; Chakour, Vincent; Chamberlain, Morgan; Miranda-Moreno, Luis F
2013-10-01
Vehicle operating speed measured on roadways is a critical component for a host of analysis in the transportation field including transportation safety, traffic flow modeling, roadway geometric design, vehicle emissions modeling, and road user route decisions. The current research effort contributes to the literature on examining vehicle speed on urban roads methodologically and substantively. In terms of methodology, we formulate a new econometric model framework for examining speed profiles. The proposed model is an ordered response formulation of a fractional split model. The ordered nature of the speed variable allows us to propose an ordered variant of the fractional split model in the literature. The proposed formulation allows us to model the proportion of vehicles traveling in each speed interval for the entire segment of roadway. We extend the model to allow the influence of exogenous variables to vary across the population. Further, we develop a panel mixed version of the fractional split model to account for the influence of site-specific unobserved effects. The paper contributes substantively by estimating the proposed model using a unique dataset from Montreal consisting of weekly speed data (collected in hourly intervals) for about 50 local roads and 70 arterial roads. We estimate separate models for local roads and arterial roads. The model estimation exercise considers a whole host of variables including geometric design attributes, roadway attributes, traffic characteristics and environmental factors. The model results highlight the role of various street characteristics including number of lanes, presence of parking, presence of sidewalks, vertical grade, and bicycle route on vehicle speed proportions. The results also highlight the presence of site-specific unobserved effects influencing the speed distribution. The parameters from the modeling exercise are validated using a hold-out sample not considered for model estimation. The results indicate
Gao, Feng-Yin; Kang, Yan-Mei; Chen, Xi; Chen, Guanrong
2018-05-01
This paper reveals the effect of fractional Gaussian noise with Hurst exponent H ∈(1 /2 ,1 ) on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise. In the paper, for the subthreshold binary signal, sufficient conditions are given based on the "forbidden interval" theorem to guarantee the occurrence of stochastic resonance, while for the suprathreshold binary signal, the simulated results show that additive fGn with Hurst exponent H ∈(1 /2 ,1 ) could increase the mutual information or bits count. The investigation indicated that the synaptic noise with the characters of long-range dependence and self-similarity might be the driving factor for the efficient encoding and decoding of the nervous system.
International Nuclear Information System (INIS)
Reis, Arlene A. dos; Cardoso, Joaquim C.S.; Lourenco, Maria Cristina
2005-01-01
The Publication 66 of International Commission of Radiological Protection (ICRP, 1994) presented the Human Respiratory tract Model that simulates the deposition and translocation of radioactive material in the air that penetrates in the body by inhalation. The main objective of this study is to evaluate the variation in fractional activity absorbed into blood when physiological and morphological parameters from Brazilian population are applied in the deposition model. The clearance model was implemented in the software Excel (version 2000) using a system of differential equations to solve simultaneous process of translocation and absorption of material deposited. After implementation were applied in the model fractional deposition calculated by deposition model using physiological and morphological parameters from Brazilian population. The results show that the variation in the clearance model depends on the material dissolution. For materials of rapid absorption, the variations calculated are not significant. Materials of moderate and slow absorption, presented variation greater than 20% in fractional activity absorbed into blood, depending on levels of exercise. (author)
Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts
Rossikhin, Yury A.; Shitikova, Marina V.
2013-06-01
The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.
Long-range transport and global fractionation of POPs: insights from multimedia modeling studies
International Nuclear Information System (INIS)
Scheringer, M.; Salzmann, M.; Stroebe, M.; Wegmann, F.; Fenner, K.; Hungerbuehler, K.
2004-01-01
The long-range transport of persistent organic pollutants (POPs) is investigated with two multimedia box models of the global system. ChemRange is a purely evaluative, one-dimensional steady-state (level III) model; CliMoChem is a two-dimensional model with different temperatures, land/water ratios and vegetation types in different latitudinal zones. Model results are presented for three case studies: (i) the effect of atmospheric aerosol particles on the long-range transport of POPs, (ii) the effect of oceanic deposition on the long-range transport of different PCB congeners, (iii) the global fractionation of different PCB congeners. The model results for these case studies show: (i) the low atmospheric half-lives estimated for several organochlorine pesticides are likely to be inconsistent with the observed long-range transport of these compounds; (ii) export to the deep sea reduces the potential for long-range transport of highly hydrophobic compounds (but does not remove these chemicals from the biosphere); (iii) there are different meanings of the term global fractionation that refer to different aspects of the fractionation process and need to be distinguished. The case-study results further indicate that the influences of varying environmental conditions on the physicochemical properties and the degradation rate constants of POPs need to be determined. - Multimedia box models are applied to case studies of the behavior of POPs
Schnell, Gretja; Spudich, Serena; Harrington, Patrick; Price, Richard W.; Swanstrom, Ronald
2009-01-01
Human immunodeficiency virus type 1 (HIV-1) invades the central nervous system (CNS) shortly after systemic infection and can result in the subsequent development of HIV-1–associated dementia (HAD) in a subset of infected individuals. Genetically compartmentalized virus in the CNS is associated with HAD, suggesting autonomous viral replication as a factor in the disease process. We examined the source of compartmentalized HIV-1 in the CNS of subjects with HIV-1–associated neurological disease and in asymptomatic subjects who were initiating antiretroviral therapy. The heteroduplex tracking assay (HTA), targeting the variable regions of env, was used to determine which HIV-1 genetic variants in the cerebrospinal fluid (CSF) were compartmentalized and which variants were shared with the blood plasma. We then measured the viral decay kinetics of individual variants after the initiation of antiretroviral therapy. Compartmentalized HIV-1 variants in the CSF of asymptomatic subjects decayed rapidly after the initiation of antiretroviral therapy, with a mean half-life of 1.57 days. Rapid viral decay was also measured for CSF-compartmentalized variants in four HAD subjects (t1/2 mean = 2.27 days). However, slow viral decay was measured for CSF-compartmentalized variants from an additional four subjects with neurological disease (t1/2 range = 9.85 days to no initial decay). The slow decay detected for CSF-compartmentalized variants was not associated with poor CNS drug penetration, drug resistant virus in the CSF, or the presence of X4 virus genotypes. We found that the slow decay measured for CSF-compartmentalized variants in subjects with neurological disease was correlated with low peripheral CD4 cell count and reduced CSF pleocytosis. We propose a model in which infiltrating macrophages replace CD4+ T cells as the primary source of productive viral replication in the CNS to maintain high viral loads in the CSF in a substantial subset of subjects with HAD
Longhi, J.
1977-01-01
A description is presented of an empirical model of fractional crystallization which predicts that slightly modified versions of certain of the proposed whole moon compositions can reproduce the major-element chemistry and mineralogy of most of the primitive highland rocks through equilibrium and fractional crystallization processes combined with accumulation of crystals and trapping of residual liquids. These compositions contain sufficient Al to form a plagioclase-rich crust 60 km thick on top of a magma ocean that was initially no deeper than about 300 km. Implicit in the model are the assumptions that all cooling and crystallization take place at low pressure and that there are no compositional or thermal gradients in the liquid. Discussions of the cooling and crystallization of the proposed magma ocean show these assumptions to be disturbingly naive when applied to the ocean as a whole. However, the model need not be applied to the whole ocean, but only to layers of cooling liquid near the surface.
Frequency dependence of complex moduli of brain tissue using a fractional Zener model
International Nuclear Information System (INIS)
Kohandel, M; Sivaloganathan, S; Tenti, G; Darvish, K
2005-01-01
Brain tissue exhibits viscoelastic behaviour. If loading times are substantially short, static tests are not sufficient to determine the complete viscoelastic behaviour of the material, and dynamic test methods are more appropriate. The concept of complex modulus of elasticity is a powerful tool for characterizing the frequency domain behaviour of viscoelastic materials. On the other hand, it is well known that classical viscoelastic models can be generalized by means of fractional calculus to describe more complex viscoelastic behaviour of materials. In this paper, the fractional Zener model is investigated in order to describe the dynamic behaviour of brain tissue. The model is fitted to experimental data of oscillatory shear tests of bovine brain tissue to verify its behaviour and to obtain the material parameters
Doubly 15N-substituted diazenylium: THz laboratory spectra and fractionation models
Dore, L.; Bizzocchi, L.; Wirström, E. S.; Degli Esposti, C.; Tamassia, F.; Charnley, S. B.
2017-07-01
Context. Isotopic fractionation in dense molecular cores has been suggested as a possible origin of large 14N/15N ratio variations in solar system materials. While chemical models can explain some observed variations with different fractionation patterns for molecules with -NH or -CN functional groups, they fail to reproduce the observed ratios in diazenylium (N2H+). Aims: Observations of doubly 15N-substituted species could provide important constraints and insights for theoretical chemical models of isotopic fractionation. However, spectroscopic data are very scarce. Methods: The rotational spectra of the fully 15N-substituted isopologues of the diazenylium ion, 15N2H+ and 15N2D+, have been investigated in the laboratory well into the THz region by using a source-modulation microwave spectrometer equipped with a negative glow discharge cell. An extended chemical reaction network has been used to estimate what ranges of 15N fractionation in doubly 15N-substituted species could be expected in the interstellar medium (ISM). Results: For each isotopologue of the H- and D-containing pair, nine rotational transitions were accurately measured in the frequency region 88 GHz-1.2 THz. The analysis of the spectrum provided very precise rest frequencies at millimeter and sub-millimeter wavelengths, useful for the radioastronomical identification of the rotational lines of 15N2H+ and 15N2D+ in the ISM.
Lubrication pressure and fractional viscous damping effects on the spring-block model of earthquakes
Tanekou, G. B.; Fogang, C. F.; Kengne, R.; Pelap, F. B.
2018-04-01
We examine the dynamical behaviours of the "single mass-spring" model for earthquakes considering lubrication pressure effects on pre-existing faults and viscous fractional damping. The lubrication pressure supports a part of the load, thereby reducing the normal stress and the associated friction across the gap. During the co-seismic phase, all of the strain accumulated during the inter-seismic duration does not recover; a fraction of this strain remains as a result of viscous relaxation. Viscous damping friction makes it possible to study rocks at depth possessing visco-elastic behaviours. At increasing depths, rock deformation gradually transitions from brittle to ductile. The fractional derivative is based on the properties of rocks, including information about previous deformation events ( i.e., the so-called memory effect). Increasing the fractional derivative can extend or delay the transition from stick-slip oscillation to a stable equilibrium state and even suppress it. For the single block model, the interactions of the introduced lubrication pressure and viscous damping are found to give rise to oscillation death, which corresponds to aseismic fault behaviour. Our result shows that the earthquake occurrence increases with increases in both the damping coefficient and the lubrication pressure. We have also revealed that the accumulation of large stresses can be controlled via artificial lubrication.
The kinetics of multi-compartmentalized systems, studied by radioactive tracers
International Nuclear Information System (INIS)
Gouveia, A.S. de.
1978-01-01
The use of compartmental models to investigate kinetic problems is presented. This use is restricted, however, to linear models. As an application of different methods, the kinetic behaviour of haemaccel labelled with iodine 131 is studied, the interval of the physically viable solutions being established. The existence of a class of solutions is explained as a result of lack of knowledge of a complete data set. The possibility of obtaining a single solution is also discussed. The formalism of the program SAAM (Simulation, Analysis and modelling) now judged very important for the study of multi-compartimental analysis is presented. (I.C.R) [pt
Dipierro, Serena; Valdinoci, Enrico
2018-07-01
Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.
Cheong, Chin Wen
2008-02-01
This article investigated the influences of structural breaks on the fractionally integrated time-varying volatility model in the Malaysian stock markets which included the Kuala Lumpur composite index and four major sectoral indices. A fractionally integrated time-varying volatility model combined with sudden changes is developed to study the possibility of structural change in the empirical data sets. Our empirical results showed substantial reduction in fractional differencing parameters after the inclusion of structural change during the Asian financial and currency crises. Moreover, the fractionally integrated model with sudden change in volatility performed better in the estimation and specification evaluations.
Fernández-Manso, O.; Fernández-Manso, A.; Quintano, C.
2014-09-01
Aboveground biomass (AGB) estimation from optical satellite data is usually based on regression models of original or synthetic bands. To overcome the poor relation between AGB and spectral bands due to mixed-pixels when a medium spatial resolution sensor is considered, we propose to base the AGB estimation on fraction images from Linear Spectral Mixture Analysis (LSMA). Our study area is a managed Mediterranean pine woodland (Pinus pinaster Ait.) in central Spain. A total of 1033 circular field plots were used to estimate AGB from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) optical data. We applied Pearson correlation statistics and stepwise multiple regression to identify suitable predictors from the set of variables of original bands, fraction imagery, Normalized Difference Vegetation Index and Tasselled Cap components. Four linear models and one nonlinear model were tested. A linear combination of ASTER band 2 (red, 0.630-0.690 μm), band 8 (short wave infrared 5, 2.295-2.365 μm) and green vegetation fraction (from LSMA) was the best AGB predictor (Radj2=0.632, the root-mean-squared error of estimated AGB was 13.3 Mg ha-1 (or 37.7%), resulting from cross-validation), rather than other combinations of the above cited independent variables. Results indicated that using ASTER fraction images in regression models improves the AGB estimation in Mediterranean pine forests. The spatial distribution of the estimated AGB, based on a multiple linear regression model, may be used as baseline information for forest managers in future studies, such as quantifying the regional carbon budget, fuel accumulation or monitoring of management practices.
A New Model of the Fractional Order Dynamics of the Planetary Gears
Directory of Open Access Journals (Sweden)
Vera Nikolic-Stanojevic
2013-01-01
Full Text Available A theoretical model of planetary gears dynamics is presented. Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. In the paper, it has been indicated that even the small disturbance in design realizations of this gear cause nonlinear properties of dynamics which are the source of vibrations and noise in the gear transmission. Dynamic model of the planetary gears with four degrees of freedom is used. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. This investigation was focused to a new model of the fractional order dynamics of the planetary gear. For this model analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes are obtained. For one planetary gear, eigen fractional modes are obtained, and a visualization is presented. By using MathCAD the solution is obtained.
DEFF Research Database (Denmark)
Stegmann, Mikkel Bille; Pedersen, Dorthe
2005-01-01
in four-dimensional MRI. The theoretical foundation of our work is the generative two-dimensional Active Appearance Models by Cootes et al., here extended to bi-temporal, three-dimensional models. Further issues treated include correction of respiratory induced slice displacements, systole detection......, and a texture model pruning strategy. Cross-validation carried out on clinical-quality scans of twelve volunteers indicates that ejection fraction and cardiac blood pool volumes can be estimated automatically and rapidly with accuracy on par with typical inter-observer variability....
Epps, Brenden; Cushman-Roisin, Benoit
2017-11-01
Fluid turbulence is an outstanding unsolved problem in classical physics, despite 120+ years of sustained effort. Given this history, we assert that a new mathematical framework is needed to make a transformative breakthrough. This talk offers one such framework, based upon kinetic theory tied to the statistics of turbulent transport. Starting from the Boltzmann equation and ``Lévy α-stable distributions'', we derive a turbulence model that expresses the turbulent stresses in the form of a fractional derivative, where the fractional order is tied to the transport behavior of the flow. Initial results are presented herein, for the cases of Couette-Poiseuille flow and 2D boundary layers. Among other results, our model is able to reproduce the logarithmic Law of the Wall in shear turbulence.
On the continuing relevance of Mandelbrot's non-ergodic fractional renewal models of 1963 to 1967
Watkins, Nicholas W.
2017-12-01
The problem of "1/f" noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, "1/f" noise and LRD, concepts which are often treated as equivalent. Contribution to the "Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Structural analysis of gluten-free doughs by fractional rheological model
Orczykowska, Magdalena; Dziubiński, Marek; Owczarz, Piotr
2015-02-01
This study examines the effects of various components of tested gluten-free doughs, such as corn starch, amaranth flour, pea protein isolate, and cellulose in the form of plantain fibers on rheological properties of such doughs. The rheological properties of gluten-free doughs were assessed by using the rheological fractional standard linear solid model (FSLSM). Parameter analysis of the Maxwell-Wiechert fractional derivative rheological model allows to state that gluten-free doughs present a typical behavior of viscoelastic quasi-solid bodies. We obtained the contribution dependence of each component used in preparations of gluten-free doughs (either hard-gel or soft-gel structure). The complicate analysis of the mechanical structure of gluten-free dough was done by applying the FSLSM to explain quite precisely the effects of individual ingredients of the dough on its rheological properties.
Modelling and simulation of a dynamical system with the Atangana-Baleanu fractional derivative
Owolabi, Kolade M.
2018-01-01
In this paper, we model an ecological system consisting of a predator and two preys with the newly derived two-step fractional Adams-Bashforth method via the Atangana-Baleanu derivative in the Caputo sense. We analyze the dynamical system for correct choice of parameter values that are biologically meaningful. The local analysis of the main model is based on the application of qualitative theory for ordinary differential equations. By using the fixed point theorem idea, we establish the existence and uniqueness of the solutions. Convergence results of the new scheme are verified in both space and time. Dynamical wave phenomena of solutions are verified via some numerical results obtained for different values of the fractional index, which have some interesting ecological implications.
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, M. A.; Vivanco, M. G.
2015-07-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and Gonzalez et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, M.A.; Vivanco, M.
2015-07-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and González et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
International Nuclear Information System (INIS)
Gonzalez, M. A.; Vivanco, M. G.
2015-01-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and Gonzalez et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Integration through Compartmentalization? Pitfalls of “Poldering” in Bangladesh
Warner, J.F.
2010-01-01
The article sketches the history of the Flood Action Plan 20 (FAP-20), an experiment with polder compartmentalization, seeking to integrate flood management, drainage, and irrigation, and make it more democratic in response to the destructive 1987 and 1988 floods in Bangladesh. As a transferred
Macroanatomy of compartmentalization in fire scars of three western conifers
Kevin T. Smith; Elaine Sutherland; Estelle Arbellay; Markus Stoffel; Donald. Falk
2013-01-01
Fire scars are visible evidence of compartmentalization and closure processes that contribute to tree survival after fire injury. Preliminary observations of dissected fire scars from trees injured within the last decade showed centripetal development of wound-initiated discoloration (WID) through 2-3 decades of former sapwood in Larix occidentalis and Pseudotsuga...
Integration through compartmentalization? Pitfalls of 'poldering' in Bangladesh
Warner, J.F.
2010-01-01
The article sketches the history of the Flood Action Plan 20 (FAP-20), an experiment with polder compartmentalization, seeking to integrate flood management, drainage, and irrigation, and make it more democratic in response to the destructive 1987 and 1988 floods in Bangladesh. As a transferred
Directory of Open Access Journals (Sweden)
Ernesto Amato
2014-03-01
Full Text Available We developed a general model for the calculation of absorbed fractions in ellipsoidal volumes of soft tissue uniformly filled with alpha, beta and gamma emitting radionuclides. The approach exploited Monte Carlo simulations with the Geant4 code to determine absorbed fractions in ellipsoids characterized by a wide range of dimensions and ellipticities, for monoenergetic emissions of each radiation type. The so-obtained absorbed fractions were put in an analytical relationship with the 'generalized radius', calculated as 3V/S, where V is the ellipsoid volume and S its surface. Radiation-specific parametric functions were obtained in order to calculate the absorbed fraction of a given radiation in a generic ellipsoidal volume. The dose from a generic radionuclide can be calculated through a process of summation and integration over the whole radionuclide emission spectrum, profitably implemented in an electronic spreadsheet. We compared the results of our analytical calculation approach with those obtained from the OLINDA/EXM computer software, finding a good agreement in a wide range of sphere radii, for the high-energy pure beta emitter 90Y, the commonly employed beta-gamma emitter 131I, and the pure alpha emitter 213Po. The generality of our approach makes it useful an easy to implement in clinical dosimetry calculations as well as in radiation safety estimations when doses from internal radionuclide uptake are to be taken into account.
Wildschut, J.; Arentz, J.; Rasrendra, C. B.; Venderbosch, R. H.; Heeres, H. J.
2009-01-01
Fast pyrolysis oil can be upgraded by a catalytic hydrotreatment (250-400 degrees C, 100-200 bar) using heterogeneous catalysts such as Ru/C to hydrocarbon-like products that can serve as liquid transportation fuels. Insight into the complex reaction pathways of the various component fractions during hydrotreatment is desirable to reduce the formation of by-products such as char and gaseous components. This paper deals with the catalytic hydrotreatment of representative model components for t...
Robertson, Andy; Schipanski, Meagan; Sherrod, Lucretia; Ma, Liwang; Ahuja, Lajpat; McNamara, Niall; Smith, Pete; Davies, Christian
2016-04-01
Agriculture, covering more than 30% of global land area, has an exciting opportunity to help combat climate change by effectively managing its soil to promote increased C sequestration. Further, newly sequestered soil carbon (C) through agriculture needs to be stored in more stable forms in order to have a lasting impact on reducing atmospheric CO2 concentrations. While land uses in different climates and soils require different management strategies, the fundamental mechanisms that regulate C sequestration and stabilisation remain the same. These mechanisms are used by a number of different systems models to simulate C dynamics, and thus assess the impacts of change in management or climate. To evaluate the accuracy of these model simulations, our research uses a multidirectional approach to compare C stocks of physicochemical soil fractions collected at two long-term agricultural sites. Carbon stocks for a number of soil fractions were measured at two sites (Lincoln, UK; Colorado, USA) over 8 and 12 years, respectively. Both sites represent managed agricultural land but have notably different climates and levels of disturbance. The measured soil fractions act as proxies for varying degrees of stability, with C contained within these fractions relatable to the C simulated within the soil pools of mechanistic systems models1. Using stable isotope techniques at the UK site, specific turnover times of C within the different fractions were determined and compared with those simulated in the pools of 3 different models of varying complexity (RothC, DayCent and RZWQM2). Further, C dynamics and N-mineralisation rates of the measured fractions at the US site were assessed and compared to results of the same three models. The UK site saw a significant increase in C stocks within the most stable fractions, with topsoil (0-30cm) sequestration rates of just over 0.3 tC ha-1 yr-1 after only 8 years. Further, the sum of all fractions reported C sequestration rates of nearly 1
Fractional calculus model of articular cartilage based on experimental stress-relaxation
Smyth, P. A.; Green, I.
2015-05-01
Articular cartilage is a unique substance that protects joints from damage and wear. Many decades of research have led to detailed biphasic and triphasic models for the intricate structure and behavior of cartilage. However, the models contain many assumptions on boundary conditions, permeability, viscosity, model size, loading, etc., that complicate the description of cartilage. For impact studies or biomimetic applications, cartilage can be studied phenomenologically to reduce modeling complexity. This work reports experimental results on the stress-relaxation of equine articular cartilage in unconfined loading. The response is described by a fractional calculus viscoelastic model, which gives storage and loss moduli as functions of frequency, rendering multiple advantages: (1) the fractional calculus model is robust, meaning that fewer constants are needed to accurately capture a wide spectrum of viscoelastic behavior compared to other viscoelastic models (e.g., Prony series), (2) in the special case where the fractional derivative is 1/2, it is shown that there is a straightforward time-domain representation, (3) the eigenvalue problem is simplified in subsequent dynamic studies, and (4) cartilage stress-relaxation can be described with as few as three constants, giving an advantage for large-scale dynamic studies that account for joint motion or impact. Moreover, the resulting storage and loss moduli can quantify healthy, damaged, or cultured cartilage, as well as artificial joints. The proposed characterization is suited for high-level analysis of multiphase materials, where the separate contribution of each phase is not desired. Potential uses of this analysis include biomimetic dampers and bearings, or artificial joints where the effective stiffness and damping are fundamental parameters.
Development of a three dimensional circulation model based on fractional step method
Directory of Open Access Journals (Sweden)
Mazen Abualtayef
2010-03-01
Full Text Available A numerical model was developed for simulating a three-dimensional multilayer hydrodynamic and thermodynamic model in domains with irregular bottom topography. The model was designed for examining the interactions between flow and topography. The model was based on the three-dimensional Navier-Stokes equations and was solved using the fractional step method, which combines the finite difference method in the horizontal plane and the finite element method in the vertical plane. The numerical techniques were described and the model test and application were presented. For the model application to the northern part of Ariake Sea, the hydrodynamic and thermodynamic results were predicted. The numerically predicted amplitudes and phase angles were well consistent with the field observations.
Directory of Open Access Journals (Sweden)
J.-P. Lhomme
1999-01-01
Full Text Available In many experimental conditions, the evaporative fraction, defined as the ratio between evaporation and available energy, has been found stable during daylight hours. This constancy is investigated over fully covering vegetation by means of a land surface scheme coupled with a mixed-layer model, which accounts for entrainment of overlying air. The evaporation rate follows the Penman-Monteith equation and the surface resistance is given by a Jarvis type parameterization involving solar radiation, saturation deficit and leaf water potential. The diurnal course of the evaporative fraction is examined, together with the influence of environmental factors (soil water availability, solar radiation input, wind velocity, saturation deficit above the well-mixed layer. In conditions of fair weather, the curves representing the diurnal course of the evaporative fraction have a typical concave-up shape. Around midday (solar time these curves appear as relatively constant, but always lower that the daytime mean value. Evaporative fraction decreases when soil water decreases or when solar energy increases. An increment of saturation deficit above the mixed-layer provokes only a slight increase of evaporative fraction, and wind velocity has almost no effect. The possibility of estimation daytime evaporation from daytime available energy multiplied by the evaporative fraction at a single time of the day is also investigated. It appears that it is possible to obtain fairly good estimates of daytime evaporation by choosing adequately the time of the measurement of the evaporative fraction. The central hours of the day, and preferably about 3 hr before or after noon, are the most appropriate to provide good estimates. The estimation appears also to be much better when soil water availability (or evaporation is high than when it is low.
Energy Technology Data Exchange (ETDEWEB)
Ludden, J.N.; Thompson, G.; Bryan, W.B.; Frey, F.A.
1980-08-10
Ferrobasalts from DSDP sites 214 and 216 on the Ninetyeast Ridge are characterized by high absolute iron (FeO>12.9 wt %), FeO/MgO>1.9, and TiO/sub 2/>2.0 wt %. Their trace element abundances indicate a tholeiitic affinity; however, they are distinct from midocean ridge incompatible element-depleted tholeiites owing to higher contents of Ba, Zr, and Sr and flat to slightly light-REE-enriched, chondrite-normalized REE patterns. Calculations using major and trace element abundances and phase compositions are generally consistent with a model relating most major elements and phase compositions in site 214 and 216 ferrobasalts by fractionation of clinopyroxene and plagio-class. However, some incompatible element abundances for site 216 basalts are not consistent with the fractional crystallization models. Baslats from site 214 can be related to andesitic rocks from the same site by fractionating clinopyroxene, plagioclase and titanomagnetite. Site 254 basalts, at the southern end of the Ninetyeast Ridge, and island tholeiites in the southern Indian Ocean (Amsterdam-St. Paul or Kerguelen-Heard volcanic provinces) possibly represent the most recent activity associated with a hot spot forming the Ninetyeast Ridge. These incompatible-element-enriched tholeiites have major element compositions consistent with those expected for a parental liquid for the site 214 and 216 ferrobasalts. However, differences in the trace element contents of the basalts from the Ninetyeast Ridge sites are not consistent with simple fractional crystallization derivation but require either a complex melting model or a heterogeneous mantle source.
Fractional Generalizations of Maxwell and Kelvin-Voigt Models for Biopolymer Characterization.
Directory of Open Access Journals (Sweden)
Bertrand Jóźwiak
Full Text Available The paper proposes a fractional generalization of the Maxwell and Kelvin-Voigt rheological models for a description of dynamic behavior of biopolymer materials. It was found that the rheological models of Maxwell-type do not work in the case of modeling of viscoelastic solids, and the model which significantly better describes the nature of changes in rheological properties of such media is the modified fractional Kelvin-Voigt model with two built-in springpots (MFKVM2. The proposed model was used to describe the experimental data from the oscillatory and creep tests of 3% (w/v kuzu starch pastes, and to determine the values of their rheological parameters as a function of pasting time. These parameters provide a lot of additional information about structure and viscoelastic properties of the medium in comparison to the classical analysis of dynamic curves G' and G" and shear creep compliance J(t. It allowed for a comprehensive description of a wide range of properties of kuzu starch pastes, depending on the conditions of pasting process.
A stochastic fractional dynamics model of space-time variability of rain
Kundu, Prasun K.; Travis, James E.
2013-09-01
varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, which allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.
International Nuclear Information System (INIS)
Pors Nielsen, S.; Baerenholdt, O.; Munck, O.
1975-01-01
By application of a power function model, fractional intestinal calcium absorption was investigated with a new technique involving whole-body counting after successive oral and intravenous administration of standard doses of 47 Ca. The fractional calcium retention 7 days after the oral load of 47 Ca was also measured. Fractional calcium retention averaged 30.3% in normal subjects and 11.5% in 11 patients with intestinal malabsorption. In the same groups fractional calcium absorption averaged 46.6% and 16.4%, respectively. Fractional calcium retention and intestinal calcium absorption were significantly correlated to body surface area, and there was a well-defined relation between fractional retention and absorption of calcium. These studies demonstrate that measurements of fractional retention and fractional intestinal absorption of calcium can be combined by the use of a whole-body counter, that fractional retention and intestinal absorption are proportional to total body surface area and therefore probably also to the total bone mass, and that fractional retention and absorption are so closely interrelated that frational absorption can be estimated from fractional retention with reasonable accuracy in normal subjects. (auth.)
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.
Recoilless fractions calculated with the nearest-neighbour interaction model by Kagan and Maslow
Kemerink, G. J.; Pleiter, F.
1986-08-01
The recoilless fraction is calculated for a number of Mössbauer atoms that are natural constituents of HfC, TaC, NdSb, FeO, NiO, EuO, EuS, EuSe, EuTe, SnTe, PbTe and CsF. The calculations are based on a model developed by Kagan and Maslow for binary compounds with rocksalt structure. With the exception of SnTe and, to a lesser extent, PbTe, the results are in reasonable agreement with the available experimental data and values derived from other models.
Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data
Directory of Open Access Journals (Sweden)
Ji Hoon Ryoo
2017-08-01
Full Text Available As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet growth modeling with non-Gaussian data is somewhat limited when considering the transformed expectation of the response via a linear predictor as a functional form of explanatory variables. In this study, we introduce a fractional polynomial model (FPM that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. The results clearly show the efficiency and flexibility of the FPM for such applications.
Energy Technology Data Exchange (ETDEWEB)
Araujo, Elaine Bortoleti de
1995-07-01
The present work reflects the clinical interest for labelling diamino dithiol compounds with technetium-99m. Both chosen compounds, L,L-Ethylene dicysteine (L,L-EC) and L,L-Ethylene dicysteine diethyl esther (L,L-ECD) were obtained with relative good yield and characterized by IR and NMR. The study of labelling conditions with technetium-99m showed the influence of the type and mass of reducing agent as well as the pH on the formation of complexes with desired biological characteristics. Radiochemical purity was determined by thin layer chromatography (TLC) and high performance liquid chromatography (HPLC). Lyophilised kits of L,L-EC and L,L-ECD for labelling with {sup 99m}Tc were obtained, with stability superior to 120 days, when stored under refrigeration, enabling the kits marketing. The ideal formulation of the kits as well as the use of liquid nitrogen in the freezing process, determined the lyophilization success. Distribution biological studies of the {sup 99m}Tc complexes were performed on mice by invasive method and on bigger animals by scintigraphic evaluation. Biological distribution studies of the complex {sup 99m}Tc-L,L-EC showed fast blood clearance, with the elimination of about 90% of the administered dose after 60 minutes, almost exclusively by the urinary system. The biological distribution results were adjusted to a three compartmental distribution model, as expected for a radiopharmaceutical designed to renal dynamic studies, with tubular elimination. The complex interaction with renal tubular receptors is related with structural characteristics of the compound, more specifically with the presence and location of polar groups. In comparison with {sup 99m}Tc-L,L-EC, biological studies of the complex {sup 99m}Tc -L,L-ECD showed different distribution aspects, despite some structural similarities. The presence of ethyl groups confers to the complex neutrality and lipophilicity. It cross the intact blood brain barrier and is retained in the brain
Zhang, Hongmei; Wang, Yue; Fatemi, Mostafa; Insana, Michael F.
2017-03-01
Kelvin-Voigt fractional derivative (KVFD) model parameters have been used to describe viscoelastic properties of soft tissues. However, translating model parameters into a concise set of intrinsic mechanical properties related to tissue composition and structure remains challenging. This paper begins by exploring these relationships using a biphasic emulsion materials with known composition. Mechanical properties are measured by analyzing data from two indentation techniques—ramp-stress relaxation and load-unload hysteresis tests. Material composition is predictably correlated with viscoelastic model parameters. Model parameters estimated from the tests reveal that elastic modulus E 0 closely approximates the shear modulus for pure gelatin. Fractional-order parameter α and time constant τ vary monotonically with the volume fraction of the material’s fluid component. α characterizes medium fluidity and the rate of energy dissipation, and τ is a viscous time constant. Numerical simulations suggest that the viscous coefficient η is proportional to the energy lost during quasi-static force-displacement cycles, E A . The slope of E A versus η is determined by α and the applied indentation ramp time T r. Experimental measurements from phantom and ex vivo liver data show close agreement with theoretical predictions of the η -{{E}A} relation. The relative error is less than 20% for emulsions 22% for liver. We find that KVFD model parameters form a concise features space for biphasic medium characterization that described time-varying mechanical properties. The experimental work was carried out at the Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. Methodological development, including numerical simulation and all data analysis, were carried out at the school of Life Science and Technology, Xi’an JiaoTong University, 710049, China.
Krieter, Detlef H; Lange, Florian; Lemke, Horst-Dieter; Bonn, Florian; Wanner, Christoph
2018-04-01
Technical problems during clinical lipid apheresis interfere with fractionator performance. Therefore, a large animal model was established to characterize a new plasma fractionation membrane. Four sheep were randomized, controlled, and crossover subjected to double ofiltration lipoprotein apheresis with three specimens of FractioPES R having slightly different HDL sieving coefficients (S K ) (FPESa, 0.30, FPESb, 0.26, and FPESc, 0.22) versus a control fractionator (EVAL). S K and reduction ratios were determined for LDL, HDL, fibrinogen, IgG, and albumin. Compared to EVAL (0.42 ± 0.04 to 0.74 ± 0.08) and FPESa (0.36 ± 0.06 to 0.64 ± 0.04), S K for HDL were lower (P < 0.05) with FPESc (0.30 ± 0.04 to 0.49 ± 0.10). Fibrinogen S K were higher (P < 0.05) with EVAL (0.02 ± 0.01 to 0.40 ± 0.08) compared to FPESb (0.05 ± 0.02 to 0.26 ± 0.34) and FPESc (0.01 ± 0.01 to 0.21 ± 0.16). No further differences were determined. The animal model distinguished between minor differences in fractionation membrane permeability, demonstrating equivalent sieving of FPESa and EVAL and slightly inferior permeability of FPESb and FPESc. © 2018 International Society for Apheresis, Japanese Society for Apheresis, and Japanese Society for Dialysis Therapy.
Generalised and Fractional Langevin Equations-Implications for Energy Balance Models
Watkins, N. W.; Chapman, S. C.; Chechkin, A.; Ford, I.; Klages, R.; Stainforth, D. A.
2017-12-01
Energy Balance Models (EBMs) have a long heritage in climate science, including their use in modelling anomalies in global mean temperature. Many types of EBM have now been studied, and this presentation concerns the stochastic EBMs, which allow direct treatment of climate fluctuations and noise. Some recent stochastic EBMs (e.g. [1]) map on to Langevin's original form of his equation, with temperature anomaly replacing velocity, and other corresponding replacements being made. Considerable sophistication has now been reached in the application of multivariate stochastic Langevin modelling in many areas of climate. Our work is complementary in intent and investigates the Mori-Kubo "Generalised Langevin Equation" (GLE) which incorporates non-Markovian noise and response in a univariate framework, as a tool for modelling GMT [2]. We show how, if it is present, long memory simplifies the GLE to a fractional Langevin equation (FLE). Evidence for long range memory in global temperature, and the success of fractional Gaussian noise in its prediction [5] has already motivated investigation of a power law response model [3,4,5]. We go beyond this work to ask whether an EBM of FLE-type exists, and what its solutions would be. [l] Padilla et al, J. Climate (2011); [2] Watkins, GRL (2013); [3] Rypdal, JGR (2012); [4] Rypdal and Rypdal, J. Climate (2014); [5] Lovejoy et al, ESDD (2015).
DEFF Research Database (Denmark)
Zhou, H. W.; Yi, H. Y.; Mishnaevsky, Leon
2017-01-01
A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog-bond-shaped......A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog......-bond-shaped GFRP composites at various stress level. A negative exponent function based on structural changes is introduced to describe the damage evolution of material properties in the process of creep test. Accordingly, a new creep constitutive equation, referred to fractional derivative Maxwell model...... by the fractional derivative Maxwell model proposed in the paper are in a good agreement with the experimental data. It is shown that the new creep constitutive model proposed in the paper needs few parameters to represent various time-dependent behaviors....
Review of compartmental analysis in ecosystem science
International Nuclear Information System (INIS)
O'Neill, R.V.
1978-01-01
The compartment model has a large number of applications in ecosystem science. An attempt is made to outline the problem areas and objectives for which this type of model has particular advantages. The areas identified are an adequate model of tracer movement through an undisturbed but non-equilibrium ecosystem; an adequate model of the movement of material in greater than tracer quantity through an ecosystem near steady state; a minimal model based on limited data; a tool for extrapolating past trends; a framework for the summarization of large data sets; and a theoretical tool for exploring and comparing limited aspects of ecosystem dynamics. The review is set in an historical perspective which helps explain why these models were adopted in ecology. References are also provided to literature which documents available mathematical techniques in an ecological context
Rifte Guaritas basin compartmentation in Camaqua
International Nuclear Information System (INIS)
Preissler, A; Rolim, S; Philipp, R.
2010-01-01
The study contributes to the knowledge of the tectonic evolution of the Guaritas rift basin in Camaqua. Were used aero magnetic geophysical data for modeling the geometry and the depth of the structures and geological units. The research was supported in processing and interpretation of Aster images (EOS-Terra), which were extracted from geophysical models and digital image
Rahimi, Zaher; Sumelka, Wojciech; Yang, Xiao-Jun
2017-11-01
The application of fractional calculus in fractional models (FMs) makes them more flexible than integer models inasmuch they can conclude all of integer and non-integer operators. In other words FMs let us use more potential of mathematics to modeling physical phenomena due to the use of both integer and fractional operators to present a better modeling of problems, which makes them more flexible and powerful. In the present work, a new fractional nonlocal model has been proposed, which has a simple form and can be used in different problems due to the simple form of numerical solutions. Then the model has been used to govern equations of the motion of the Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT). Next, free vibration of the Timoshenko and Euler-Bernoulli simply-supported (S-S) beam has been investigated. The Galerkin weighted residual method has been used to solve the non-linear governing equations.
Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections
Hermanns, M.; Kimchi, I.; Knolle, J.
2018-03-01
Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples - they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li)2IrO3 iridates and RuCl3. In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.
A predictor-corrector algorithm to estimate the fractional flow in oil-water models
International Nuclear Information System (INIS)
Savioli, Gabriela B; Berdaguer, Elena M Fernandez
2008-01-01
We introduce a predictor-corrector algorithm to estimate parameters in a nonlinear hyperbolic problem. It can be used to estimate the oil-fractional flow function from the Buckley-Leverett equation. The forward model is non-linear: the sought- for parameter is a function of the solution of the equation. Traditionally, the estimation of functions requires the selection of a fitting parametric model. The algorithm that we develop does not require a predetermined parameter model. Therefore, the estimation problem is carried out over a set of parameters which are functions. The algorithm is based on the linearization of the parameter-to-output mapping. This technique is new in the field of nonlinear estimation. It has the advantage of laying aside parametric models. The algorithm is iterative and is of predictor-corrector type. We present theoretical results on the inverse problem. We use synthetic data to test the new algorithm.
Energy Technology Data Exchange (ETDEWEB)
Fiorino, Claudio, E-mail: fiorino.claudio@hsr.it [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy); Cozzarini, Cesare [Department of Radiotherapy, San Raffaele Scientific Institute, Milan (Italy); Rancati, Tiziana [Prostate Cancer Program, Fondazione Istituto di Ricovero e Cura a Carattere Scientifico Istituto Nazionale dei Tumori, Milan (Italy); Briganti, Alberto [Department of Urology, San Raffaele Scientific Institute, Milan (Italy); Cattaneo, Giovanni Mauro; Mangili, Paola [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy); Di Muzio, Nadia Gisella [Department of Radiotherapy, San Raffaele Scientific Institute, Milan (Italy); Calandrino, Riccardo [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy)
2014-12-01
Purpose: To fit urinary toxicity data of patients treated with postprostatectomy radiation therapy with the linear quadratic (LQ) model with/without introducing a time factor. Methods and Materials: Between 1993 and 2010, 1176 patients were treated with conventional fractionation (1.8 Gy per fraction, median 70.2 Gy, n=929) or hypofractionation (2.35-2.90 Gy per fraction, n=247). Data referred to 2004-2010 (when all schemes were in use, n=563; conventional fractionation: 316; hypofractionation: 247) were fitted as a logit function of biological equivalent dose (BED), according to the LQ model with/without including a time factor γ (fixing α/β = 5 Gy). The 3-year risks of severe urethral stenosis, incontinence, and hematuria were considered as endpoints. Best-fit parameters were derived, and the resulting BEDs were taken in multivariable backward logistic models, including relevant clinical variables, considering the whole population. Results: The 3-year incidences of severe stenosis, incontinence, and hematuria were, respectively, 6.6%, 4.8%, and 3.3% in the group treated in 2004-2010. The best-fitted α/β values were 0.81 Gy and 0.74 Gy for incontinence and hematuria, respectively, with the classic LQ formula. When fixing α/β = 5 Gy, best-fit values for γ were, respectively, 0.66 Gy/d and 0.85 Gy/d. Sensitivity analyses showed reasonable values for γ (0.6-1.0 Gy/d), with comparable goodness of fit for α/β values between 3.5 and 6.5 Gy. Likelihood ratio tests showed that the fits with/without including γ were equivalent. The resulting multivariable backward logistic models in the whole population included BED, pT4, and use of antihypertensives (area under the curve [AUC] = 0.72) for incontinence and BED, pT4, and year of surgery (AUC = 0.80) for hematuria. Stenosis data could not be fitted: a 4-variable model including only clinical factors (acute urinary toxicity, pT4, year of surgery, and use of antihypertensives) was suggested (AUC
International Nuclear Information System (INIS)
Fiorino, Claudio; Cozzarini, Cesare; Rancati, Tiziana; Briganti, Alberto; Cattaneo, Giovanni Mauro; Mangili, Paola; Di Muzio, Nadia Gisella; Calandrino, Riccardo
2014-01-01
Purpose: To fit urinary toxicity data of patients treated with postprostatectomy radiation therapy with the linear quadratic (LQ) model with/without introducing a time factor. Methods and Materials: Between 1993 and 2010, 1176 patients were treated with conventional fractionation (1.8 Gy per fraction, median 70.2 Gy, n=929) or hypofractionation (2.35-2.90 Gy per fraction, n=247). Data referred to 2004-2010 (when all schemes were in use, n=563; conventional fractionation: 316; hypofractionation: 247) were fitted as a logit function of biological equivalent dose (BED), according to the LQ model with/without including a time factor γ (fixing α/β = 5 Gy). The 3-year risks of severe urethral stenosis, incontinence, and hematuria were considered as endpoints. Best-fit parameters were derived, and the resulting BEDs were taken in multivariable backward logistic models, including relevant clinical variables, considering the whole population. Results: The 3-year incidences of severe stenosis, incontinence, and hematuria were, respectively, 6.6%, 4.8%, and 3.3% in the group treated in 2004-2010. The best-fitted α/β values were 0.81 Gy and 0.74 Gy for incontinence and hematuria, respectively, with the classic LQ formula. When fixing α/β = 5 Gy, best-fit values for γ were, respectively, 0.66 Gy/d and 0.85 Gy/d. Sensitivity analyses showed reasonable values for γ (0.6-1.0 Gy/d), with comparable goodness of fit for α/β values between 3.5 and 6.5 Gy. Likelihood ratio tests showed that the fits with/without including γ were equivalent. The resulting multivariable backward logistic models in the whole population included BED, pT4, and use of antihypertensives (area under the curve [AUC] = 0.72) for incontinence and BED, pT4, and year of surgery (AUC = 0.80) for hematuria. Stenosis data could not be fitted: a 4-variable model including only clinical factors (acute urinary toxicity, pT4, year of surgery, and use of antihypertensives) was suggested (AUC
International Nuclear Information System (INIS)
Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer
2013-01-01
Purpose: Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the “five Rs” (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider “stem-like cancer cells” (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. Methods: The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. Results: In sample calculations with linear quadratic parameters α = 0.3 per Gy, α/β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. Conclusions: The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are
Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer
2013-12-01
Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the "five Rs" (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider "stem-like cancer cells" (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. In sample calculations with linear quadratic parameters α = 0.3 per Gy, α∕β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are the ones appropriate for individualized
Anticonvulsant activity of DNS II fraction in the acute seizure models.
Raza, Muhammad Liaquat; Zeeshan, Mohammad; Ahmad, Manzoor; Shaheen, Farzana; Simjee, Shabana U
2010-04-21
Delphinium nordhagenii belongs to family Ranunculaceae, it is widely found in tropical areas of Pakistan. Other species of Delphinium are reported as anticonvulsant and are traditionally used in the treatment of epilepsy. Delphinium nordhagenii is used by local healer in Pakistan but never used for scientific investigation as anticonvulsant. Thus, Delphinium nordhagenii was subjected to bioassay-guided fractionation and the most active fraction, i.e. DNS II acetone was chosen for further testing in the acute seizure models of epilepsy to study the antiepileptic potential in male mice. Different doses (60, 65 and 70mg/kg, i.p.) of DNS II acetone fraction of Delphinium nordhagenii was administered 30min prior the chemoconvulsant's injection in the male mice. Convulsive doses of chemoconvulsants (pentylenetetrazole 90mg/kg, s.c. and picrotoxin 3.15mg/kg, s.c.) were used. The mice were observed 45-90min for the presence of seizures. Moreover, four different doses of DNS II (60, 65, 70 and 100mg/kg, i.p.) were tested in the MES test. The DNS II acetone fraction of Delphinium nordhagenii has exhibited the anticonvulsant actions by preventing the seizures against PTZ- and picrotoxin-induced seizure as well as 100% seizure protection in MES test. The results are comparable with standard AEDs (diazepam 7.5mg/kg, i.p. and phenytoin 20mg/kg, i.p.). These findings suggest that the Delphinium nordhagenii possesses the anticonvulsant activity. Further analysis is needed to confirm the structure and target the extended activity profile. Copyright 2010 Elsevier Ireland Ltd. All rights reserved.
Interreligious dialogue: Moving between compartmentalization and complexity
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Anne Hege Grung
2011-05-01
Full Text Available Interreligious dialogues as organized activities establish religious difference among its participants as a premise. This article discusses how various ways of signifying religious difference in interreligious dialogues can impact culturally by looking at the dynamics between the dialogues’ ‘insides’ and ‘outsides’, especially regarding the ways in which differences are conceptualized. The current criticism of interreligious dialogue and the current perspectives on the dialogues’ alleged effects on conceptualizing differences are examined in the examples presented in this article. Finally, two models of interreligious dialogue are suggested. First, a model where religious differences are apprehended as ‘constitutive’, and second, a model where religious differences are viewed as ‘challenge’. The first relates to a multicultural view of differences, and the second to a perspective of cultural complexity. Lastly, the two models are discussed in relation to the notion of strategic essentialism. Anne Hege Grung is a researcher at the Faculty of Theology, University of Oslo.
International Nuclear Information System (INIS)
Pitkaenen, Maunu.
1986-04-01
X-ray induced changes in rat and human bone and bone marrow vasculature and in rat brain vasculature were measured as a function of time after irradiation and absorbed dose. The absorbed dose in the organ varied from 5 to 25 Gy for single dose irradiations and from 19 to 58 Gy for fractionated irradiations.The number of fractions varied from 3 to 10 for the rats and from 12 to 25 for the human. Blood flow changes were measured using an ''1''2''5I antipyrine or ''8''6RbCl extraction technique. The red blood cell (RBC) volume was examined by ''5''1Cr labelled red cells. Different fractionation models have been compared. Radiation induced reduction of bone and bone marrow blood flow were both time and dose dependent. Reduced blood flow 3 months after irradiation would seem to be an important factor in the subsequent atrophy of bones. With a single dose of 10 Gy the bone marrow blood flow returned to the control level by 7 months after irradiation. In the irradiated bone the RBC volume was about same as that in the control side but in bone marrow the reduction was from 32 to 59%. The dose levels predicted by the nominal standard dose (NSD) formula produced about the same damage to the rat femur seven months after irradiation when the extraction of ''8''6Rb chloride and the dry weight were concerned as the end points. However, the results suggest that the NSB formula underestimates the late radiation damage in bone marrow when a small number of large fractions are used. In the irradiated brains of the rats the blood flow was on average 20.4% higher compared to that in the control group. There was no significant difference in brain blood flow between different fractionation schemes. The value of 0.42 for the exponent of N corresponds to the average value for central nervous system tolerance in the literature. The model used may be sufficiently accurate for clinical work provided the treatment schemes used do not depart too radically from standard practice
Intracellular compartmentalization of skeletal muscle glycogen metabolism and insulin signalling
DEFF Research Database (Denmark)
Prats Gavalda, Clara; Gomez-Cabello, Alba; Vigelsø Hansen, Andreas
2011-01-01
The interest in skeletal muscle metabolism and insulin signalling has increased exponentially in recent years as a consequence of their role in the development of type 2 diabetes mellitus. Despite this, the exact mechanisms involved in the regulation of skeletal muscle glycogen metabolism...... and insulin signalling transduction remain elusive. We believe that one of the reasons is that the role of intracellular compartmentalization as a regulator of metabolic pathways and signalling transduction has been rather ignored. This paper briefly reviews the literature to discuss the role of intracellular...... compartmentalization in the regulation of skeletal muscle glycogen metabolism and insulin signalling. As a result, a hypothetical regulatory mechanism is proposed by which cells could direct glycogen resynthesis towards different pools of glycogen particles depending on the metabolic needs. Furthermore, we discuss...
Financial analysis of technology acquisition using fractionated lasers as a model.
Jutkowitz, Eric; Carniol, Paul J; Carniol, Alan R
2010-08-01
Ablative fractional lasers are among the most advanced and costly devices on the market. Yet, there is a dearth of published literature on the cost and potential return on investment (ROI) of such devices. The objective of this study was to provide a methodological framework for physicians to evaluate ROI. To facilitate this analysis, we conducted a case study on the potential ROI of eight ablative fractional lasers. In the base case analysis, a 5-year lease and a 3-year lease were assumed as the purchase option with a $0 down payment and 3-month payment deferral. In addition to lease payments, service contracts, labor cost, and disposables were included in the total cost estimate. Revenue was estimated as price per procedure multiplied by total number of procedures in a year. Sensitivity analyses were performed to account for variability in model assumptions. Based on the assumptions of the model, all lasers had higher ROI under the 5-year lease agreement compared with that for the 3-year lease agreement. When comparing results between lasers, those with lower operating and purchase cost delivered a higher ROI. Sensitivity analysis indicates the model is most sensitive to purchase method. If physicians opt to purchase the device rather than lease, they can significantly enhance ROI. ROI analysis is an important tool for physicians who are considering making an expensive device acquisition. However, physicians should not rely solely on ROI and must also consider the clinical benefits of a laser. (c) Thieme Medical Publishers.
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Ana Paula Delowski Ciniello
Full Text Available Abstract The present paper aims at presenting a methodology for characterizing viscoelastic materials in time domain, taking into account the fractional Zener constitutive model and the influence of temperature through Williams, Landel, and Ferry’s model. To that effect, a set of points obtained experimentally through uniaxial tensile tests with different constant strain rates is considered. The approach is based on the minimization of the quadratic relative distance between the experimental stress-strain curves and the corresponding ones given by the theoretical model. In order to avoid the local minima in the process of optimization, a hybrid technique based on genetic algorithms and non-linear programming techniques is used. The methodology is applied in the characterization of two different commercial viscoelastic materials. The results indicate that the proposed methodology is effective in identifying thermorheologically simple viscoelastic materials.
Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport
Gherardi, Marco; Calabrese, Ludovico; Tamm, Mikhail; Cosentino Lagomarsino, Marco
2017-10-01
The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E. coli. This analysis yields the characteristic time scales for intermittency. Finally, we discuss the possible shortcomings of this model, and show that an increase in the effective local noise felt by the chromosome associates to the active relocations.
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Luciano Mescia
2017-11-01
Full Text Available Electromagnetic fields are involved in several therapeutic and diagnostic applications such as hyperthermia and electroporation. For these applications, pulsed electric fields (PEFs and transient phenomena are playing a key role for understanding the biological response due to the exposure to non-ionizing wideband pulses. To this end, the PEF propagation in the six-layered planar structure modeling the human head has been studied. The electromagnetic field and the specific absorption rate (SAR have been calculated through an accurate finite-difference time-domain (FDTD dispersive modeling based on the fractional derivative operator. The temperature rise inside the tissues due to the electromagnetic field exposure has been evaluated using both the non-thermoregulated and thermoregulated Gagge’s two-node models. Moreover, additional parametric studies have been carried out with the aim to investigate the thermal response by changing the amplitude and duration of the electric pulses.
A Numerical Simulation for a Deterministic Compartmental ...
African Journals Online (AJOL)
In this work, an earlier deterministic mathematical model of HIV/AIDS is revisited and numerical solutions obtained using Eulers numerical method. Using hypothetical values for the parameters, a program was written in VISUAL BASIC programming language to generate series for the system of difference equations from the ...
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Yunfeng Jiang
2016-07-01
Full Text Available A fractional derivative system identification approach for modeling battery dynamics is presented in this paper, where fractional derivatives are applied to approximate non-linear dynamic behavior of a battery system. The least squares-based state-variable filter (LSSVF method commonly used in the identification of continuous-time models is extended to allow the estimation of fractional derivative coefficents and parameters of the battery models by monitoring a charge/discharge demand signal and a power storage/delivery signal. In particular, the model is combined by individual fractional differential models (FDMs, where the parameters can be estimated by a least-squares algorithm. Based on experimental data, it is illustrated how the fractional derivative model can be utilized to predict the dynamics of the energy storage and delivery of a lithium iron phosphate battery (LiFePO 4 in real-time. The results indicate that a FDM can accurately capture the dynamics of the energy storage and delivery of the battery over a large operating range of the battery. It is also shown that the fractional derivative model exhibits improvements on prediction performance compared to standard integer derivative model, which in beneficial for a battery management system.
Field Testing of Compartmentalization Methods for Multifamily Construction
Energy Technology Data Exchange (ETDEWEB)
Ueno, K. [Building Science Corporation, Westford, MA (United States); Lstiburek, J. [Building Science Corporation, Westford, MA (United States)
2015-03-01
The 2012 IECC has an airtightness requirement of 3 air changes per hour at 50 Pascals test pressure for both single-family and multifamily construction in Climate Zones 3-8. Other programs (LEED, ASHRAE 189, ASHRAE 62.2) have similar or tighter compartmentalization requirements, driving the need for easier and more effective methods of compartmentalization in multifamily buildings. Builders and practitioners have found that fire-resistance rated wall assemblies are a major source of difficulty in air sealing/compartmentalization, particularly in townhouse construction. This problem is exacerbated when garages are “tucked in” to the units and living space is located over the garages. In this project, Building Science Corporation examined the taping of exterior sheathing details to improve air sealing results in townhouse and multifamily construction, when coupled with a better understanding of air leakage pathways. Current approaches are cumbersome, expensive, time consuming, and ineffective; these details were proposed as a more effective and efficient method. The effectiveness of these air sealing methods was tested with blower door testing, including “nulled” or “guarded” testing (adjacent units run at equal test pressure to null out inter-unit air leakage, or “pressure neutralization”). Pressure diagnostics were used to evaluate unit-to-unit connections and series leakage pathways (i.e., air leakage from exterior, into the fire-resistance rated wall assembly, and to the interior).
International Nuclear Information System (INIS)
Craiem, Damian; Magin, Richard L
2010-01-01
New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress–strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues. (perspective)
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Olaniyi Samuel Iyiola
2014-09-01
Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.
Craiem, Damian; Magin, Richard L
2010-01-20
New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress-strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues.
Muserere, Simon Takawira; Hoko, Zvikomborero; Nhapi, Innocent
Varying conditions are required for different species of microorganisms for the complex biological processes taking place within the activated sludge treatment system. It is against the requirement to manage this complex dynamic system that computer simulators were developed to aid in optimising activated sludge treatment processes. These computer simulators require calibration with quality data input that include wastewater fractionation among others. Thus, this research fractionated raw sewage, at Firle Sewage Treatment Works (STW), for calibration of the BioWin simulation model. Firle STW is a 3-stage activated sludge system. Wastewater characteristics of importance for activated sludge process design can be grouped into carbonaceous, nitrogenous and phosphorus compounds. Division of the substrates and compounds into their constituent fractions is called fractionation and is a valuable tool for process assessment. Fractionation can be carried out using bioassay methods or much simpler physico-chemical methods. The bioassay methods require considerable experience with experimental activated sludge systems and associated measurement techniques while the physico-chemical methods are straight forward. Plant raw wastewater fractionation was carried out through two 14-day campaign periods, the first being from 3 to 16 July 2013 and the second was from 1 to 14 October 2013. According to the Zimbabwean Environmental Management Act, and based on the sensitivity of its catchment, Firle STW effluent discharge regulatory standards in mg/L are COD (<60), TN (<10), ammonia (<0.2), and TP (<1). On the other hand Firle STW Unit 4 effluent quality results based on City of Harare records in mg/L during the period of study were COD (90 ± 35), TN (9.0 ± 3.0), ammonia (0.2 ± 0.4) and TP (3.0 ± 1.0). The raw sewage parameter concentrations measured during the study in mg/L and fractions for raw sewage respectively were as follows total COD (680 ± 37), slowly biodegradable COD
In vivo kinematics of a robot-assisted uni- and multi-compartmental knee arthroplasty.
Watanabe, Toshifumi; Abbasi, Ali Z; Conditt, Michael A; Christopher, Jennifer; Kreuzer, Stefan; Otto, Jason K; Banks, Scott A
2014-07-01
There is great interest in providing reliable and durable treatments for one- and two-compartment arthritic degeneration of the cruciate-ligament intact knee. One approach is to resurface only the diseased compartments with discrete unicompartmental components, retaining the undamaged compartment(s). However, placing multiple small implants into the knee presents a greater surgical challenge than total knee arthroplasty, so it is not certain that the natural knee mechanics can be maintained or restored. The goal of this study was to determine whether near-normal knee kinematics can be obtained with a robot-assisted multi-compartmental knee arthroplasty. Thirteen patients with 15 multi-compartmental knee arthroplasties using haptic robotic-assisted bone preparation were involved in this study. Nine subjects received a medial unicompartmental knee arthroplasty (UKA), three subjects received a medial UKA and patellofemoral (PF) arthroplasty, and three subjects received medial and lateral bi-unicondylar arthroplasty. Knee motions were recorded using video-fluoroscopy an average of 13 months (6-29 months) after surgery during stair and kneeling activities. The three-dimensional position and orientation of the implant components were determined using model-image registration techniques. Knee kinematics during maximum flexion kneeling showed femoral external rotation and posterior lateral condylar translation. All knees showed femoral external rotation and posterior condylar translation with flexion during the step activity. Knees with medial UKA and PF arthroplasty showed the most femoral external rotation and posterior translation, and knees with bicondylar UKA showed the least. Knees with accurately placed uni- or bi-compartmental arthroplasty exhibited stable knee kinematics consistent with intact and functioning cruciate ligaments. The patterns of tibiofemoral motion were more similar to natural knees than commonly has been observed in knees with total knee
Modelling the fine and coarse fraction of heavy metals in Spain
García Vivanco, Marta; González, M. Angeles
2014-05-01
Heavy metals, such as cadmium, lead, nickel, arsenic, copper, chrome, zinc and selenium, are present in the air due to natural and anthropogenic emissions, normally joined to particles. These metals can affect life organisms via inhalation or ingestion, causing damages in human health and ecosystems. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT (Madrid, Spain) modelling group. Vivanco et al. (2011) and González et al. (2012) showed the model performance for some metals in Spain and Europe. However, in these studies, metals were considered as fine particles. Some studies based on observed heavy metals air concentration indicate the presence of metals also in the coarse fraction, in special for Cu and Zn. For this reason, a new attempt of modelling metals considering a fine (Arsenic, Lead, Cadmium and Nickel Ambient Air Concentrations in Spain, 2011. Proceedings of the 11 th International Conference on Computational Science and Its Applications (ICCSA 11) 243-246 - González, Ma Vivanco, Marta; Palomino, Inmaculada; Garrido, Juan; Santiago, Manuel; Bessagnet, Bertrand Modelling Some Heavy Metals Air Concentration in Europe. // Water, Air & Soil Pollution;Sep2012, Vol. 223 Issue 8, p5227
Compartmental architecture and dynamics of hematopoiesis.
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David Dingli
Full Text Available BACKGROUND: Blood cell formation is maintained by the replication of hematopoietic stem cells (HSC that continuously feed downstream "compartments" where amplification and differentiation of cells occurs, giving rise to all blood lineages. Whereas HSC replicate slowly, committed cells replicate faster as they become more differentiated. METHODOLOGY/SIGNIFICANT FINDING: We propose a multi-compartment model of hematopoiesis, designed on the principle of cell flow conservation under stationary conditions. Cells lost from one compartment due to differentiation are replaced by cells from the upstream compartment. We assume that there is a constant relationship between cell input and output in each compartment and fix the single parameter of the model using data available for granulocyte maturation. We predict that approximately 31 mitotic events separate the HSC from the mature cells observed in the circulation. Besides estimating the number of compartments, our model allows us to estimate the size of each compartment, the rate of cell replication within each compartment, the mean time a given cell type contributes to hematopoiesis, the amplification rate in each compartment, as well as the mean time separating stem-cell replication and mature blood-cell formation. CONCLUSIONS: Despite its simplicity, the model agrees with the limited in vivo data available and can make testable predictions. In particular, our prediction of the average lifetime of a PIG-A mutated clone agrees closely with the experimental results available for the PIG-A gene mutation in healthy adults. The present elucidation of the compartment structure and dynamics of hematopoiesis may prove insightful in further understanding a variety of hematopoietic disorders.
M. M. Clark; T. H. Fletcher; R. R. Linn
2010-01-01
The chemical processes of gas phase combustion in wildland fires are complex and occur at length-scales that are not resolved in computational fluid dynamics (CFD) models of landscape-scale wildland fire. A new approach for modelling fire chemistry in HIGRAD/FIRETEC (a landscape-scale CFD wildfire model) applies a mixtureâ fraction model relying on thermodynamic...
Energy Technology Data Exchange (ETDEWEB)
Choi, A. S.; Flach, G. P.; Martino, C. J.; Zamecnik, J. R.; Harris, M. K.; Wilmarth, W. R.; Calloway, T. B.
2005-03-23
In order to accelerate waste treatment and disposal of Hanford tank waste by 2028, the Department of Energy (DOE) and CH2M Hill Hanford Group (CHG), Inc. are evaluating alternative technologies which will be used in conjunction with the Waste Treatment Plant (WTP) to safely pretreat and immobilize the tank waste. Several technologies (Bulk Vitrification and Steam Reforming) are currently being evaluated for immobilizing the pretreated waste. Since the WTP does not have sufficient capacity to pretreat all the waste going to supplemental treatment by the 2028 milestone, two technologies (Selective Dissolution and Fractional Crystallization) are being considered for pretreatment of salt waste. The scope of this task was to: (1) evaluate the recent Savannah River Site (SRS) Tank 41 dissolution campaign and other literature to provide a more complete understanding of selective dissolution, (2) provide an update on the progress of salt dissolution and modeling activities at SRS, (3) investigate SRS experience and outside literature sources on industrial equipment and experimental results of previous fractional crystallization processes, and (4) evaluate recent Hanford AP104 boildown experiments and modeling results and recommend enhancements to the Environmental Simulation Program (ESP) to improve its predictive capabilities. This report provides a summary of this work and suggested recommendations.
Skovbølling Haak, Christina; Illes, Monica; Paasch, Uwe; Hædersdal, Merete
2011-07-01
Ablative fractional resurfacing (AFR) represents a new treatment potential for various skin conditions and new laser devices are being introduced. It is important to gain information about the impact of laser settings on the dimensions of the created laser channels for obtaining a safe and efficient treatment outcome. The aim of this study was to establish a standard model to document the histological tissue damage profiles after AFR and to test a new laser device at diverse settings. Ex vivo abdominal pig skin was treated with a MedArt 620, prototype fractional carbon dioxide (CO(2)) laser (Medart, Hvidovre, Denmark) delivering single microbeams (MB) with a spot size of 165 μm. By using a constant pulse duration of 2 ms, intensities of 1-18 W, single and 2-4 stacked pulses, energies were delivered in a range from 2-144 mJ/MB. Histological evaluations included 3-4 high-quality histological measurements for each laser setting (n = 28). AFR created cone-shaped laser channels. Ablation depths varied from reaching the superficial dermis (2 mJ, median 41 μm) to approaching the subcutaneous fat (144 mJ, median 1,943 μm) and correlated to the applied energy levels in an approximate linear relation (r(2) = 0.84, p skin model to characterize AFR laser channels histologically.
Directory of Open Access Journals (Sweden)
Lazarević Mihailo P.
2013-01-01
Full Text Available In this paper, the applications of biologically inspired modeling and control of (biomechanical (nonredundant mechanisms are presented, as well as newly obtained results of author in mechanics which are based on using fractional calculus. First, it is proposed to use biological analog-synergy due to existence of invariant features in the execution of functional motion. Second, the model of (biomechanical system may be obtained using another biological concept called distributed positioning (DP, which is based on the inertial properties and actuation of joints of considered mechanical system. In addition, it is proposed to use other biological principles such as: principle of minimum interaction, which takes a main role in hierarchical structure of control and self-adjusting principle (introduce local positive/negative feedback on control with great amplifying, which allows efficiently realization of control based on iterative natural learning. Also, new, recently obtained results of the author in the fields of stability, electroviscoelasticity, and control theory are presented which are based on using fractional calculus (FC. [Projekat Ministarstva nauke Republike Srbije, br. 35006
Energy Technology Data Exchange (ETDEWEB)
Morais, A. P. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Salgado de Oliveira University, Marechal Deodoro Street, 217 – Centro, Niterói, Rio de Janeiro (Brazil); Pino, A. V. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Souza, M. N. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Electronics Department at Polytechnic School, Federal University of Rio de Janeiro, Centro de Tecnologia Bloco H sala 217, Ilha do Fundão, Rio de Janeiro (Brazil)
2016-08-15
This in vitro study evaluated the diagnostic performance of an alternative electric bioimpedance spectroscopy technique (BIS-STEP) detect questionable occlusal carious lesions. Six specialists carried out the visual (V), radiography (R), and combined (VR) exams of 57 sound or non-cavitated occlusal carious lesion teeth classifying the occlusal surfaces in sound surface (H), enamel caries (EC), and dentinal caries (DC). Measurements were based on the current response to a step voltage excitation (BIS-STEP). A fractional electrical model was used to predict the current response in the time domain and to estimate the model parameters: Rs and Rp (resistive parameters), and C and α (fractional parameters). Histological analysis showed caries prevalence of 33.3% being 15.8% hidden caries. Combined examination obtained the best traditional diagnostic results with specificity = 59.0%, sensitivity = 70.9%, and accuracy = 60.8%. There were statistically significant differences in bioimpedance parameters between the H and EC groups (p = 0.016) and between the H and DC groups (Rs, p = 0.006; Rp, p = 0.022, and α, p = 0.041). Using a suitable threshold for the Rs, we obtained specificity = 60.7%, sensitivity = 77.9%, accuracy = 73.2%, and 100% of detection for deep lesions. It can be concluded that BIS-STEP method could be an important tool to improve the detection and management of occlusal non-cavitated primary caries and pigmented sites.
International Nuclear Information System (INIS)
Morais, A. P.; Pino, A. V.; Souza, M. N.
2016-01-01
This in vitro study evaluated the diagnostic performance of an alternative electric bioimpedance spectroscopy technique (BIS-STEP) detect questionable occlusal carious lesions. Six specialists carried out the visual (V), radiography (R), and combined (VR) exams of 57 sound or non-cavitated occlusal carious lesion teeth classifying the occlusal surfaces in sound surface (H), enamel caries (EC), and dentinal caries (DC). Measurements were based on the current response to a step voltage excitation (BIS-STEP). A fractional electrical model was used to predict the current response in the time domain and to estimate the model parameters: Rs and Rp (resistive parameters), and C and α (fractional parameters). Histological analysis showed caries prevalence of 33.3% being 15.8% hidden caries. Combined examination obtained the best traditional diagnostic results with specificity = 59.0%, sensitivity = 70.9%, and accuracy = 60.8%. There were statistically significant differences in bioimpedance parameters between the H and EC groups (p = 0.016) and between the H and DC groups (Rs, p = 0.006; Rp, p = 0.022, and α, p = 0.041). Using a suitable threshold for the Rs, we obtained specificity = 60.7%, sensitivity = 77.9%, accuracy = 73.2%, and 100% of detection for deep lesions. It can be concluded that BIS-STEP method could be an important tool to improve the detection and management of occlusal non-cavitated primary caries and pigmented sites.
The fractional diffusion limit of a kinetic model with biochemical pathway
Perthame, Benoît; Sun, Weiran; Tang, Min
2018-06-01
Kinetic-transport equations that take into account the intracellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intracellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.
Fractional Response Models - A Replication Exercise of Papke and Wooldridge (1996
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Harald Oberhofer
2012-09-01
Full Text Available This paper replicates the estimates of a fractional response model for share data reported in the seminal paper of Leslie E. Papke and Jeffrey M. Wooldridge published in the Journal of Applied Econometrics 11(6, 1996, pp.619-632. We have been able to replicate all of the reported estimation results concerning the determinants of employee participation rates in 401(k pension plans using the standard routines provided in Stata. As an alternative, we estimate a two-part model that is capable of coping with the excessive number of boundary values equalling one in the data. The estimated marginal effects are similar to those derived in the paper. A small-scale Monte Carlo simulation exercise suggests that the RESET tests proposed by Papke and Wooldridge in their robust form are useful for detecting neglected non-linearities in small samples.
Evidence of a fractional quantum Hall nematic phase in a microscopic model
Regnault, N.; Maciejko, J.; Kivelson, S. A.; Sondhi, S. L.
2017-07-01
At small momenta, the Girvin-MacDonald-Platzman (GMP) mode in the fractional quantum Hall (FQH) effect can be identified with gapped nematic fluctuations in the isotropic FQH liquid. This correspondence would be exact as the GMP mode softens upon approach to the putative point of a quantum phase transition to a FQH nematic. Motivated by these considerations as well as by suggestive evidence of an FQH nematic in tilted field experiments, we have sought evidence of such a nematic FQHE in a microscopic model of interacting electrons in the lowest Landau level at filling factor 1/3. Using a family of anisotropic Laughlin states as trial wave functions, we find a continuous quantum phase transition between the isotropic Laughlin liquid and the FQH nematic. Results of numerical exact diagonalization also suggest that rotational symmetry is spontaneously broken, and that the phase diagram of the model contains both a nematic and a stripe phase.
Directory of Open Access Journals (Sweden)
Jagdev Singh
2017-07-01
Full Text Available In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM, to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian’s decomposition method (ADM. The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter ℏ and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.
Álvarez-Yela, Astrid Catalina; Gómez-Cano, Fabio; Zambrano, María Mercedes; Husserl, Johana; Danies, Giovanna; Restrepo, Silvia; González-Barrios, Andrés Fernando
2017-01-01
Soil microbial communities are responsible for a wide range of ecological processes and have an important economic impact in agriculture. Determining the metabolic processes performed by microbial communities is crucial for understanding and managing ecosystem properties. Metagenomic approaches allow the elucidation of the main metabolic processes that determine the performance of microbial communities under different environmental conditions and perturbations. Here we present the first compartmentalized metabolic reconstruction at a metagenomics scale of a microbial ecosystem. This systematic approach conceives a meta-organism without boundaries between individual organisms and allows the in silico evaluation of the effect of agricultural intervention on soils at a metagenomics level. To characterize the microbial ecosystems, topological properties, taxonomic and metabolic profiles, as well as a Flux Balance Analysis (FBA) were considered. Furthermore, topological and optimization algorithms were implemented to carry out the curation of the models, to ensure the continuity of the fluxes between the metabolic pathways, and to confirm the metabolite exchange between subcellular compartments. The proposed models provide specific information about ecosystems that are generally overlooked in non-compartmentalized or non-curated networks, like the influence of transport reactions in the metabolic processes, especially the important effect on mitochondrial processes, as well as provide more accurate results of the fluxes used to optimize the metabolic processes within the microbial community. PMID:28767679
Directory of Open Access Journals (Sweden)
María Camila Alvarez-Silva
Full Text Available Soil microbial communities are responsible for a wide range of ecological processes and have an important economic impact in agriculture. Determining the metabolic processes performed by microbial communities is crucial for understanding and managing ecosystem properties. Metagenomic approaches allow the elucidation of the main metabolic processes that determine the performance of microbial communities under different environmental conditions and perturbations. Here we present the first compartmentalized metabolic reconstruction at a metagenomics scale of a microbial ecosystem. This systematic approach conceives a meta-organism without boundaries between individual organisms and allows the in silico evaluation of the effect of agricultural intervention on soils at a metagenomics level. To characterize the microbial ecosystems, topological properties, taxonomic and metabolic profiles, as well as a Flux Balance Analysis (FBA were considered. Furthermore, topological and optimization algorithms were implemented to carry out the curation of the models, to ensure the continuity of the fluxes between the metabolic pathways, and to confirm the metabolite exchange between subcellular compartments. The proposed models provide specific information about ecosystems that are generally overlooked in non-compartmentalized or non-curated networks, like the influence of transport reactions in the metabolic processes, especially the important effect on mitochondrial processes, as well as provide more accurate results of the fluxes used to optimize the metabolic processes within the microbial community.
Rebouche, C J; Engel, A G
1984-01-01
The human primary carnitine deficiency syndromes are potentially fatal disorders affecting children and adults. The molecular etiologies of these syndromes have not been determined. In this investigation, we considered the hypothesis that these syndromes result from defective transport of carnitine into tissues, particularly skeletal muscle. The problem was approached by mathematical modeling, by using the technique of kinetic compartmental analysis. A tracer dose of L-[methyl-3H]carnitine wa...
Druhan, J. L.; Giannetta, M.; Sanford, R. A.
2017-12-01
, resulting in model behavior which is, in effect, a microbial redox analog to the variable observed fractionation factor resulting from a transition state theory rate law as derived by DePaolo (2011).
Numerically pricing American options under the generalized mixed fractional Brownian motion model
Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying
2016-06-01
In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.
A novel patient-specific model to compute coronary fractional flow reserve.
Kwon, Soon-Sung; Chung, Eui-Chul; Park, Jin-Seo; Kim, Gook-Tae; Kim, Jun-Woo; Kim, Keun-Hong; Shin, Eun-Seok; Shim, Eun Bo
2014-09-01
The fractional flow reserve (FFR) is a widely used clinical index to evaluate the functional severity of coronary stenosis. A computer simulation method based on patients' computed tomography (CT) data is a plausible non-invasive approach for computing the FFR. This method can provide a detailed solution for the stenosed coronary hemodynamics by coupling computational fluid dynamics (CFD) with the lumped parameter model (LPM) of the cardiovascular system. In this work, we have implemented a simple computational method to compute the FFR. As this method uses only coronary arteries for the CFD model and includes only the LPM of the coronary vascular system, it provides simpler boundary conditions for the coronary geometry and is computationally more efficient than existing approaches. To test the efficacy of this method, we simulated a three-dimensional straight vessel using CFD coupled with the LPM. The computed results were compared with those of the LPM. To validate this method in terms of clinically realistic geometry, a patient-specific model of stenosed coronary arteries was constructed from CT images, and the computed FFR was compared with clinically measured results. We evaluated the effect of a model aorta on the computed FFR and compared this with a model without the aorta. Computationally, the model without the aorta was more efficient than that with the aorta, reducing the CPU time required for computing a cardiac cycle to 43.4%. Copyright © 2014. Published by Elsevier Ltd.
Kumar, Dinesh; Rai, K N
2017-07-01
In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy. Copyright © 2017 Elsevier Ltd. All rights reserved.
Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad
2017-07-01
This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.
N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem
2015-01-01
, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate orders of a fractional viscoelastic fluids system, which exhibits chaos, are presented as well.
Mathematical modelling of the mass-spring-damper system - A fractional calculus approach
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Jesus Bernal Alvarado
2012-08-01
Full Text Available In this paper the fractional differential equation for the mass-spring-damper system in terms of the fractional time derivatives of the Caputo type is considered. In order to be consistent with the physical equation, a new parameter is introduced. This parameter characterizes the existence of fractional components in the system. A relation between the fractional order time derivative and the new parameter is found. Different particular cases are analyzed
Black holes in multi-fractional and Lorentz-violating models
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [CSIC, Instituto de Estructura de la Materia, Madrid (Spain); Rodriguez Fernandez, David [Universidad de Oviedo, Department of Physics, Oviedo (Spain); Ronco, Michele [Universita di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); INFN, Rome (Italy)
2017-05-15
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l{sub *}. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l{sub *}. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)
Modeling of radial gas fraction profiles for bubble flow in vertical pipes
Energy Technology Data Exchange (ETDEWEB)
Lucas, D.; Krepper, E.; Prasser, H.-M. [Forschungszentrum Rossendorf e.V., Institute of Safety Research, Dresden (Germany)
2001-07-01
The paper presents a method for the prediction of radial gas fraction profiles from a given bubble size distribution. The method is based on the assumption of the equilibrium of the forces acting on a bubble perpendicularly to the flow direction. Assuming a large number of bubble size classes radial distributions are calculated separately for all bubble classes. The sum of these distributions is the radial profile of the gas fraction. The results of the model are compared with experimental data for a number of gas and liquid volume flow rates. The experiments were performed at a vertical test loop (inner diameter 50 mm) in FZ-Rossendorf using a wire mesh sensor. The sensor enables the determination of void distributions in the cross section of the loop. A special evaluation procedure supplies bubble size distributions as well as local distributions of bubbles within a predefined interval of bubble sizes. There is a good agreement between experimental and calculated data. In particular the change from wall peaking to core peaking is well predicted. (authors)
Black holes in multi-fractional and Lorentz-violating models
International Nuclear Information System (INIS)
Calcagni, Gianluca; Rodriguez Fernandez, David; Ronco, Michele
2017-01-01
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l_*. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l_*. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)
Modeling of radial gas fraction profiles for bubble flow in vertical pipes
International Nuclear Information System (INIS)
Lucas, D.; Krepper, E.; Prasser, H.-M.
2001-01-01
The paper presents a method for the prediction of radial gas fraction profiles from a given bubble size distribution. The method is based on the assumption of the equilibrium of the forces acting on a bubble perpendicularly to the flow direction. Assuming a large number of bubble size classes radial distributions are calculated separately for all bubble classes. The sum of these distributions is the radial profile of the gas fraction. The results of the model are compared with experimental data for a number of gas and liquid volume flow rates. The experiments were performed at a vertical test loop (inner diameter 50 mm) in FZ-Rossendorf using a wire mesh sensor. The sensor enables the determination of void distributions in the cross section of the loop. A special evaluation procedure supplies bubble size distributions as well as local distributions of bubbles within a predefined interval of bubble sizes. There is a good agreement between experimental and calculated data. In particular the change from wall peaking to core peaking is well predicted. (authors)
Black holes in multi-fractional and Lorentz-violating models.
Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele
2017-01-01
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q -derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length [Formula: see text]. In the q -derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to [Formula: see text]. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q -derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.
An actual load forecasting methodology by interval grey modeling based on the fractional calculus.
Yang, Yang; Xue, Dingyü
2017-07-17
The operation processes for thermal power plant are measured by the real-time data, and a large number of historical interval data can be obtained from the dataset. Within defined periods of time, the interval information could provide important information for decision making and equipment maintenance. Actual load is one of the most important parameters, and the trends hidden in the historical data will show the overall operation status of the equipments. However, based on the interval grey parameter numbers, the modeling and prediction process is more complicated than the one with real numbers. In order not lose any information, the geometric coordinate features are used by the coordinates of area and middle point lines in this paper, which are proved with the same information as the original interval data. The grey prediction model for interval grey number by the fractional-order accumulation calculus is proposed. Compared with integer-order model, the proposed method could have more freedom with better performance for modeling and prediction, which can be widely used in the modeling process and prediction for the small amount interval historical industry sequence samples. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Fayssal, Iyad A; Moukalled, Fadl; Alam, Samir; Isma'eel, Hussain
2018-04-01
This paper reports on a new boundary condition formulation to model the total coronary myocardial flow and resistance characteristics of the myocardial vascular bed for any specific patient when considered for noninvasive diagnosis of ischemia. The developed boundary condition model gives an implicit representation of the downstream truncated coronary bed. Further, it is based on incorporating patient-specific physiological parameters that can be noninvasively extracted to account for blood flow demand to the myocardium at rest and hyperemic conditions. The model is coupled to a steady three-dimensional (3D) collocated pressure-based finite volume flow solver and used to characterize the "functional significance" of a patient diseased coronary artery segment without the need for predicting the hemodynamics of the entire arterial system. Predictions generated with this boundary condition provide a deep understanding of the inherent challenges behind noninvasive image-based diagnostic techniques when applied to human diseased coronary arteries. The overall numerical method and formulated boundary condition model are validated via two computational-based procedures and benchmarked with available measured data. The newly developed boundary condition is used via a designed computational methodology to (a) confirm the need for incorporating patient-specific physiological parameters when modeling the downstream coronary resistance, (b) explain the discrepancies presented in the literature between measured and computed fractional flow reserve (FFRCT), and (c) discuss the current limitations and future challenges in shifting to noninvasive assessment of ischemia.
Energy Technology Data Exchange (ETDEWEB)
Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Chen, Jinghua, E-mail: cjhdzdz@163.com [School of Sciences, Jimei University, Xiamen, Fujian, 361021 (China)
2015-07-15
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.
Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua
2015-07-01
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.
International Nuclear Information System (INIS)
Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua
2015-01-01
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series
Estimation of pharmacokinetic parameters from non-compartmental variables using Microsoft Excel.
Dansirikul, Chantaratsamon; Choi, Malcolm; Duffull, Stephen B
2005-06-01
This study was conducted to develop a method, termed 'back analysis (BA)', for converting non-compartmental variables to compartment model dependent pharmacokinetic parameters for both one- and two-compartment models. A Microsoft Excel spreadsheet was implemented with the use of Solver and visual basic functions. The performance of the BA method in estimating pharmacokinetic parameter values was evaluated by comparing the parameter values obtained to a standard modelling software program, NONMEM, using simulated data. The results show that the BA method was reasonably precise and provided low bias in estimating fixed and random effect parameters for both one- and two-compartment models. The pharmacokinetic parameters estimated from the BA method were similar to those of NONMEM estimation.
Directory of Open Access Journals (Sweden)
Fuqiang Zhao
2017-01-01
Full Text Available In the current study, a numerical technique for solving one-dimensional fractional nonsteady heat transfer model is presented. We construct the second kind Chebyshev wavelet and then derive the operational matrix of fractional-order integration. The operational matrix of fractional-order integration is utilized to reduce the original problem to a system of linear algebraic equations, and then the numerical solutions obtained by our method are compared with those obtained by CAS wavelet method. Lastly, illustrated examples are included to demonstrate the validity and applicability of the technique.
Modeling anomalous diffusion by a subordinated fractional Lévy-stable process
International Nuclear Information System (INIS)
Teuerle, Marek; Wyłomańska, Agnieszka; Sikora, Grzegorz
2013-01-01
Two phenomena that can be discovered in systems with anomalous diffusion are long-range dependence and trapping events. The first effect concerns events that are arbitrarily distant but still influence each other exceptionally strongly, which is characteristic for anomalous regimes. The second corresponds to the presence of constant values of the underlying process. Motivated by the relatively poor class of models that can cover these two phenomena, we introduce subordinated fractional Lévy-stable motion with tempered stable waiting times. We present in detail its main properties, propose a simulation scheme and give an estimation procedure for its parameters. The last part of the paper is a presentation, via the Monte Carlo approach, of the effectiveness of the estimation of the parameters. (paper)
International Nuclear Information System (INIS)
Liu Yaozong; Yu Dianlong; Zhao Honggang; Wen Jihong; Wen Xisen
2008-01-01
Wave propagation in two-dimensional phononic crystals (PCs) with viscoelasticity is investigated using a finite-difference-time-domain (FDTD) method. The viscoelasticity is evaluated using the Kelvin-Voigt model with fractional derivatives (FDs) so that both the dispersion and dissipation are considered. Numerical approximation of FDs is integrated into the FDTD scheme to simulate wave propagation in such PCs. All the constituent materials are treated as isotropic and homogeneous. The gaps are substantially displaced and widened and the attenuation is noticeably enhanced due to the dispersion and dissipation of host material and the complicated multiple scattering between scatterers. These results indicate that the viscoelasticity of the damping host has significant influence on wave propagation in PCs and should be considered
Space-fractional model for the spreading of matter in heterogeneous porous media
International Nuclear Information System (INIS)
Krepysheva, N.; Neel, M.Ch.
2005-01-01
In very heterogeneous porous media (like the soil, or an aquifer, for instance), experimental results showed that mass transport sometimes does not obey Fourier's law. Continuous Time Random Walks in the form of L y Flights provide a small scale model for super diffusive spreading of a tracer plume, dissolved in a fluid, itself enclosed in a porous medium. In an infinite medium, the corresponding behavior of the concentration of solute is known to obey a variant of Fourier's law, with a Riesz-Feller operator in place of the Laplacian. Here we show that with some modifications the result extends to semi infinite media. A numerical method allowing for the simulation of fractional derivatives is adapted to semi infinite media, with special attention to convective terms, associated to a possibly non zero global trough flow. (authors)
Space-fractional model for the spreading of matter in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Krepysheva, N. [Institut National de Recherches Agronomiques (INRA), UMRA Climat-Sol-Environnement, 84 - Avignon (France); Neel, M.Ch. [Universite d' Avignon, Faculte des Sciences, UMRA Climat-Sol-Environnement, 84 - Avignon (France)
2005-07-01
In very heterogeneous porous media (like the soil, or an aquifer, for instance), experimental results showed that mass transport sometimes does not obey Fourier's law. Continuous Time Random Walks in the form of L y Flights provide a small scale model for super diffusive spreading of a tracer plume, dissolved in a fluid, itself enclosed in a porous medium. In an infinite medium, the corresponding behavior of the concentration of solute is known to obey a variant of Fourier's law, with a Riesz-Feller operator in place of the Laplacian. Here we show that with some modifications the result extends to semi infinite media. A numerical method allowing for the simulation of fractional derivatives is adapted to semi infinite media, with special attention to convective terms, associated to a possibly non zero global trough flow. (authors)
Hypo-fractionated treatment in radiotherapy: radio-biological models Tcp and NTCP
International Nuclear Information System (INIS)
Astudillo V, A. J.; Mitsoura, E.; Paredes G, L.; Resendiz G, G.
2014-08-01
At the present time the breast cancer in Mexico has the first place of incidence of the malignant neoplasia s in the women, and represents 11.34% of all the cancer cases. On the other hand, the treatments for cancer by means of ionizing radiations have been dominated under the approaches of the medical radio-oncologists which have been based on test and error by many years. The radio-biological models, as the Tcp, NTCP and dosimetric variables, for their clinical application in the conventional radiotherapy with hypo-fractionation have as purpose predicting personalized treatment plans that they present most probability of tumor control and minor probability of late reactions, becoming this way support tools in the decisions taking for the patient treatments planning of Medical Physicists and Radio-oncologists. (Author)
The iDuo Bi-compartmental Knee Replacement: Our Early Experience.
Directory of Open Access Journals (Sweden)
Peter Jemmett
2016-12-01
Our early results suggest that the iDuo knee is a good option for those with isolated bi-compartmental disease and outcome scores are comparable with those reported for the BKA. This bi-compartmental design may bridge the gap between the uni-compartmental and total knee replacement. The choice between monolithic or modular designs remains in debate. We will continue to use this prosthesis for a carefully selected group of patients.
International Nuclear Information System (INIS)
Wennberg, Berit M.; Baumann, Pia; Gagliardi, Giovanna
2011-01-01
Background. In SBRT of lung tumours no established relationship between dose-volume parameters and the incidence of lung toxicity is found. The aim of this study is to compare the LQ model and the universal survival curve (USC) to calculate biologically equivalent doses in SBRT to see if this will improve knowledge on this relationship. Material and methods. Toxicity data on radiation pneumonitis grade 2 or more (RP2+) from 57 patients were used, 10.5% were diagnosed with RP2+. The lung DVHs were corrected for fractionation (LQ and USC) and analysed with the Lyman- Kutcher-Burman (LKB) model. In the LQ-correction α/β = 3 Gy was used and the USC parameters used were: α/β = 3 Gy, D 0 = 1.0 Gy, n = 10, α 0.206 Gy-1 and d T = 5.8 Gy. In order to understand the relative contribution of different dose levels to the calculated NTCP the concept of fractional NTCP was used. This might give an insight to the questions of whether 'high doses to small volumes' or 'low doses to large volumes' are most important for lung toxicity. Results and Discussion. NTCP analysis with the LKB-model using parameters m = 0.4, D50 = 30 Gy resulted for the volume dependence parameter (n) with LQ correction n = 0.87 and with USC correction n = 0.71. Using parameters m = 0.3, D 50 = 20 Gy n = 0.93 with LQ correction and n 0.83 with USC correction. In SBRT of lung tumours, NTCP modelling of lung toxicity comparing models (LQ,USC) for fractionation correction, shows that low dose contribute less and high dose more to the NTCP when using the USC-model. Comparing NTCP modelling of SBRT data and data from breast cancer, lung cancer and whole lung irradiation implies that the response of the lung is treatment specific. More data are however needed in order to have a more reliable modelling
Functional compartmentalization of the human superficial masseter muscle.
Directory of Open Access Journals (Sweden)
Rodrigo A Guzmán-Venegas
Full Text Available Some muscles have demonstrated a differential recruitment of their motor units in relation to their location and the nature of the motor task performed; this involves functional compartmentalization. There is little evidence that demonstrates the presence of a compartmentalization of the superficial masseter muscle during biting. The aim of this study was to describe the topographic distribution of the activity of the superficial masseter (SM muscle's motor units using high-density surface electromyography (EMGs at different bite force levels. Twenty healthy natural dentate participants (men: 4; women: 16; age 20±2 years; mass: 60±12 kg, height: 163±7 cm were selected from 316 volunteers and included in this study. Using a gnathodynamometer, bites from 20 to 100% maximum voluntary bite force (MVBF were randomly requested. Using a two-dimensional grid (four columns, six electrodes located on the dominant SM, EMGs in the anterior, middle-anterior, middle-posterior and posterior portions were simultaneously recorded. In bite ranges from 20 to 60% MVBF, the EMG activity was higher in the anterior than in the posterior portion (p-value = 0.001.The center of mass of the EMG activity was displaced towards the posterior part when bite force increased (p-value = 0.001. The topographic distribution of EMGs was more homogeneous at high levels of MVBF (p-value = 0.001. The results of this study show that the superficial masseter is organized into three functional compartments: an anterior, a middle and a posterior compartment. However, this compartmentalization is only seen at low levels of bite force (20-60% MVBF.
Directory of Open Access Journals (Sweden)
Yu Zhang
2015-10-01
Full Text Available In this article, we begin with the non-homogeneous model for the non-differentiable heat flow, which is described using the local fractional vector calculus, from the first law of thermodynamics in fractal media point view. We employ the local fractional variational iteration algorithm II to solve the fractal heat equations. The obtained results show the non-differentiable behaviors of temperature fields of fractal heat flow defined on Cantor sets.
Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics.
Teka, Wondimu W; Upadhyay, Ranjit Kumar; Mondal, Argha
2017-09-01
Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF) model. Models with fractional (non-integer) order differentiation that generalize power law dynamics can be used to describe complex temporal voltage dynamics. The main characteristic of FLIF model is that it depends on all past values of the voltage that causes long-term memory. The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing. Copyright © 2017 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Wei Wang
2013-01-01
Full Text Available The precipitation of wax/solid paraffin during production, transportation, and processing of crude oil is a serious problem. It is essential to have a reliable model to predict the wax appearance temperature and the amount of solid precipitated at different conditions. This paper presents a work to predict the solid precipitation based on solid-liquid equilibrium with regular solution-molecular thermodynamic theory and characterization of the crude oil plus fraction. Due to the differences of solubility characteristics between solid and liquid phase, the solubility parameters of liquid and solid phase are calculated by a modified model. The heat capacity change between solid and liquid phase is considered and estimated in the thermodynamic model. An activity coefficient based thermodynamic method combined with two characteristic methods to calculate wax precipitation in crude oil, especially heavy oil, has been tested with experimental data. The results show that the wax appearance temperature and the amount of weight precipitated can be predicted well with the experimental data.
A generic interference model for uplink OFDMA networks with fractional frequency reuse
Tabassum, Hina
2014-03-01
Fractional frequency reuse (FFR) has emerged as a viable solution to coordinate and mitigate cochannel interference (CCI) in orthogonal frequency-division multiple-access (OFDMA)-based wireless cellular networks. The incurred CCI in cellular networks with FFR is highly uncertain and varies as a function of various design parameters that include the user scheduling schemes, the transmit power distribution among multiple allocated subcarriers, the partitioning of the cellular region into cell-edge and cell-center zones, the allocation of spectrum within each zone, and the channel reuse factors. To this end, this paper derives a generic analytical model for uplink CCI in multicarrier OFDMA networks with FFR. The derived expressions capture several network design parameters and are applicable to any composite fading-channel models. The accuracy of the derivations is verified via Monte Carlo simulations. Moreover, their usefulness is demonstrated by obtaining closed-form expressions for the Rayleigh fading-channel model and by evaluating important network performance metrics such as ergodic capacity. Numerical results provide useful system design guidelines and highlight the trade-offs associated with the deployment of FFR schemes in OFDMA-based networks. © 2013 IEEE.
NMR signals within the generalized Langevin model for fractional Brownian motion
Lisý, Vladimír; Tóthová, Jana
2018-03-01
The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.
A generic interference model for uplink OFDMA networks with fractional frequency reuse
Tabassum, Hina; Dawy, Zaher; Alouini, Mohamed-Slim; Yilmaz, Ferkan
2014-01-01
Fractional frequency reuse (FFR) has emerged as a viable solution to coordinate and mitigate cochannel interference (CCI) in orthogonal frequency-division multiple-access (OFDMA)-based wireless cellular networks. The incurred CCI in cellular networks with FFR is highly uncertain and varies as a function of various design parameters that include the user scheduling schemes, the transmit power distribution among multiple allocated subcarriers, the partitioning of the cellular region into cell-edge and cell-center zones, the allocation of spectrum within each zone, and the channel reuse factors. To this end, this paper derives a generic analytical model for uplink CCI in multicarrier OFDMA networks with FFR. The derived expressions capture several network design parameters and are applicable to any composite fading-channel models. The accuracy of the derivations is verified via Monte Carlo simulations. Moreover, their usefulness is demonstrated by obtaining closed-form expressions for the Rayleigh fading-channel model and by evaluating important network performance metrics such as ergodic capacity. Numerical results provide useful system design guidelines and highlight the trade-offs associated with the deployment of FFR schemes in OFDMA-based networks. © 2013 IEEE.
Bentil, Sarah A; Dupaix, Rebecca B
2014-02-01
The ability of the fractional Zener constitutive model to predict the behavior of postmortem swine brain tissue was examined in this work. Understanding tissue behavior attributed to degradation is invaluable in many fields such as the forensic sciences or cases where only cadaveric tissue is available. To understand how material properties change with postmortem age, the fractional Zener model was considered as it includes parameters to describe brain stiffness and also the parameter α, which quantifies the viscoelasticity of a material. The relationship between the viscoelasticity described by α and tissue degradation was examined by fitting the model to data collected in a previous study (Bentil, 2013). This previous study subjected swine neural tissue to in vitro unconfined compression tests using four postmortem age groups (week). All samples were compressed to a strain level of 10% using two compressive rates: 1mm/min and 5mm/min. Statistical analysis was used as a tool to study the influence of the fractional Zener constants on factors such as tissue degradation and compressive rate. Application of the fractional Zener constitutive model to the experimental data showed that swine neural tissue becomes less stiff with increased postmortem age. The fractional Zener model was also able to capture the nonlinear viscoelastic features of the brain tissue at low strain rates. The results showed that the parameter α was better correlated with compressive rate than with postmortem age. © 2013 Published by Elsevier Ltd.
Maggi, F.; Riley, W. J.
2009-12-01
The composition and location of 15N atoms on N2O isotopomers and isotopologues during isotope speciation has been used to characterize soil biological N cycling and N2O surface emissions. Although there exist few experimental observations, no attempt has been made to model N2O isotopomer speciation. The mathematical treatment of biological kinetic reactions in isotopic applications normally makes use of first-order and quasi steady-state complexation assumptions without taking into account changes in enzyme concentration, reaction stoichiometry, and isotopologue and isotopomer speciation. When multiatomic isotopically-labeled reactants are used in a multi-molecurar reaction, these assumptions may fail since they always lead to a constant fractionation factor and cannot describe speciation of isotopologues and isotopomers. We have developed a mathematical framework that is capable of describing isotopologue and isotopmer speciation and fractionation under the assumption of non-steady complexation during biological kinetic reactions that overcome the limitations mentioned above. This framework was applied to a case study of non-steady (variable and inverse) isotopic effects observed during N2O production and consumption in soils. Our mathematical treatment has led to generalized kinetic equations which replicate experimental observations with high accuracy and help interpret non-steady isotopic effects and isotopologue and isotopomer speciation. The kinetic equations introduced and applied here have general validity in describing isotopic effects in any biochemical reactions by considering: changing enzyme concentrations, mass and isotope conservation, and reaction stoichiometry. The equations also describe speciation of any isotopologue and isotopomer product from any isotopologue and isotopmer reactant.
Joel W. Homan; Charles H. Luce; James P. McNamara; Nancy F. Glenn
2011-01-01
Describing the spatial variability of heterogeneous snowpacks at a watershed or mountain-front scale is important for improvements in large-scale snowmelt modelling. Snowmelt depletion curves, which relate fractional decreases in snowcovered area (SCA) against normalized decreases in snow water equivalent (SWE), are a common approach to scale-up snowmelt models....
DEFF Research Database (Denmark)
Nielsen, Joakim Refslund; Dellwik, Ebba; Hahmann, Andrea N.
2014-01-01
A method is presented for development of satellite green vegetation fraction (GVF) time series for use in the Weather Research and Forecasting (WRF) model. The GVF data is in the WRF model used to describe the temporal evolution of many land surface parameters, in addition to the evolution of veg...
Compartmentation and equilibration of abscisic acid in isolated Xanthium cells
International Nuclear Information System (INIS)
Bray, E.A.; Zeevaart, J.A.D.
1986-01-01
The compartmentation of endogenous abscisic acid (ABA), applied (+/-)-[ 3 H]ABA, and (+/-)-trans-ABA was measured in isolated mesophyll cells of the Chicago strain of Xanthium strumarium L. The release of ABA to the medium in the presence or absence of DMSO was used to determine the equilibration of ABA in the cells. It was found that a greater percentage of the (+/-)-[ 3 H]ABA and the (+/-)-trans-ABA was released into the medium than of the endogenous ABA, indicating that applied ABA did not equilibrate with the endogenous material. Therefore, in further investigations only the compartmentation of endogenous ABA was studied. Endogenous ABA was released from Xanthium cells according to the pH gradients among the various cellular compartments. Thus, darkness, high external pH, KNO 2 , and drought-stress all increased the efflux of ABA from the cells. Efflux of ABA from the cells in the presence of 0.6 M mannitol occurred within 30 seconds, but only 8% of the endogenous material was released during the 20 minute treatment
The monitoring of relative changes in compartmental compliances of brain
International Nuclear Information System (INIS)
Kim, Dong-Joo; Carrera, Emmanuel; Castellani, Gianluca; Zweifel, Christian; Smielewski, Peter; Pickard, John D; Czosnyka, Marek; Kasprowicz, Magdalena; Lavinio, Andrea; Sutcliffe, Michael P F
2009-01-01
The study aimed to develop a computational method for assessing relative changes in compartmental compliances within the brain: the arterial bed and the cerebrospinal space. The method utilizes the relationship between pulsatile components in the arterial blood volume, arterial blood pressure (ABP) and intracranial pressure (ICP). It was verified by using clinical recordings of intracranial pressure plateau waves, when massive vasodilatation accompanying plateau waves produces changes in brain compliances of the arterial bed (C a ) and compliance of the cerebrospinal space (C i ). Ten patients admitted after head injury with a median Glasgow Coma Score of 6 were studied retrospectively. ABP was directly monitored from the radial artery. Changes in the cerebral arterial blood volume were assessed using Transcranial Doppler (TCD) ultrasonography by digital integration of inflow blood velocity. During plateau waves, ICP increased (P = 0.001), CPP decreased (P = 0.001), ABP remained constant (P = 0.532), blood flow velocity decreased (P = 0.001). Calculated compliance of the arterial bed C a increased significantly (P = 0.001); compliance of the CSF space C i decreased (P = 0.001). We concluded that the method allows for continuous monitoring of relative changes in brain compartmental compliances. Plateau waves affect the balance between vascular and CSF compartments, which is reflected by the inverse change of compliance of the cerebral arterial bed and global compliance of the CSF space
DEFF Research Database (Denmark)
Manfredi, Simone; Tonini, Davide; Christensen, Thomas Højlund
2011-01-01
and environmental factors involved, including energy generation from landfill gas and storage of biogenic carbon. Leachate and gas emissions associated to each individual waste fraction have been estimated by means of a mathematical modelling. This approach towards landfilling emissions allows for a more precise...... quantification of the landfill impacts when comparing management options for selected waste fractions.Results from the life-cycle impact assessment (LCIA) show that the environmental performance estimated for landfilling with energy recovery of the fractions “organics” and “recyclable paper” is comparable...... with composting (for “organics”) and incineration (for “recyclable paper”). This however requires high degree of control over gas and leachate emissions, high gas collection efficiency and extensive gas utilization at the landfill. For the other waste fractions, recycling and incineration are favourable, although...
Lisý, Vladimír; Tóthová, Jana
2018-02-01
Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.
Directory of Open Access Journals (Sweden)
Pietro Bia
2016-01-01
Full Text Available The interaction of electromagnetic fields and biological tissues has become a topic of increasing interest for new research activities in bioelectrics, a new interdisciplinary field combining knowledge of electromagnetic theory, modeling, and simulations, physics, material science, cell biology, and medicine. In particular, the feasibility of pulsed electromagnetic fields in RF and mm-wave frequency range has been investigated with the objective to discover new noninvasive techniques in healthcare. The aim of this contribution is to illustrate a novel Finite-Difference Time-Domain (FDTD scheme for simulating electromagnetic pulse propagation in arbitrary dispersive biological media. The proposed method is based on the fractional calculus theory and a general series expansion of the permittivity function. The spatial dispersion effects are taken into account, too. The resulting formulation is explicit, it has a second-order accuracy, and the need for additional storage variables is minimal. The comparison between simulation results and those evaluated by using an analytical method based on the Fourier transformation demonstrates the accuracy and effectiveness of the developed FDTD model. Five numerical examples showing the plane wave propagation in a variety of dispersive media are examined.
Supporting Students’ Reasoning About Multiplication of Fractions by Constructing an Array Model
Directory of Open Access Journals (Sweden)
Ronal Rifandi
2017-08-01
Full Text Available The aim of the research is to support students in constructing an array model as a bridge from their informal knowledge to the formal one in understanding the part-whole relation concept. The part-whole relation concept is important for students to reason about multiplication of fractions. Realistic Mathematics Education which is in Indonesia adapted as Pendidikan Matematika Realistik Indonesia (PMRI is used as an approach in designing a series of lessons. For this purpose, hypothetical learning trajectory (HLT became the base for conducting a teaching experiment and designing its learning materials. The research was conducted in the fifth grade of SD Al Hikmah Surabaya, an elementary school in Indonesia, with five students as the participants. The collected data were qualitative data in the form of students’ written works and the transcript of video recording during the lesson. The data were analyzed retrospectively by confronting the conjecture of students’ thinking in the HLT with the fact in the teaching experiment. The result of the research shows that most students could use the contextual problem in promoting their ability on constructing their own array model to reason about part-whole relation.
Rho, a Fraction From Rhodiola crenulate, Ameliorates Hepatic Steatosis in Mice Models
Directory of Open Access Journals (Sweden)
Qin Yi
2018-03-01
Full Text Available The prevalence of non-alcoholic fatty liver disease (NAFLD, which is developed from hepatic steatosis, is increasing worldwide. However, no specific drugs for NAFLD have been approved yet. To observe the effects of Rho, a fraction from Rhodiola crenulate, on non-alcoholic hepatic steatosis, three mouse models with characteristics of NAFLD were used including high-fat diet (HFD-induced obesity (DIO mice, KKAy mice, and HFD combined with tetracycline stimulated Model-T mice. Hepatic lipid accumulation was determined via histopathological analysis and/or hepatic TG determination. The responses to insulin were evaluated by insulin tolerance test (ITT, glucose tolerance test (GTT, and hyperinsulinemic-euglycemic clamp, respectively. The pathways involved in hepatic lipid metabolism were observed via western-blot. Furthermore, the liver microcirculation was observed by inverted microscopy. The HPLC analysis indicated that the main components of Rho were flavan polymers. The results of histopathological analysis showed that Rho could ameliorate hepatic steatosis in DIO, KKAy, and Model-T hepatic steatosis mouse models, respectively. After Rho treatment in DIO mice, insulin resistance was improved with increasing glucose infusion rate (GIR in hyperinsulinemic-euglycemic clamp, and decreasing areas under the blood glucose-time curve (AUC in both ITT and GTT; the pathways involved in fatty acid uptake and de novo lipogenesis were both down-regulated, respectively. However, the pathways involved in beta-oxidation and VLDL-export on hepatic steatosis were not changed significantly. The liver microcirculation disturbances were also improved by Rho in DIO mice. These results suggest that Rho is a lead nature product for hepatic steatosis treatment. The mechanism is related to enhancing insulin sensitivity, suppressing fatty acid uptake and inhibiting de novo lipogenesis in liver.
Energy Technology Data Exchange (ETDEWEB)
Cimpan, Emil
2004-09-15
water fraction. The model intended to employ existent formulas of the medium parameters worked out by Maxwell, Bruggeman and Ramu and Rao. However, to calculate the loss due to the induced eddy currents within the medium in the particular case of the oil continuous phase, other mathematical models expressing (equivalent) medium conductivity and permittivity were required and developed in this work. Although the resonance frequency of the coil was decreasing with increasing medium conductivity, this variation was not as significant as the variation of the coil impedance. This raised the question as to whether coils having the same self-resonance frequency in different media could be constructed. This was worth investigating because it could simplify the mathematical modelling. This was indeed the case and coils featuring approximately the same resonance frequency in different media were made. Concluding, the measuring device based on the HFMFT, which was constructed, investigated and described in this work can be developed into a practical instrument for monitoring the water fraction in multiphase flows. The overall measurement accuracy when using this technique would depend on the analytical models expressing the medium parameters and circumscribing the HFMFT itself. When the mathematical modelling of the HFMFT was finalised, it was understood that many other applications of the technique were also possible. Some of these applications, which might be of interest such as a conductivity meter and a three-component ratio meter, are briefly discussed.
DEFF Research Database (Denmark)
Jala, Ram Chandra Reddy; Guo, Zheng; Bjerring, Thomas
2010-01-01
A multi-stage temperature-programmed fractionating crystallization process was carried out to examine the effects of the presence of stearic acid (SA), oleic acid (OA), and linoleic acid (LA) on the separation of elaidic acid (EA). The results showed that the efficiency of fractionating...
Asphaltene self-association: Modeling and effect of fractionation with a polar solvent
DEFF Research Database (Denmark)
Garcia, Daniel Merino; Murgich, J; Andersen, Simon Ivar
2004-01-01
of DeltaH(a) obtained suggest that a fraction of asphaltenes is not active in the calorimetric experiments. Asphaltenes from Venezuela (LM1) and Mexico (KU) have been fractionated by precipitation with a mixture of acetone and toluene. It is considered that the most polar compounds are collected...
An economical and environmentally friendly whey protein fractionation process was developed using supercritical carbon dioxide (sCO2) as an acid to produce enriched fractions of alpha-lactalbumin (alpha-La) and beta-lactoglobulin (beta-Lg) from a commercial whey protein isolate (WPI) containing 55% ...
DEFF Research Database (Denmark)
Christensen, Bent Jesper; Kruse, Robinson; Sibbertsen, Philipp
We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional...
Kochunov, P; Chiappelli, J; Hong, L E
2013-01-01
Diffusion tensor imaging (DTI) assumes a single pool of anisotropically diffusing water to calculate fractional anisotropy (FA) and is commonly used to ascertain white matter (WM) deficits in schizophrenia. At higher b-values, diffusion-signal decay becomes bi-exponential, suggesting the presence of two, unrestricted and restricted, water pools. Theoretical work suggests that semi-permeable cellular membrane rather than the presence of two physical compartments is the cause. The permeability-diffusivity (PD) parameters measured from bi-exponential modeling may offer advantages, over traditional DTI-FA, in identifying WM deficits in schizophrenia. Imaging was performed in N = 26/26 patients/controls (age = 20-61 years, average age = 40.5 ± 12.6). Imaging consisted of fifteen b-shells: b = 250-3800 s/mm(2) with 30 directions/shell, covering seven slices of mid-sagittal corpus callosum (CC) at 1.7 × 1.7 × 4.6 mm. 64-direction DTI was also collected. Permeability-diffusivity-index (PDI), the ratio of restricted to unrestricted apparent diffusion coefficients, and the fraction of unrestricted compartment (Mu) were calculated for CC and cingulate gray matter (GM). FA values for CC were calculated using tract-based-spatial-statistics. Patients had significantly reduced PDI in CC (p ≅ 10(- 4)) and cingulate GM (p = 0.002), while differences in CC FA were modest (p ≅ .03). There was no group-related difference in Mu. Additional theoretical-modeling analysis suggested that reduced PDI in patients may be caused by reduced cross-membrane water molecule exchanges. PDI measurements for cerebral WM and GM yielded more robust patient-control differences than DTI-FA. Theoretical work offers an explanation that patient-control PDI differences should implicate abnormal active membrane permeability. This would implicate abnormal activities in ion-channels that use water as substrate for ion exchange, in cerebral tissues of schizophrenia patients.
Dou, Ruifeng; Phillion, A. B.
2016-08-01
Hot tearing susceptibility is commonly assessed using a pressure drop equation in the mushy zone that includes the effects of both tensile deformation perpendicular to the thermal gradient as well as shrinkage feeding. In this study, a Pore Fraction hot tearing model, recently developed by Monroe and Beckermann (JOM 66:1439-1445, 2014), is extended to additionally include the effect of strain rate parallel to the thermal gradient. The deformation and shrinkage pore fractions are obtained on the basis of the dimensionless Niyama criterion and a scaling variable method. First, the model is applied to the binary Al-Cu system under conditions of directional solidification. It is shown that for the same Niyama criterion, a decrease in the cooling rate increases both the deformation and shrinkage pore fractions because of an increase in the time spent in the brittle temperature region. Second, the model is applied to the industrial aluminum alloy AA5182 as part of a finite element simulation of the Direct Chill (DC) casting process. It is shown that an increase in the casting speed during DC casting increases the deformation and shrinkage pore fractions, causing the maximum point of pore fraction to move towards the base of the casting. These results demonstrate that including the strain rate parallel to the thermal gradient significantly improves the predictive quality of hot tearing criteria based on the pressure drop equation.
Experimental studies and model analysis of noble gas fractionation in porous media
Ding, Xin; Kennedy, B. Mack.; Evans, William C.; Stonestrom, David A.
2016-01-01
The noble gases, which are chemically inert under normal terrestrial conditions but vary systematically across a wide range of atomic mass and diffusivity, offer a multicomponent approach to investigating gas dynamics in unsaturated soil horizons, including transfer of gas between saturated zones, unsaturated zones, and the atmosphere. To evaluate the degree to which fractionation of noble gases in the presence of an advective–diffusive flux agrees with existing theory, a simple laboratory sand column experiment was conducted. Pure CO2 was injected at the base of the column, providing a series of constant CO2 fluxes through the column. At five fixed sampling depths within the system, samples were collected for CO2 and noble gas analyses, and ambient pressures were measured. Both the advection–diffusion and dusty gas models were used to simulate the behavior of CO2 and noble gases under the experimental conditions, and the simulations were compared with the measured depth-dependent concentration profiles of the gases. Given the relatively high permeability of the sand column (5 ´ 10−11 m2), Knudsen diffusion terms were small, and both the dusty gas model and the advection–diffusion model accurately predicted the concentration profiles of the CO2 and atmospheric noble gases across a range of CO2 flux from ?700 to 10,000 g m−2 d−1. The agreement between predicted and measured gas concentrations demonstrated that, when applied to natural systems, the multi-component capability provided by the noble gases can be exploited to constrain component and total gas fluxes of non-conserved (CO2) and conserved (noble gas) species or attributes of the soil column relevant to gas transport, such as porosity, tortuosity, and gas saturation.
Alvarez-Zaldívar, Pablo; Imfeld, Gwenaël; Maier, Uli; Centler, Florian; Thullner, Martin
2013-04-01
In recent years, the use of (constructed) wetlands has gained significant attention for the in situ remediation of groundwater contaminated with (chlorinated) organic hydrocarbons. Although many sophisticated experimental methods exist for the assessment of contaminant removal in such wetlands the understanding how changes in wetland hydrochemistry affect the removal processes is still limited. This knowledge gap might be reduced by the use of biogeochemical reactive transport models. This study presents the reactive transport simulation of a small-scale constructed wetland treated with groundwater containing cis-1,2-dichloroethene (cDCE). Simulated processes consider different cDCE biodegradation pathways and the associated carbon isotope fractionation, a set of further (bio)geochemical processes as well as the activity of the plant roots. Spatio-temporal hydrochemical and isotope data from a long-term constructed wetland experiment [1] are used to constrain the model. Simulation results for the initial oxic phase of the wetland experiment indicate carbon isotope enrichment factors typical for cometabolic DCE oxidation, which suggests that aerobic treatment of cDCE is not an optimal remediation strategy. For the later anoxic phase of the experiment model derived enrichment factors indicate reductive dechlorination pathways. This degradation is promoted at all wetland depths by a sufficient availability of electron donor and carbon sources from root exudates, which makes the anoxic treatment of groundwater in such wetlands an effective remediation strategy. In combination with the previous experimental data results from this study suggest that constructed wetlands are viable remediation means for the treatment of cDCE contaminated groundwater. Reactive transport models can improve the understanding of the factors controlling chlorinated ethenes removal, and the used model approach would also allow for an optimization of the wetland operation needed for a complete
Yang, Chen; Liu, Ying
2017-08-01
A two-dimensional depth-integrated numerical model is refined in this paper to simulate the hydrodynamics, graded sediment transport process and the fate of faecal bacteria in estuarine and coastal waters. The sediment mixture is divided into several fractions according to the grain size. A bed evolution model is adopted to simulate the processes of the bed elevation change and sediment grain size sorting. The faecal bacteria transport equation includes enhanced source and sink terms to represent bacterial kinetic transformation and disappearance or reappearance due to sediment deposition or re-suspension. A novel partition ratio and dynamic decay rates of faecal bacteria are adopted in the numerical model. The model has been applied to the turbid water environment in the Bristol Channel and Severn estuary, UK. The predictions by the present model are compared with field data and those by non-fractionated model.
Molina-Romero, Miguel; Gómez, Pedro A; Sperl, Jonathan I; Czisch, Michael; Sämann, Philipp G; Jones, Derek K; Menzel, Marion I; Menze, Bjoern H
2018-03-23
The compartmental nature of brain tissue microstructure is typically studied by diffusion MRI, MR relaxometry or their correlation. Diffusion MRI relies on signal representations or biophysical models, while MR relaxometry and correlation studies are based on regularized inverse Laplace transforms (ILTs). Here we introduce a general framework for characterizing microstructure that does not depend on diffusion modeling and replaces ill-posed ILTs with blind source separation (BSS). This framework yields proton density, relaxation times, volume fractions, and signal disentanglement, allowing for separation of the free-water component. Diffusion experiments repeated for several different echo times, contain entangled diffusion and relaxation compartmental information. These can be disentangled by BSS using a physically constrained nonnegative matrix factorization. Computer simulations, phantom studies, together with repeatability and reproducibility experiments demonstrated that BSS is capable of estimating proton density, compartmental volume fractions and transversal relaxations. In vivo results proved its potential to correct for free-water contamination and to estimate tissue parameters. Formulation of the diffusion-relaxation dependence as a BSS problem introduces a new framework for studying microstructure compartmentalization, and a novel tool for free-water elimination. © 2018 International Society for Magnetic Resonance in Medicine.
Abdulhameed, M.; Vieru, D.; Roslan, R.
2017-10-01
This paper investigates the electro-magneto-hydrodynamic flow of the non-Newtonian behavior of biofluids, with heat transfer, through a cylindrical microchannel. The fluid is acted by an arbitrary time-dependent pressure gradient, an external electric field and an external magnetic field. The governing equations are considered as fractional partial differential equations based on the Caputo-Fabrizio time-fractional derivatives without singular kernel. The usefulness of fractional calculus to study fluid flows or heat and mass transfer phenomena was proven. Several experimental measurements led to conclusion that, in such problems, the models described by fractional differential equations are more suitable. The most common time-fractional derivative used in Continuum Mechanics is Caputo derivative. However, two disadvantages appear when this derivative is used. First, the definition kernel is a singular function and, secondly, the analytical expressions of the problem solutions are expressed by generalized functions (Mittag-Leffler, Lorenzo-Hartley, Robotnov, etc.) which, generally, are not adequate to numerical calculations. The new time-fractional derivative Caputo-Fabrizio, without singular kernel, is more suitable to solve various theoretical and practical problems which involve fractional differential equations. Using the Caputo-Fabrizio derivative, calculations are simpler and, the obtained solutions are expressed by elementary functions. Analytical solutions of the biofluid velocity and thermal transport are obtained by means of the Laplace and finite Hankel transforms. The influence of the fractional parameter, Eckert number and Joule heating parameter on the biofluid velocity and thermal transport are numerically analyzed and graphic presented. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in microfluidic devices used for biological
Pseudo Phase Plane and Fractional Calculus modeling of western global economic downturn
Tenreiro Machado, J. A.; Mata, Maria Eugénia
2015-05-01
This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries' PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972-2012) does not conclude for other partners' global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.
Eyuboglu, Atilla Adnan; Uysal, Cagri A; Ozgun, Gonca; Coskun, Erhan; Markal Ertas, Nilgun; Haberal, Mehmet
2018-03-01
Stasis zone is the surrounding area of the coagulation zone which is an important part determining the extent of the necrosis in burn patients. In our study we aim to salvage the stasis zone by injecting adipose derived stromal vascular fraction (ADSVF). Thermal injury was applied on dorsum of Sprague-Dawley rats (n=20) by the "comb burn" model as described previously. When the burn injury was established on Sprague-Dawley rats (30min); rat dorsum was separated into 2 equal parts consisting of 4 burn zones (3 stasis zone) on each pair. ADSVF cells harvested from inguinal fat pads of Sprague-Dawley rats (n=5) were injected on the right side while same amount of phosphate buffered saline (PBS) injected on the left side of the same animal. One week later, average vital tissue on the statis zone was determined by macroscopy, angiography and microscopy. Vascular density, inflammatory cell density, gradient of fibrosis and epithelial thickness were determined via immunohistochemical assay. Macroscopic stasis zone tissue viability (32±3.28%, 57±4.28%) (p51, 1.50±0.43) (pzone on acute burn injuries. Copyright © 2017 Elsevier Ltd and ISBI. All rights reserved.
Model-Based Normalization of a Fractional-Crystal Collimator for Small-Animal PET Imaging.
Li, Yusheng; Matej, Samuel; Karp, Joel S; Metzler, Scott D
2017-05-01
Previously, we proposed to use a coincidence collimator to achieve fractional-crystal resolution in PET imaging. We have designed and fabricated a collimator prototype for a small-animal PET scanner, A-PET. To compensate for imperfections in the fabricated collimator prototype, collimator normalization, as well as scanner normalization, is required to reconstruct quantitative and artifact-free images. In this study, we develop a normalization method for the collimator prototype based on the A-PET normalization using a uniform cylinder phantom. We performed data acquisition without the collimator for scanner normalization first, and then with the collimator from eight different rotation views for collimator normalization. After a reconstruction without correction, we extracted the cylinder parameters from which we generated expected emission sinograms. Single scatter simulation was used to generate the scattered sinograms. We used the least-squares method to generate the normalization coefficient for each LOR based on measured, expected and scattered sinograms. The scanner and collimator normalization coefficients were factorized by performing two normalizations separately. The normalization methods were also verified using experimental data acquired from A-PET with and without the collimator. In summary, we developed a model-base collimator normalization that can significantly reduce variance and produce collimator normalization with adequate statistical quality within feasible scan time.
Directory of Open Access Journals (Sweden)
Jorge A. Orrego-Ruiz
2014-06-01
Full Text Available In this work, prediction models of Saturates, Aromatics, Resins and Asphaltenes fractions (SARA from thirty-seven vacuum residues of representative Colombian crudes and eighteen fractions of molecular distillation process were obtained. Mid-Infrared (MIR Attenuated Total Reflection (ATR spectroscopy in combination with partial least squares (PLS regression analysis was used to estimate accurately SARA analysis in these kind of samples. Calibration coefficients of prediction models were for saturates, aromatics, resins and asphaltenes fractions, 0.99, 0.96, 0.97 and 0.99, respectively. This methodology permits to control the molecular distillation process since small differences in chemical composition can be detected. Total time elapsed to give the SARA analysis per sample is 10 minutes.
Directory of Open Access Journals (Sweden)
Xin Lu
2018-03-01
Full Text Available In recent years, the fractional order model has been employed to state of charge (SOC estimation. The non integer differentiation order being expressed as a function of recursive factors defining the fractality of charge distribution on porous electrodes. The battery SOC affects the fractal dimension of charge distribution, therefore the order of the fractional order model varies with the SOC at the same condition. This paper proposes a new method to estimate the SOC. A fractional continuous variable order model is used to characterize the fractal morphology of charge distribution. The order identification results showed that there is a stable monotonic relationship between the fractional order and the SOC after the battery inner electrochemical reaction reaches balanced. This feature makes the proposed model particularly suitable for SOC estimation when the battery is in the resting state. Moreover, a fast iterative method based on the proposed model is introduced for SOC estimation. The experimental results showed that the proposed iterative method can quickly estimate the SOC by several iterations while maintaining high estimation accuracy.
Directory of Open Access Journals (Sweden)
Adailton S. Borges
Full Text Available Abstract A broad class of engineering systems can be satisfactory modeled under the assumptions of small deformations and linear material properties. However, many mechanical systems used in modern applications, like structural elements typical of aerospace and petroleum industries, have been characterized by increased slenderness and high static and dynamic loads. In such situations, it becomes indispensable to consider the nonlinear geometric effects and/or material nonlinear behavior. At the same time, in many cases involving dynamic loads, there comes the need for attenuation of vibration levels. In this context, this paper describes the development and validation of numerical models of viscoelastic slender beam-like structures undergoing large displacements. The numerical approach is based on the combination of the nonlinear Cosserat beam theory and a viscoelastic model based on Fractional Derivatives. Such combination enables to derive nonlinear equations of motion that, upon finite element discretization, can be used for predicting the dynamic behavior of the structure in the time domain, accounting for geometric nonlinearity and viscoelastic damping. The modeling methodology is illustrated and validated by numerical simulations, the results of which are compared to others available in the literature.
Xin, X.; Li, F.; Peng, Z.; Qinhuo, L.
2017-12-01
Land surface heterogeneities significantly affect the reliability and accuracy of remotely sensed evapotranspiration (ET), and it gets worse for lower resolution data. At the same time, temporal scale extrapolation of the instantaneous latent heat flux (LE) at satellite overpass time to daily ET are crucial for applications of such remote sensing product. The purpose of this paper is to propose a simple but efficient model for estimating daytime evapotranspiration considering heterogeneity of mixed pixels. In order to do so, an equation to calculate evapotranspiration fraction (EF) of mixed pixels was derived based on two key assumptions. Assumption 1: the available energy (AE) of each sub-pixel equals approximately to that of any other sub-pixels in the same mixed pixel within acceptable margin of bias, and as same as the AE of the mixed pixel. It's only for a simpification of the equation, and its uncertainties and resulted errors in estimated ET are very small. Assumption 2: EF of each sub-pixel equals to the EF of the nearest pure pixel(s) of same land cover type. This equation is supposed to be capable of correcting the spatial scale error of the mixed pixels EF and can be used to calculated daily ET with daily AE data.The model was applied to an artificial oasis in the midstream of Heihe River. HJ-1B satellite data were used to estimate the lumped fluxes at the scale of 300 m after resampling the 30-m resolution datasets to 300 m resolution, which was used to carry on the key step of the model. The results before and after correction were compare to each other and validated using site data of eddy-correlation systems. Results indicated that the new model is capable of improving accuracy of daily ET estimation relative to the lumped method. Validations at 12 sites of eddy-correlation systems for 9 days of HJ-1B overpass showed that the R² increased to 0.82 from 0.62; the RMSE decreased to 1.60 MJ/m² from 2.47MJ/m²; the MBE decreased from 1.92 MJ/m² to 1
International Nuclear Information System (INIS)
Eberstadt, P.L.
1981-10-01
Using a model for the two-compartmental open system and experiments on animals (rabbits and dogs) as well as on human healthy volunteers, an attempt was made to study the advantages and limitations of different radionuclide methods for glomerular filtration rate determination. Labelled compounds used in different combinations were: 3 H-inulin, sup(113m)In-EDTA, 131 I-iothalamate, sup(99m)Tc-DTPA and 14 C-creatinine. The results of the study lead to some working hypotheses concerning the value of creatinine and other labelled substances in the measurement of glomerular filtration rate in clinical practice. The advantages and disadvantages of individual methods summarized in the final report are generally in agreement with the present views of many research workers. Also the hypothesis can be justified that the different labelled compounds which have been studied might be handled independently by the membranes involved but at the long run produce similar homeostatic balance
Tamrat, Yohannes; Nedi, Teshome; Assefa, Solomon; Teklehaymanot, Tilahun; Shibeshi, Workineh
2017-09-29
Many people still experience pain and inflammation regardless of the available drugs for treatments. In addition, the available drugs have many side effects, which necessitated a quest for new drugs from several sources in which medicinal plants are the major one. This study evaluated the analgesic and anti- inflammatory activity of the solvent fractions of Moringa stenopetala in rodent models of pain and inflammation. Successive soxhlet and maceration were used as methods of extractions using solvents of increasing polarity; chloroform, methanol and water. Swiss albino mice models were used in radiant tail flick latency, acetic acid induced writhing and carrageenan induced paw edema to assess the analgesic and anti-inflammatory activities. The test groups received different doses (100 mg/kg, 200 mg/kg and 400 mg/kg) of the three fractions (chloroform, methanol and aqueous). The positive control groups received morphine (20 mg/kg) or aspirin (100 mg/kg or 150 mg/kg) based on the respective models. The negative control groups received the 10 ml/kg of vehicles (distilled water or 2% Tween 80). In all models, the chloroform fraction had protections only at a dose of 400 mg/kg. However, the methanol and aqueous fraction at all doses have shown significant central and peripheral analgesic activities with a comparable result to the standards. The aqueous and methanol fractions significantly reduced carrageenan induced inflammation in a dose dependent manner, in which the highest reduction of inflammation was observed in aqueous fraction at 400 mg/kg. This study provided evidence on the traditionally claimed uses of the plant in pain and inflammatory diseases, and Moringa stenopetala could be potential source for development of new analgesic and anti-inflammatory drugs.
Synapse-specific and compartmentalized expression of presynaptic homeostatic potentiation
Li, Xiling; Goel, Pragya; Chen, Catherine; Angajala, Varun; Chen, Xun
2018-01-01
Postsynaptic compartments can be specifically modulated during various forms of synaptic plasticity, but it is unclear whether this precision is shared at presynaptic terminals. Presynaptic homeostatic plasticity (PHP) stabilizes neurotransmission at the Drosophila neuromuscular junction, where a retrograde enhancement of presynaptic neurotransmitter release compensates for diminished postsynaptic receptor functionality. To test the specificity of PHP induction and expression, we have developed a genetic manipulation to reduce postsynaptic receptor expression at one of the two muscles innervated by a single motor neuron. We find that PHP can be induced and expressed at a subset of synapses, over both acute and chronic time scales, without influencing transmission at adjacent release sites. Further, homeostatic modulations to CaMKII, vesicle pools, and functional release sites are compartmentalized and do not spread to neighboring pre- or post-synaptic structures. Thus, both PHP induction and expression mechanisms are locally transmitted and restricted to specific synaptic compartments. PMID:29620520
The human NAD metabolome: Functions, metabolism and compartmentalization
Nikiforov, Andrey; Kulikova, Veronika; Ziegler, Mathias
2015-01-01
Abstract The metabolism of NAD has emerged as a key regulator of cellular and organismal homeostasis. Being a major component of both bioenergetic and signaling pathways, the molecule is ideally suited to regulate metabolism and major cellular events. In humans, NAD is synthesized from vitamin B3 precursors, most prominently from nicotinamide, which is the degradation product of all NAD-dependent signaling reactions. The scope of NAD-mediated regulatory processes is wide including enzyme regulation, control of gene expression and health span, DNA repair, cell cycle regulation and calcium signaling. In these processes, nicotinamide is cleaved from NAD+ and the remaining ADP-ribosyl moiety used to modify proteins (deacetylation by sirtuins or ADP-ribosylation) or to generate calcium-mobilizing agents such as cyclic ADP-ribose. This review will also emphasize the role of the intermediates in the NAD metabolome, their intra- and extra-cellular conversions and potential contributions to subcellular compartmentalization of NAD pools. PMID:25837229
Compartmentalization of NO signaling cascade in skeletal muscles
International Nuclear Information System (INIS)
Buchwalow, Igor B.; Minin, Evgeny A.; Samoilova, Vera E.; Boecker, Werner; Wellner, Maren; Schmitz, Wilhelm; Neumann, Joachim; Punkt, Karla
2005-01-01
Skeletal muscle functions regulated by NO are now firmly established. However, the literature on the compartmentalization of NO signaling in myocytes is highly controversial. To address this issue, we examined localization of enzymes engaged in L-arginine-NO-cGMP signaling in the rat quadriceps muscle. Employing immunocytochemical labeling complemented with tyramide signal amplification and electron microscopy, we found NO synthase expressed not only in the sarcolemma, but also along contractile fibers, in the sarcoplasmic reticulum and mitochondria. The expression pattern of NO synthase in myocytes showed striking parallels with the enzymes engaged in L-arginine-NO-cGMP signaling (arginase, phosphodiesterase, and soluble guanylyl cyclase). Our findings are indicative of an autocrine fashion of NO signaling in skeletal muscles at both cellular and subcellular levels, and challenge the notion that the NO generation is restricted to the sarcolemma
Imaging and compartmental classification of solid pelvic tumours in children
International Nuclear Information System (INIS)
Hugosson, C.; Nyman, R.; Jacobsson, B.; Jorulf, H.; McDonald, P.; Sackey, K.
1996-01-01
Thirty-five children aged from 1 day to 16 years (median 5 years) with solid pelvic tumours were investigated with US, CT and MR. All three methods gave similar estimates of tumour size. For defining location of the tumours, the pelvis was divided into three midline compartments (anterior, middle and posterior) and a right and left lateral compartment. CT and MR were accurate and equally reliable in determining the tumour location, US was less accurate. Evaluation of confinement to organ of origin was uncertain, regardless of imaging modality. Tissue characteristics with CT and MR did not contribute to the differentiation of the various tumour types, and contrast medium enhancement did not improve the discrimination. Compartmental localization was equally well assessed by CT and MR and, together with sex, was found to correlate with the tumour type. (orig.). With 7 figs., 5 tabs
Yang, Jason H.; Polanowska-Grabowska, Renata K.; Smith, Jeffrey S.; Shields, Charles W.; Saucerman, Jeffrey J.
2014-01-01
β-adrenergic signaling is spatiotemporally heterogeneous in the cardiac myocyte, conferring exquisite control to sympathetic stimulation. Such heterogeneity drives the formation of protein kinase A (PKA) signaling microdomains, which regulate Ca2+ handling and contractility. Here, we test the hypothesis that the nucleus independently comprises a PKA signaling microdomain regulating myocyte hypertrophy. Spatially-targeted FRET reporters for PKA activity identified slower PKA activation and lower isoproterenol sensitivity in the nucleus (t50 = 10.60±0.68 min; EC50 = 89.00 nmol/L) than in the cytosol (t50 = 3.71±0.25 min; EC50 = 1.22 nmol/L). These differences were not explained by cAMP or AKAP-based compartmentation. A computational model of cytosolic and nuclear PKA activity was developed and predicted that differences in nuclear PKA dynamics and magnitude are regulated by slow PKA catalytic subunit diffusion, while differences in isoproterenol sensitivity are regulated by nuclear expression of protein kinase inhibitor (PKI). These were validated by FRET and immunofluorescence. The model also predicted differential phosphorylation of PKA substrates regulating cell contractility and hypertrophy. Ca2+ and cell hypertrophy measurements validated these predictions and identified higher isoproterenol sensitivity for contractile enhancements (EC50 = 1.84 nmol/L) over cell hypertrophy (EC50 = 85.88 nmol/L). Over-expression of spatially targeted PKA catalytic subunit to the cytosol or nucleus enhanced contractile and hypertrophic responses, respectively. We conclude that restricted PKA catalytic subunit diffusion is an important PKA compartmentation mechanism and the nucleus comprises a novel PKA signaling microdomain, insulating hypertrophic from contractile β-adrenergic signaling responses. PMID:24225179
International Nuclear Information System (INIS)
Bastin, Kenneth; Mehta, Minesh
1997-01-01
Purpose/Objective: To develop a rabbit model enabling single or fractionated optic nerve irradiation, measure post-irradiation visual evoked potentials (VEP), fundoscopic and histopathologic changes, and relate different radiation dosing fractions to these measurable physiologic changes. Materials and Methods: Forty male New Zealand white rabbits underwent surgical right orbital prolapse with template-guided optic nerve irradiation using an iridium-192 high dose rate afterloader. Rabbits were randomized into single fraction groups (0 (control), 10, 12.5, 15, 20, and 30 Gy (3 per group); or two fraction groups of 0 (control) 5, 7.5, 10, 15, and 20 Gy (3 per group); or three fractions groups of 10 and 15 Gy (2 per group). Bilateral fundoscopy and pattern-reversal VEPs (0.5 and 1 c/deg, 1 hertz) were performed at 6 and 12 months (mos) following scheduled irradiation. VEP peaks (P1) were measured. Sacrifice and necropsy followed 12 month evaluation, allowing for histological changes. Results: Excluding deaths from anesthesia (2), CNS mite infection (2), sepsis, pyothorax, 'undetermined' and technically non-analyzable VEP recordings, 24 complete rabbit data sets were evaluated. Fundoscopy demonstrated no gross changes at any dose. Histopathology demonstrated generalized optic nerve atrophy without radiation dose correlation. Among single fraction groups, VEP showed a 6 mos post-irradiation P1 prolongation only in the 20 and 30 Gy groups (maximum 67%). At 12 mos lower dose single fraction groups had a prolonged P1 peak. All fractionated groups above 5 Gy x 2 had P1 prolongation times at 6 mos (maximum 46% in the 15 Gy x 3 data set) but by 12 mos these groups had non-measurable, deteriorated VEPs. Correlating VEP P1 latency with the calculated linear quadratic formula (LQM) biologically equivalent dose (BED,α/β=3) for each group demonstrated a general correlation (t-Test P<.001) as shown: Conclusion: Using a rabbit model for selective optic nerve irradiation we conclude
Use of Angle Model to Understand Addition and Subtraction of Fractions
Muzwangowenyu Mukwambo; Kenneth Ngcoza; Lineo Florence Ramasike
2018-01-01
Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and learning (TMATL) of operations of fraction. With the hope of engaging the reformed mathematical approach of teaching and learning (RMATL) this study inves...
Directory of Open Access Journals (Sweden)
Kangning Xu
Full Text Available The loss and injury of neurons play an important role in the onset of various neurodegenerative diseases, while both microgliosis and astrocyte loss or dysfunction are significant causes of neuronal degeneration. Previous studies have suggested that an extract enriched panaxadiol saponins from ginseng has more neuroprotective potential than the total saponins of ginseng. The present study investigated whether a fraction of highly purified panaxadiol saponins (termed as Rb fraction was protective for both glia and neurons, especially GABAergic interneurons, against kainic acid (KA-induced excitotoxicity in rats. Rats received Rb fraction at 30 mg/kg (i.p., 40 mg/kg (i.p. or saline followed 40 min later by an intracerebroventricular injection of KA. Acute hippocampal injury was determined at 48 h after KA, and impairment of hippocampus-dependent learning and memory as well as delayed neuronal injury was determined 16 to 21 days later. KA injection produced significant acute hippocampal injuries, including GAD67-positive GABAergic interneuron loss in CA1, paralbumin (PV-positive GABAergic interneuron loss, pyramidal neuron degeneration and astrocyte damage accompanied with reactive microglia in both CA1 and CA3 regions of the hippocampus. There was also a delayed loss of GAD67-positive interneurons in CA1, CA3, hilus and dentate gyrus. Microgliosis also became more severe 21 days later. Accordingly, KA injection resulted in hippocampus-dependent spatial memory impairment. Interestingly, the pretreatment with Rb fraction at 30 or 40 mg/kg significantly protected the pyramidal neurons and GABAergic interneurons against KA-induced acute excitotoxicity and delayed injury. Rb fraction also prevented memory impairments and protected astrocytes from KA-induced acute excitotoxicity. Additionally, microglial activation, especially the delayed microgliosis, was inhibited by Rb fraction. Overall, this study demonstrated that Rb fraction protected both
Isolated hepatocytes and liver S9 fractions have been used to collect in vitro biotransformation data for fish as a means of improving modeled estimates of chemical bioaccumulation. To date, however, there have been few direct comparisons of these two methods. In the present st...
International Nuclear Information System (INIS)
Simon, M.; Scherzer, R.; Enge, W.
1977-01-01
In cosmic ray propagation calculations one can usually assume a homogeneous distribution of interstellar matter. The crucial astrophysical parameters in these models are: The path length distribution, the age of the cosmic ray particles and the interstellar matter density. These values are interrelated. The surviving fraction of radioactive cosmic ray isotopes is often used to determine a mean matter density of that region, where the cosmic ray particles may mainly reside. Using a Monte Carlo Propagation Program we calculated the change in the surviving fraction quantitatively assuming a region around the sources with higher matter density. (author)
Wang, Zhen; Wang, Xiaohong; Li, Yuxia; Huang, Xia
2017-12-01
In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory of fractional-order differential equations and Laplace transforms, several new sufficient conditions, which ensure the stability of the system are derived. Taking the time delay as the bifurcation parameter, Hopf bifurcation is investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. Finally, two representative numerical examples are given to show the effectiveness of the theoretical results.
DEFF Research Database (Denmark)
Huang, Sunhua; Zhou, Bin; Li, Canbing
2018-01-01
represent complex dynamic behaviours with chaotic and unstable states on the energy conservation, carbon emissions, economic growth, and renewable energy development, and have a great impact on the formulation of government energy policies. Furthermore, based on the fractional Lyapunov stability and robust......, and the fractional-order model of the energy-saving and emission-reduction system (FOESERS) is formulated. With the proposed FOESERS, all of the equilibrium points and the corresponding eigenvalues are obtained, and the instability region and the state trajectories of FOESERS are also given. The FOESERS can...
Compartmental analysis of the disposition of benzo[a]pyrene in rats.
Bevan, D R; Weyand, E H
1988-11-01
We have previously reported the disposition of benzo[a]pyrene (B[a]P) and its metabolites in male Sprague-Dawley rats following intratracheal instillation of [3H]B[a]P [Weyand, E.H. and Bevan, D.R. (1986) Cancer Res., 46, 5655-5661]. In some experiments, cannulas were implanted in the bile duct of the animals prior to administration of [3H]B[a]P [Weyand, E.H. and Bevan, D.R. (1987) Drug Metab. Disposition, 15, 442-448]. Based on these data, we have developed a compartmental model of the distribution of radioactivity to provide a quantitative description of the fate of B[a]P and its metabolites in rats. Modeling of the distribution of radioactivity was performed using the Simulation, Analysis and Modeling (SAAM) and conversational SAAM (CONSAM) computer programs. Compartments in the model included organs into which the largest amounts of radioactivity were distributed as well as pathways for excretion of radioactivity from the animals. Data from animals with and without cannulas implanted in the bile duct were considered simultaneously during modeling. Radioactivity was so rapidly absorbed from the lungs that an absorption phase into blood was not apparent at the earliest sampling times. Using the model of extrapolate to shorter times, it was predicted that the maximum amount of radioactivity was present in blood within 2 min after administration. In addition, considerable recycling of radioactivity back to lungs from blood was predicted by the model. Transfer of radioactivity from blood to liver and carcass (skin, muscle, bones, fat and associated blood) also was extensive. Carcass was modeled as the sum of two compartments to obtain agreement between the model and experimental data. The model accounted for enterohepatic circulation of B[a]P metabolites; data also required that intestinal secretion be included in the model. Quantitative data obtained from compartmental analysis included rate constants for transfer of radioactivity among compartments as well as
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Knee joint femorotibial (uni-compartmental) metal... Devices § 888.3535 Knee joint femorotibial (uni-compartmental) metal/polymer porous-coated uncemented prosthesis. (a) Identification. A knee joint femorotibial (uni-compartmental) metal/polymer porous-coated...
International Nuclear Information System (INIS)
Song, William; Battista, Jerry; Van Dyk, Jake
2004-01-01
The convolution method can be used to model the effect of random geometric uncertainties into planned dose distributions used in radiation treatment planning. This is effectively done by linearly adding infinitesimally small doses, each with a particular geometric offset, over an assumed infinite number of fractions. However, this process inherently ignores the radiobiological dose-per-fraction effect since only the summed physical dose distribution is generated. The resultant potential error on predicted radiobiological outcome [quantified in this work with tumor control probability (TCP), equivalent uniform dose (EUD), normal tissue complication probability (NTCP), and generalized equivalent uniform dose (gEUD)] has yet to be thoroughly quantified. In this work, the results of a Monte Carlo simulation of geometric displacements are compared to those of the convolution method for random geometric uncertainties of 0, 1, 2, 3, 4, and 5 mm (standard deviation). The α/β CTV ratios of 0.8, 1.5, 3, 5, and 10 Gy are used to represent the range of radiation responses for different tumors, whereas a single α/β OAR ratio of 3 Gy is used to represent all the organs at risk (OAR). The analysis is performed on a four-field prostate treatment plan of 18 MV x rays. The fraction numbers are varied from 1-50, with isoeffective adjustments of the corresponding dose-per-fractions to maintain a constant tumor control, using the linear-quadratic cell survival model. The average differences in TCP and EUD of the target, and in NTCP and gEUD of the OAR calculated from the convolution and Monte Carlo methods reduced asymptotically as the total fraction number increased, with the differences reaching negligible levels beyond the treatment fraction number of ≥20. The convolution method generally overestimates the radiobiological indices, as compared to the Monte Carlo method, for the target volume, and underestimates those for the OAR. These effects are interconnected and attributed
Directory of Open Access Journals (Sweden)
S. L. Heck
2012-02-01
Full Text Available There is a widely recognized need to improve our understanding of biosphere-atmosphere carbon exchanges in areas of complex terrain including the United States Mountain West. CO2 fluxes over mountainous terrain are often difficult to measure due to unusual and complicated influences associated with atmospheric transport. Consequently, deriving regional fluxes in mountain regions with carbon cycle inversion of atmospheric CO2 mole fraction is sensitive to filtering of observations to those that can be represented at the transport model resolution. Using five years of CO2 mole fraction observations from the Regional Atmospheric Continuous CO2 Network in the Rocky Mountains (Rocky RACCOON, five statistical filters are used to investigate a range of approaches for identifying regionally representative CO2 mole fractions. Test results from three filters indicate that subsets based on short-term variance and local CO2 gradients across tower inlet heights retain nine-tenths of the total observations and are able to define representative diel variability and seasonal cycles even for difficult-to-model sites where the influence of local fluxes is much larger than regional mole fraction variations. Test results from two other filters that consider measurements from previous and following days using spline fitting or sliding windows are overly selective. Case study examples showed that these windowing-filters rejected measurements representing synoptic changes in CO2, which suggests that they are not well suited to filtering continental CO2 measurements. We present a novel CO2 lapse rate filter that uses CO2 differences between levels in the model atmosphere to select subsets of site measurements that are representative on model scales. Our new filtering techniques provide guidance for novel approaches to assimilating mountain-top CO2 mole fractions in carbon cycle inverse models.
Sales, T. P.; Marques, Flávio D.; Pereira, Daniel A.; Rade, Domingos A.
2018-06-01
Nonlinear aeroelastic systems are prone to the appearance of limit cycle oscillations, bifurcations, and chaos. Such problems are of increasing concern in aircraft design since there is the need to control nonlinear instabilities and improve safety margins, at the same time as aircraft are subjected to increasingly critical operational conditions. On the other hand, in spite of the fact that viscoelastic materials have already been successfully used for the attenuation of undesired vibrations in several types of mechanical systems, a small number of research works have addressed the feasibility of exploring the viscoelastic effect to improve the behavior of nonlinear aeroelastic systems. In this context, the objective of this work is to assess the influence of viscoelastic materials on the aeroelastic features of a three-degrees-of-freedom typical section with hardening structural nonlinearities. The equations of motion are derived accounting for the presence of viscoelastic materials introduced in the resilient elements associated to each degree-of-freedom. A constitutive law based on fractional derivatives is adopted, which allows the modeling of temperature-dependent viscoelastic behavior in time and frequency domains. The unsteady aerodynamic loading is calculated based on the classical linear potential theory for arbitrary airfoil motion. The aeroelastic behavior is investigated through time domain simulations, and subsequent frequency transformations, from which bifurcations are identified from diagrams of limit cycle oscillations amplitudes versus airspeed. The influence of the viscoelastic effect on the aeroelastic behavior, for different values of temperature, is also investigated. The numerical simulations show that viscoelastic damping can increase the flutter speed and reduce the amplitudes of limit cycle oscillations. These results prove the potential that viscoelastic materials have to increase aircraft components safety margins regarding aeroelastic
Directory of Open Access Journals (Sweden)
Andrea Sorzia
2016-01-01
Full Text Available A tensile test until breakage and a creep and relaxation test on a polypropylene fibre are carried out and the resulting creep and stress relaxation curves are fit by a model adopting a fraction-exponential kernel in the viscoelastic operator. The models using fraction-exponential functions are simpler than the complex ones obtained from combination of dashpots and springs and, furthermore, are suitable for fitting experimental data with good approximation allowing, at the same time, obtaining inverse Laplace transform in closed form. Therefore, the viscoelastic response of polypropylene fibres can be modelled straightforwardly through analytical methods. Addition of polypropylene fibres greatly improves the tensile strength of composite materials with concrete matrix. The proposed analytical model can be employed for simulating the mechanical behaviour of composite materials with embedded viscoelastic fibres.
International Nuclear Information System (INIS)
Storb, R.; Raff, R.F.; Graham, T.; Appelbaum, F.R.; Deeg, H.J.; Schuening, F.G.; Shulman, H.; Pepe, M.
1993-01-01
The authors explored in dogs the marrow toxicity of single dose total body irradiation delivered from two opposing 60 Co sources at a rate of 10 cGy/min and compared results to those seen with total body irradiation administered in 100 cGy fractions with minimum interfraction intervals of 6 hr. Dogs were not given marrow transplants. They found that 200 cGy single dose total body irradiation was sublethal, with 12 of 13 dogs showing hematopoietic recovery and survival. Seven of 21 dogs given 300 cGy single dose total body irradiation survived compared to 6 of 10 dogs given 300 cGy fractionated total body irradiation. One of 28 dogs given 400 cGy single dose total body irradiation survived compared to none of six given fractionated radiation. With granulocyte colony stimulating factor (GCSF) administered from day 0-21 after 400 cGy total body irradiation, most dogs survived with hematological recovery. Because of the almost uniform success with GCSF after 400 cGy single dose total body irradiation, a study of GCSF after 400 cGy fractionated total body irradiation was deemed not to be informative and, thus, not carried out. Additional comparisons between single dose and fractionated total body irradiation were carried out with GCSF administered after 500 and 600 cGy of total body irradiation. As with lower doses of total body irradiation, no significant survival differences were seen between the two modes of total body irradiation, and only 3 of 26 dogs studied survived with complete hematological recovery. Overall, therefore, survival among dogs given single dose total body irradiation was not different from that of dogs given fractionated total body irradiation (p = .67). Similarly, the slopes of the postirradiation declines of granulocyte and platelet counts and the rates of their recovery in surviving dogs given equal total doses of single versus fractionated total body irradiation were indistinguishable. 24 refs., 3 figs., 2 tabs
International Nuclear Information System (INIS)
Mattiolo-Marchese, Sandra Regina
1998-01-01
From the ecological point of view, 137 Cs is a critical radionuclide because its physical half-life is long (30 years), and it has a high fission yield. Besides, it presents similar characteristics to sodium and potassium, fundamental elements for the living organisms, in great concentration in all cells. This work has as aim to study the 137 Cs accumulation and elimination by the alga Gracilaria caudata and by the fish Abudefduf saxatilis as well as to obtain the transfer constants of the 137 Cs from the water into the organisms. The concentration factor found for the fish was 5.6 +- 0.2 and for the alga, 13.0 +- 0,6. With 7 and 22 days, the fish and alga respectively had already eliminated half of the accumulated radionuclide. The 137 Cs ingestion efficiency by the fish was also studied and it was verified that the fish assimilated only 47.6 % of the cesium content in the food; and within of 4 days it had eliminated more than half of ingested cesium. A compartmental model was proposed to explain the distribution of cesium in the compartments (water - alga and water - fish). Data obtained from the experiments of 137 Cs accumulation and elimination were applied in the Ana Comp Program. This program permits the compartmental analysis, and quantifies the cesium distribution from the sea-water to the organisms, and vice versa, through the transfer constants (k). The Ana Comp Program also allowed to calculate the dose that one would receive by the consumption of fish contaminated by cesium. Levels of 137 Cs from the global fallout in environmental samples, from Sao Sebastiao, northern coast of Sao Paulo, (where the 'Centro de Biologia Marinha da Universidade de Sao Paulo - CEBIMar - USP' is located), were verified. (author)
A survival model for fractionated radiotherapy with an application to prostate cancer
Energy Technology Data Exchange (ETDEWEB)
Zaider, Marco [Department of Medical Physics, Memorial Sloan-Kettering Cancer Center, New York, NY (United States)]. E-mail: Zaiderm@mskcc.org; Zelefsky, Michael J.; Leibel, Steven A. [Department of Radiation Oncology, Memorial Sloan-Kettering Cancer Center, New York, NY (United States); Hanin, Leonid G. [Department of Mathematics, Idaho State University, Pocatello, ID (United States); Tsodikov, Alexander D.; Yakovlev, Andrei Y. [Department of Oncological Sciences, Huntsman Cancer Institute, University of Utah, Salt Lake City, UT (United States)
2001-10-01
This paper explores the applicability of a mechanistic survival model, based on the distribution of clonogens surviving a course of fractionated radiation therapy, to clinical data on patients with prostate cancer. The study was carried out using data on 1100 patients with clinically localized prostate cancer who were treated with three-dimensional conformal radiation therapy. The patients were stratified by radiation dose (group 1: <67.5 Gy; group 2: 67.5-72.5 Gy; group 3: 72.5-77.5 Gy; group 4: 77.5-87.5 Gy) and prognosis category (favourable, intermediate and unfavourable as defined by pre-treatment PSA and Gleason score). A relapse was recorded when tumour recurrence was diagnosed or when three successive prostate specific antigen (PSA) elevations were observed from a post-treatment nadir PSA level. PSA relapse-free survival was used as the primary end point. The model, which is based on an iterated Yule process, is specified in terms of three parameters: the mean number of tumour clonogens that survive the treatment, the mean of the progression time of post-treatment tumour development and its standard deviation. The model parameters were estimated by the maximum likelihood method. The fact that the proposed model provides an excellent description both of the survivor function and of the hazard rate is prima facie evidence of the validity of the model because closeness of the two survivor functions (empirical and model-based) does not generally imply closeness of the corresponding hazard rates. The estimated cure probabilities for the favourable group are 0.80, 0.74 and 0.87 (for dose groups 1-3, respectively); for the intermediate group: 0.25, 0.51, 0.58 and 0.78 (for dose groups 1-4, respectively) and for the unfavourable group: 0.0, 0.27, 0.33 and 0.64 (for dose groups 1-4, respectively). The distribution of progression time to tumour relapse was found to be independent of prognosis group but dependent on dose. As the dose increases the mean progression
Fractional Dynamics and Control
Machado, José; Luo, Albert
2012-01-01
Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science. Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics Develops new methods for control and synchronization of...
Directory of Open Access Journals (Sweden)
Koca Ilknur
2017-01-01
Full Text Available Recently Hristov using the concept of a relaxation kernel with no singularity developed a new model of elastic heat diffusion equation based on the Caputo-Fabrizio fractional derivative as an extended version of Cattaneo model of heat diffusion equation. In the present article, we solve exactly the Cattaneo-Hristov model and extend it by the concept of a derivative with non-local and non-singular kernel by using the new Atangana-Baleanu derivative. The Cattaneo-Hristov model with the extended derivative is solved analytically with the Laplace transform, and numerically using the Crank-Nicholson scheme.
DEFF Research Database (Denmark)
Hattel, Jesper Henri; Pryds, Nini
2006-01-01
the atomisation stage taking thermal coupling into consideration and the deposition of the droplets at the surface of the billet taking geometrical aspects such as shading into account. The coupling between these two models is accomplished by ensuring that the total droplet size distribution of the spray......In this paper, the relationship between the Gas to Melt Ratio (GMR) and the solid fraction of an evolving billet surface is investigated numerically. The basis for the analysis is a recently developed integrated procedure for modelling the entire spray forming process. This model includes...... is the summation of “local” droplet size distributions along the r-axis of the spray cone. The criterion for a successful process has been a predefined process window characterised by a desired solid fraction range at a certain distance from the atomizer. Inside this process window, the gas and melt flows have...
International Nuclear Information System (INIS)
Todo, A.S.
1980-01-01
Presently, the estimates of specific absorbed fractions in various organs of a heterogeneous phantom are based on Monte Carlo calculation for monoenergetic photons uniformly distributed in the organs of an adult phantom. But, it is known that the kidney and some other organs (for example the skeleton) do not retain the radionuclides in an uniform manner in its internal region. So, we developed a model for the kidney including the cortex, medulla and collecting region. This model was utilized to estimate the specific absorbed fractions, for monoenergetic photons or electrons, in various organs of a heterogeneous phantom, when sources were uniformly distributed in each region of the kidney. All results obtained in this work were compared with those using a homogeneous model for the kidney as presented in ORNL-5000. (Author) [pt
Higher fractions theory of fractional hall effect
International Nuclear Information System (INIS)
Kostadinov, I.Z.; Popov, V.N.
1985-07-01
A theory of fractional quantum Hall effect is generalized to higher fractions. N-particle model interaction is used and the gap is expressed through n-particles wave function. The excitation spectrum in general and the mean field critical behaviour are determined. The Hall conductivity is calculated from first principles. (author)
Use of Angle Model to Understand Addition and Subtraction of Fractions
Mukwambo, Muzwangowenyu; Ngcoza, Kenneth; Ramasike, Lineo Florence
2018-01-01
Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and…
DEFF Research Database (Denmark)
Olesen, Mikkel Vestergaard; Needham, Esther Kjær; Pakkenberg, Bente
2017-01-01
present the optical fractionator in conjunction with BrdU immunohistochemistry to estimate the production and survival of newly-formed neurons in the granule cell layer (including the sub-granular zone) of the rat hippocampus following electroconvulsive stimulation, which is among the most potent...
Wildschut, J.; Arentz, J.; Rasrendra, C. B.; Venderbosch, R. H.; Heeres, H. J.
2009-01-01
Fast pyrolysis oil can be upgraded by a catalytic hydrotreatment (250-400 degrees C, 100-200 bar) using heterogeneous catalysts such as Ru/C to hydrocarbon-like products that can serve as liquid transportation fuels. Insight into the complex reaction pathways of the various component fractions
A No-Arbitrage Fractional Cointegration Model for Futures and Spot Daily Ranges
DEFF Research Database (Denmark)
Rossi, Eduardo; Santucci de Magistris, Paolo
2013-01-01
The no-arbitrage relation between futures and spot prices implies an analogous relation between futures and spot daily ranges. The long-memory features of the range-based volatility estimators are analyzed, and fractional cointegration is tested in a semi-parametric framework. In particular, the no...
Bae, Jung Min; Jung, Han Mi; Goo, Boncheol; Park, Young Min
2015-07-01
Alopecia is one of the most common dermatological problems in the elderly; however, current therapies for it are limited by low efficacy and undesirable side effects. Although clinical reports on fractional laser treatment for various alopecia types are increasing, the exact mechanism remains to be clarified. The purposes of this study were to demonstrate the effect of ablative fractional laser treatment on hair follicle regrowth in vivo and investigate the molecular mechanism after laser treatment. Ablative CO2 fractional laser was applied to the shaved dorsal skin of 7-week-old C57BL/6 mice whose hair was in the telogen stage. After 12 mice were treated at various energy (10-40 mJ/spot) and density (100-400 spots/cm(2) ) settings to determine the proper dosage for maximal effect. Six mice were then treated at the decided dosage and skin specimens were sequentially obtained by excision biopsy from the dorsal aspect of each mouse. Tissue samples were used for the immunohistochemistry and reverse transcription polymerase chain reaction assays to examine hair follicle status and their related molecules. The most effective dosage was the 10 mJ/spot and 300 spots/cm(2) setting. The anagen conversion of hair was observed in the histopathological examination, while Wnt/β-catenin expression was associated with hair regrowth in the immunohistochemistry and molecular studies. Ablative fractional lasers appear to be effective for inducing hair regrowth via activation of the Wnt/β-catenin pathway in vivo. Our findings indicate that fractional laser treatment can potentially be developed as new treatment options for stimulating hair regrowth. © 2015 Wiley Periodicals, Inc.
Compartmentation of sucrose during radial transfer in mature sorghum culm
Directory of Open Access Journals (Sweden)
Vietor Donald M
2007-06-01
Full Text Available Abstract Background The sucrose that accumulates in the culm of sorghum (Sorghum bicolor (L. Moench and other large tropical andropogonoid grasses can be of commercial value, and can buffer assimilate supply during development. Previous study conducted with intact plants showed that sucrose can be radially transferred to the intracellular compartment of mature ripening sorghum internode without being hydrolysed. In this study, culm-infused radiolabelled sucrose was traced between cellular compartments and among related metabolites to determine if the compartmental path of sucrose during radial transfer in culm tissue was symplasmic or included an apoplasmic step. This transfer path was evaluated for elongating and ripening culm tissue of intact plants of two semidwarf grain sorghums. The metabolic path in elongating internode tissue was also evaluated. Results On the day after culm infusion of the tracer sucrose, the specific radioactivity of sucrose recovered from the intracellular compartment of growing axillary-branch tissue was greater (nearly twice than that in the free space, indicating that sucrose was preferentially transferred through symplasmic routes. In contrast, the sucrose specific radioactivity in the intracellular compartment of the mature (ripening culm tissue was probably less (about 3/4's than that in free space indicating that sucrose was preferentially transferred through routes that included an apoplasmic step. In growing internodes of the axillary branch of sorghum, the tritium label initially provided in the fructose moiety of sucrose molecules was largely (81% recovered in the fructose moiety, indicating that a large portion of sucrose molecules is not hydrolysed and resynthesized during radial transfer. Conclusion During radial transfer of sucrose in ripening internodes of intact sorghum plants, much of the sucrose is transferred intact (without hydrolysis and resynthesis and primarily through a path that includes an
Comparison of bolus versus fractionated oral applications of [13C]-linoleic acid in humans.
Demmelmair, H; Iser, B; Rauh-Pfeiffer, A; Koletzko, B
1999-07-01
The endogenous conversion of linoleic acid into long-chain polyunsaturated fatty acids is of potential importance for meeting substrate requirements, particularly in young infants. After application of [13C]-linoleic acid, we estimated its conversion to dihomo-gamma-linolenic and arachidonic acids from only two blood samples. Oral tracer doses were given to five healthy adults as a single bolus. In four subjects the tracer was given in nine equal portions over 3 days. Concentration and 13C content of fatty acids from serum phospholipids were analysed by gas chromatography combustion isotope ratio-mass spectrometry. Areas under the tracer-concentration curves were calculated, and fractional transfer and turnover rates estimated from compartmental models. The median fractional turnover of linoleic acid was 93.7% per day (interquartile range 25.3) in the bolus group and 80. 0% per day (6.3) in the fraction group (NS). Fractional conversion of linoleic to dihomo-gamma-linolenic acid was 1.5% (0.9) vs. 2.1% (0.7) (bolus vs. fraction, P /= 0.94, P < 0.05) with the ratio of areas under the curve. Using areas under the curve overestimates the conversion, because different residence times are not considered. Estimation of conversion intensity appears possible with only one blood sample obtained after tracer application.
Guetschow, H. A.; Nelson, B. K.
2002-12-01
Depth of crystal fractionation influences the chemical evolution of ocean island basalts and has significant implications for the physical structures of these volcanoes. In contrast to dominantly shallow systems such as Hawaii, a range of fractionation depths have been reported for Canary Islands lavas. Magmas erupted on La Palma preserve fluid- and melt-inclusion evidence for high-pressure (> 10 kbar) crystallization (Klügel et al., 1998; Hansteen et al., 1998; Nikogosian et al., 2002). If high-pressure fractional crystallization were an early and dominant process, it would generate specific patterns in rock and phase chemistry of eruptive sequences. Alkalic basalts from Taburiente volcano display coherent major element trends consistent with evolution dominated by fractional crystallization while their phenocryst compositions, trace elements, and isotopic trends require mixing between multiple sources. The current model confirms the importance of both fractionation and mixing to achieve the full range of lavas observed. A low-pressure (1 kbar) thermodynamic fractional crystallization model performed with the MELTS (Ghiorso and Sack, 1995) software closely reproduces major element trends from two stratigraphic sequences. This model also predicts the observed sequence of groundmass clinopyroxene compositions and phenocryst zoning reversals. In all low pressure simulations, olivine remains a modally significant liquidus phase during the first 20% and last 30% of the crystallization sequence, resulting in a negative correlation between the CaO and Fo content of olivine. These results are consistent with the presence of olivine phenocrysts that bear petrographic evidence of early crystallization, as well as observed compositional trends of groundmass olivine and clinopyroxene in Taburiente lavas. MELTS models that include an initial period of high pressure (12 kbar) clinopyroxene fractionation produce major element trends comparable to the low pressure model, but
DEFF Research Database (Denmark)
Cavaliere, Giuseppe; Nielsen, Morten Ørregaard; Taylor, Robert
We consider the problem of conducting estimation and inference on the parameters of univariate heteroskedastic fractionally integrated time series models. We first extend existing results in the literature, developed for conditional sum-of squares estimators in the context of parametric fractional...... time series models driven by conditionally homoskedastic shocks, to allow for conditional and unconditional heteroskedasticity both of a quite general and unknown form. Global consistency and asymptotic normality are shown to still obtain; however, the covariance matrix of the limiting distribution...... of the estimator now depends on nuisance parameters derived both from the weak dependence and heteroskedasticity present in the shocks. We then investigate classical methods of inference based on the Wald, likelihood ratio and Lagrange multiplier tests for linear hypotheses on either or both of the long and short...
Aman, Sidra; Khan, Ilyas; Ismail, Zulkhibri; Salleh, Mohd Zuki; Tlili, I.
2018-06-01
In this article the idea of Caputo time fractional derivatives is applied to MHD mixed convection Poiseuille flow of nanofluids with graphene nanoparticles in a vertical channel. The applications of nanofluids in solar energy are argued for various solar thermal systems. It is argued in the article that using nanofluids is an alternate source to produce solar energy in thermal engineering and solar energy devices in industries. The problem is modelled in terms of PDE's with initial and boundary conditions and solved analytically via Laplace transform method. The obtained solutions for velocity, temperature and concentration are expressed in terms of Wright's function. These solutions are significantly controlled by the variations of parameters including thermal Grashof number, Solutal Grashof number and nanoparticles volume fraction. Expressions for skin-friction, Nusselt and Sherwood numbers are also determined on left and right walls of the vertical channel with important numerical results in tabular form. It is found that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters.
Verma, Neeraj; Singh, Anil P; Amresh, G; Sahu, P K; Rao, Ch V
2011-05-01
To evaluate the hepatoprotective potential of ethyl acetate fraction of Rhododendron arboreum (Family: Ericaceae) in Wistar rats against carbon tetrachloride (CCl(4))-induced liver damage in preventive and curative models. Fraction at a dose of 100, 200, and 400 mg/kg was administered orally once daily for 14 days in CCl(4)-treated groups (II, III, IV, V and VI). The serum levels of glutamic oxaloacetic transaminase (SGOT), glutamate pyruvate transaminase (SGPT), alkaline phosphatase (SALP), γ-glutamyltransferase (γ -GT), and bilirubin were estimated along with activities of glutathione S-transferase (GST), glutathione reductase, hepatic malondialdehyde formation, and glutathione content. The substantially elevated serum enzymatic activities of SGOT, SGPT, SALP, γ-GT, and bilirubin due to CCl(4) treatment were restored toward normal in a dose-dependent manner. Meanwhile, the decreased activities of GST and glutathione reductase were also restored toward normal. In addition, ethyl acetate fraction also significantly prevented the elevation of hepatic malondialdehyde formation and depletion of reduced glutathione content in the liver of CCl(4)-intoxicated rats in a dose-dependent manner. Silymarin used as standard reference also exhibited significant hepatoprotective activity on post-treatment against CCl(4)-induced hepatotoxicity in rats. The biochemical observations were supplemented with histopathological examination of rat liver sections. The results of this study strongly indicate that ethyl acetate fraction has a potent hepatoprotective action against CCl(4)-induced hepatic damage in rats.
Q-balls of quasi-particles in a (2,0)-theory model of the fractional quantum Hall effect
Ganor, O.J.; Hong, Y.P.; Moore, N.; Sun, H.Y.; Tan, H.S.; Torres-Chicon, N.R.
2015-01-01
A toy model of the fractional quantum Hall effect appears as part of the low-energy description of the Coulomb branch of the A(1) (2, 0)-theory formulated on (S-1 x R-2)/Z(k), where the generator of Z(k) acts as a combination of translation on S-1 and rotation by 2 pi/k on R-2. At low energy the
The 4D Nucleome: Genome Compartmentalization in an Evolutionary Context.
Cremer, T; Cremer, M; Cremer, C
2018-04-01
4D nucleome research aims to understand the impact of nuclear organization in space and time on nuclear functions, such as gene expression patterns, chromatin replication, and the maintenance of genome integrity. In this review we describe evidence that the origin of 4D genome compartmentalization can be traced back to the prokaryotic world. In cell nuclei of animals and plants chromosomes occupy distinct territories, built up from ~1 Mb chromatin domains, which in turn are composed of smaller chromatin subdomains and also form larger chromatin domain clusters. Microscopic evidence for this higher order chromatin landscape was strengthened by chromosome conformation capture studies, in particular Hi-C. This approach demonstrated ~1 Mb sized, topologically associating domains in mammalian cell nuclei separated by boundaries. Mutations, which destroy boundaries, can result in developmental disorders and cancer. Nucleosomes appeared first as tetramers in the Archaea kingdom and later evolved to octamers built up each from two H2A, two H2B, two H3, and two H4 proteins. Notably, nucleosomes were lost during the evolution of the Dinoflagellata phylum. Dinoflagellate chromosomes remain condensed during the entire cell cycle, but their chromosome architecture differs radically from the architecture of other eukaryotes. In summary, the conservation of fundamental features of higher order chromatin arrangements throughout the evolution of metazoan animals suggests the existence of conserved, but still unknown mechanism(s) controlling this architecture. Notwithstanding this conservation, a comparison of metazoans and protists also demonstrates species-specific structural and functional features of nuclear organization.
Pathways and Subcellular Compartmentation of NAD Biosynthesis in Human Cells
Nikiforov, Andrey; Dölle, Christian; Niere, Marc; Ziegler, Mathias
2011-01-01
NAD is a vital redox carrier, and its degradation is a key element of important regulatory pathways. NAD-mediated functions are compartmentalized and have to be fueled by specific biosynthetic routes. However, little is known about the different pathways, their subcellular distribution, and regulation in human cells. In particular, the route(s) to generate mitochondrial NAD, the largest subcellular pool, is still unknown. To visualize organellar NAD changes in cells, we targeted poly(ADP-ribose) polymerase activity into the mitochondrial matrix. This activity synthesized immunodetectable poly(ADP-ribose) depending on mitochondrial NAD availability. Based on this novel detector system, detailed subcellular enzyme localizations, and pharmacological inhibitors, we identified extracellular NAD precursors, their cytosolic conversions, and the pathway of mitochondrial NAD generation. Our results demonstrate that, besides nicotinamide and nicotinic acid, only the corresponding nucleosides readily enter the cells. Nucleotides (e.g. NAD and NMN) undergo extracellular degradation resulting in the formation of permeable precursors. These precursors can all be converted to cytosolic and mitochondrial NAD. For mitochondrial NAD synthesis, precursors are converted to NMN in the cytosol. When taken up into the organelles, NMN (together with ATP) serves as substrate of NMNAT3 to form NAD. NMNAT3 was conclusively localized to the mitochondrial matrix and is the only known enzyme of NAD synthesis residing within these organelles. We thus present a comprehensive dissection of mammalian NAD biosynthesis, the groundwork to understand regulation of NAD-mediated processes, and the organismal homeostasis of this fundamental molecule. PMID:21504897
Nuclear Pore-Like Structures in a Compartmentalized Bacterium.
Directory of Open Access Journals (Sweden)
Evgeny Sagulenko
Full Text Available Planctomycetes are distinguished from other Bacteria by compartmentalization of cells via internal membranes, interpretation of which has been subject to recent debate regarding potential relations to Gram-negative cell structure. In our interpretation of the available data, the planctomycete Gemmata obscuriglobus contains a nuclear body compartment, and thus possesses a type of cell organization with parallels to the eukaryote nucleus. Here we show that pore-like structures occur in internal membranes of G.obscuriglobus and that they have elements structurally similar to eukaryote nuclear pores, including a basket, ring-spoke structure, and eight-fold rotational symmetry. Bioinformatic analysis of proteomic data reveals that some of the G. obscuriglobus proteins associated with pore-containing membranes possess structural domains found in eukaryote nuclear pore complexes. Moreover, immunogold labelling demonstrates localization of one such protein, containing a β-propeller domain, specifically to the G. obscuriglobus pore-like structures. Finding bacterial pores within internal cell membranes and with structural similarities to eukaryote nuclear pore complexes raises the dual possibilities of either hitherto undetected homology or stunning evolutionary convergence.
Compartmental analysis and dosimetric aspects applied to cholesterol with 3H labeled
International Nuclear Information System (INIS)
Oliveira, Adriano dos Santos
2015-01-01
Cardiovascular diseases (CVDs) are one of the major reasons of death around the world according to the World Health Organization (WHO). It is well known that changes in levels of plasma lipoproteins, which are responsible for the transport of cholesterol into the bloodstream, are associated with cardiovascular diseases. For this reason to know the biokinetic parameters of plasma lipoproteins and quantifies them is important to correct and deep understanding about the diseases associated with these disorders. The main aim of this study is to provide a biokinetic model and estimate the radiometric doses for 3 H-Cholesterol, a radioactive tracer widely used in physiological and metabolic studies. The model was based on [Schwartz et al. 2004] about the distribution of cholesterol by the lipoprotein and gastrointestinal model [ICRP 30, 1979]. The doses distribution in compartments of the model and other organs and tissues of a standard adult described in [ICRP 106, 2008] was calculated using MIRD method (Medical Internal Radiation Dose) and compartmental analysis using the computer program Matlab®. The dose coefficients were estimated for a standard phantom man (73 kg) described in [ICRP 60, 1991]. The estimated doses for both model and for other organs were low and did not exceed the highest dose obtained that was in the upper large intestine, as 44,8 μGy these parameters will assist in ethics committee's opinions on the use of works that use the 3 H-cholesterol which radioactive tracer. (author)
Maria Klimikova
2010-01-01
Understanding the reasons of the present financial problems lies In understanding the substance of fractional reserve banking. The substance of fractional banking is in lending more money than the bankers have. Banking of partial reserves is an alternative form which links deposit banking and credit banking. Fractional banking is causing many unfavorable economic impacts in the worldwide system, specifically an inflation.
Analytical modeling for fractional multi-dimensional diffusion equations by using Laplace transform
Directory of Open Access Journals (Sweden)
Devendra Kumar
2015-01-01
Full Text Available In this paper, we propose a simple numerical algorithm for solving multi-dimensional diffusion equations of fractional order which describes density dynamics in a material undergoing diffusion by using homotopy analysis transform method. The fractional derivative is described in the Caputo sense. This homotopy analysis transform method is an innovative adjustment in Laplace transform method and makes the calculation much simpler. The technique is not limited to the small parameter, such as in the classical perturbation method. The scheme gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.
Haanstra, Jurgen R.; Bakker, Barbara M.; Michels, Paul A. M.
Trypanosomatids sequester large parts of glucose metabolism inside specialised peroxisomes, called glycosomes. Many studies have shown that correct glycosomal compartmentalization of glycolytic enzymes is essential for bloodstream-form Trypanosoma brucel. The recent finding of pore-forming
An Empirical Model Of Fractionally Cointegrated Daily High And Low Stock Market Prices
Czech Academy of Sciences Publication Activity Database
Baruník, Jozef; Dvořáková, S.
2015-01-01
Roč. 45, č. 1 (2015), s. 193-206 ISSN 0264-9993 R&D Projects: GA ČR(CZ) GBP402/12/G097 Keywords : fractional cointegration * long memory * range * volatility * daily high and low prices Subject RIV: AH - Economics Impact factor: 0.997, year: 2015 http://library.utia.cas.cz/separaty/2014/E/barunik-0434888.pdf
Energy Technology Data Exchange (ETDEWEB)
Brown, Judith Alice [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Long, Kevin Nicholas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-05-01
This work was done to support customer questions about whether a Sylgard/Glass Microballoon (GMB) potting material in current use could be replaced with pure Sylgard and if this would significantly change stresses imparted to internal components under thermal cycling conditions. To address these questions, we provide micromechanics analysis of Sylgard/GMB materials using both analytic composite theory and finite element simulations to better understand the role of the GMB volume fraction in determining thermal expansion coefficient, elastic constants, and behavior in both confined and unconfined compression boundary value problems. A key finding is that damage accumulation in the material from breakage of GMBs significantly limits the global stress magnitude and results in a plateau stress behavior over large ranges of compressive strain. The magnitude of this plateau stress is reduced with higher volume fractions of GMBs. This effect is particularly pronounced in confined compression, which we estimate bears the most similarity to the application of interest. This stress-limiting damage mechanism is not present in pure Sylgard, however, and the result is much higher stresses under confined compression. Thus, we recommend that some volume fraction greater than 10% GMBs be used for confined deformation applications.
Numerical Methods for Pricing American Options with Time-Fractional PDE Models
Directory of Open Access Journals (Sweden)
Zhiqiang Zhou
2016-01-01
Full Text Available In this paper we develop a Laplace transform method and a finite difference method for solving American option pricing problem when the change of the option price with time is considered as a fractal transmission system. In this scenario, the option price is governed by a time-fractional partial differential equation (PDE with free boundary. The Laplace transform method is applied to the time-fractional PDE. It then leads to a nonlinear equation for the free boundary (i.e., optimal early exercise boundary function in Laplace space. After numerically finding the solution of the nonlinear equation, the Laplace inversion is used to transform the approximate early exercise boundary into the time space. Finally the approximate price of the American option is obtained. A boundary-searching finite difference method is also proposed to solve the free-boundary time-fractional PDEs for pricing the American options. Numerical examples are carried out to compare the Laplace approach with the finite difference method and it is confirmed that the former approach is much faster than the latter one.
Court, Felipe A.; Hewitt, Jane E.; Davies, Kay; Patton, Bruce L.; Uncini, Antonino; Wrabetz, Lawrence; Feltri, M. Laura
2009-01-01
Animal and plant cells compartmentalize to perform morphogenetic functions. Compartmentalization of myelin-forming Schwann cells may favor elongation of myelin segments to the size required for efficient conduction of nerve impulses. Compartments in myelinated fibers were described by Ramon-y-Cajal and depend on periaxin, mutated in the hereditary neuropathy Charcot-Marie-Tooth 4F. Lack of periaxin in mice causes loss of compartments, formation of short myelin segments (internodes) and reduce...
Povstenko, Yuriy
2015-01-01
This book is devoted to fractional thermoelasticity, i.e. thermoelasticity based on the heat conduction equation with differential operators of fractional order. Readers will discover how time-fractional differential operators describe memory effects and space-fractional differential operators deal with the long-range interaction. Fractional calculus, generalized Fourier law, axisymmetric and central symmetric problems and many relevant equations are featured in the book. The latest developments in the field are included and the reader is brought up to date with current research. The book contains a large number of figures, to show the characteristic features of temperature and stress distributions and to represent the whole spectrum of order of fractional operators. This work presents a picture of the state-of-the-art of fractional thermoelasticity and is suitable for specialists in applied mathematics, physics, geophysics, elasticity, thermoelasticity and engineering sciences. Corresponding sections of ...
Wilkerson, Trena L.; Bryan, Tommy; Curry, Jane
2012-01-01
This article describes how using candy bars as models gives sixth-grade students a taste for learning to represent fractions whose denominators are factors of twelve. Using paper models of the candy bars, students explored and compared fractions. They noticed fewer different representations for one-third than for one-half. The authors conclude…
Q-balls of quasi-particles in a (2, 0)-theory model of the fractional quantum Hall effect
Ganor, Ori J.; Hong, Yoon Pyo; Moore, Nathan; Sun, Hao-Yu; Tan, Hai Siong; Torres-Chicon, Nesty R.
2015-09-01
A toy model of the fractional quantum Hall effect appears as part of the low-energy description of the Coulomb branch of the A 1 (2 , 0)-theory formulated on ({S}^1× {{R}}^2)/{{Z}}_k , where the generator of {{Z}}_k acts as a combination of translation on S 1 and rotation by 2 π/k on {{R}}^2 . At low energy the configuration is described in terms of a 4+1D Super-Yang-Mills theory on a cone ({{R}}^2/{{Z}}_k) with additional 2+1D degrees of freedom at the tip of the cone that include fractionally charged particles. These fractionally charged "quasi-particles" are BPS strings of the (2 , 0)-theory wrapped on short cycles. We analyze the large k limit, where a smooth cigar-geometry provides an alternative description. In this framework a W-boson can be modeled as a bound state of k quasi-particles. The W-boson becomes a Q-ball, and it can be described as a soliton solution of Bogomolnyi monopole equations on a certain auxiliary curved space. We show that axisymmetric solutions of these equations correspond to singular maps from AdS 3 to AdS 2, and we present some numerical results and an asymptotic expansion.
Spinal Cord Tolerance to Reirradiation With Single-Fraction Radiosurgery: A Swine Model
Energy Technology Data Exchange (ETDEWEB)
Medin, Paul M., E-mail: Paul.medin@utsouthwestern.edu [Department of Radiation Oncology, University of Texas Southwestern Medical Center, Dallas, Texas (United States); Foster, Ryan D. [Department of Radiation Oncology, University of Texas Southwestern Medical Center, Dallas, Texas (United States); Kogel, Albert J. van der [Department of Radiation Oncology, Radboud University Medical Center Nijmegen, Nijmegen (Netherlands); Sayre, James W. [Department of Biostatistics and Radiology, University of California Los Angeles, Los Angeles, California (United States); McBride, William H. [Department of Radiation Oncology, University of California Los Angeles, Los Angeles, California (United States); Solberg, Timothy D. [Department of Radiation Oncology, University of Texas Southwestern Medical Center, Dallas, Texas (United States)
2012-07-01
Purpose: This study was performed to determine swine spinal cord tolerance to single-fraction, partial-volume irradiation 1 year after receiving uniform irradiation to 30 Gy in 10 fractions. Methods and Materials: A 10-cm length of spinal cord (C3-T1) was uniformly irradiated to 30 Gy in 10 consecutive fractions and reirradiated 1 year later with a single radiosurgery dose centered within the previously irradiated segment. Radiosurgery was delivered to a cylindrical volume approximately 5 cm in length and 2 cm in diameter, which was positioned laterally to the cervical spinal cord, resulting in a dose distribution with the 90%, 50%, and 10% isodose lines traversing the ipsilateral, central, and contralateral spinal cord, respectively. Twenty-three pigs were stratified into six dose groups with mean maximum spinal cord doses of 14.9 {+-} 0.1 Gy (n = 2), 17.1 {+-} 0.3 Gy (n = 3), 19.0 {+-} 0.1 Gy (n = 5), 21.2 {+-} 0.1 Gy (n = 5), 23.4 {+-} 0.2 Gy (n = 5), and 25.4 {+-} 0.4 Gy (n = 3). The mean percentage of spinal cord volumes receiving {>=}10 Gy for the same groups were 34% {+-} 1%, 40% {+-} 1%, 46% {+-} 3%, 52% {+-} 1%, 56 {+-} 3%, and 57% {+-} 1%. The study endpoint was motor neurologic deficit as determined by a change in gait during a 1- year follow-up period. Results: A steep dose-response curve was observed with a 50% incidence of paralysis (ED{sub 50}) for the maximum point dose of 19.7 Gy (95% confidence interval, 17.4-21.4). With two exceptions, histology was unremarkable in animals with normal neurologic status, while all animals with motor deficits showed some degree of demyelination and focal white matter necrosis on the irradiated side, with relative sparing of gray matter. Histologic comparison with a companion study of de novo irradiated animals revealed that retreatment responders had more extensive tissue damage, including infarction of gray matter, only at prescription doses >20 Gy. Conclusion: Pigs receiving spinal radiosurgery 1 year after
An analysis of heat conduction in polar bear hairs using one-dimensional fractional model
Directory of Open Access Journals (Sweden)
Zhu Wei-Hong
2016-01-01
Full Text Available Hairs of a polar bear are of superior properties such as the excellent thermal protection. The polar bears can perennially live in an extremely cold environment and can maintain body temperature at around 37 °C. Why do polar bears can resist such cold environment? Its membrane-pore structure plays an important role. In the previous work, we established a 1-D fractional heat conduction equation to reveal the hidden mechanism for the hairs. In this paper, we further discuss solutions and parameters of the equation established and analyze heat conduction in polar bear hairs.
Energy Technology Data Exchange (ETDEWEB)
Beccari, M; Longo, G; Majone, M; Rolle, E; Scarinci, A [Rome ' ' La Sapienza' ' Univ. (Italy). Dept. of Chemistry
1993-01-01
The organic fraction of municipal solid waste represents a potential feedstock to be treated through biorefining. However, the process feasibility strongly depends on the effectiveness of a chemical pretreatment. Consequently, experimentation aimed at choosing the optimal type of reagent (alkali or acids) and optimal operating conditions was carried out. The best results were obtained using NaOH at room temperature. Solubilization data are in good agreement with a kinetics based on two competing reactions. Simulation of the overall process (pretreatment and acidogenic fermentation) taking place in two CFSTR reactors shows that an optimum ratio exists between the hydraulic residence times of the two stages of the process. (author)
On Drift Parameter Estimation in Models with Fractional Brownian Motion by Discrete Observations
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Yuliya Mishura
2014-06-01
Full Text Available We study a problem of an unknown drift parameter estimation in a stochastic differen- tial equation driven by fractional Brownian motion. We represent the likelihood ratio as a function of the observable process. The form of this representation is in general rather complicated. However, in the simplest case it can be simplified and we can discretize it to establish the a. s. convergence of the discretized version of maximum likelihood estimator to the true value of parameter. We also investigate a non-standard estimator of the drift parameter showing further its strong consistency.
Directory of Open Access Journals (Sweden)
Renxin Xiao
2016-03-01
Full Text Available In order to properly manage lithium-ion batteries of electric vehicles (EVs, it is essential to build the battery model and estimate the state of charge (SOC. In this paper, the fractional order forms of Thevenin and partnership for a new generation of vehicles (PNGV models are built, of which the model parameters including the fractional orders and the corresponding resistance and capacitance values are simultaneously identified based on genetic algorithm (GA. The relationships between different model parameters and SOC are established and analyzed. The calculation precisions of the fractional order model (FOM and integral order model (IOM are validated and compared under hybrid test cycles. Finally, extended Kalman filter (EKF is employed to estimate the SOC based on different models. The results prove that the FOMs can simulate the output voltage more accurately and the fractional order EKF (FOEKF can estimate the SOC more precisely under dynamic conditions.
Compartmentation and complexation of metals in hyperaccumulator plants
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Barbara eLeitenmaier
2013-09-01
Full Text Available Hyperaccumulators are being intensely investigated. They are not only interesting in scientific context due to their strange behaviour in terms of dealing with high concentrations of metals, but also because of their use in phytoremediation and phytomining, for which understanding the mechanisms of hyperaccumulation is crucial. Hyperaccumulators naturally use metal accumulation as a defence against herbivores and pathogens, and therefore deal with accumulated metals in very specific ways of complexation and compartmentation, different from non-hyperaccumulator plants and also non-hyperaccumulated metals. For example, in contrast to non-hyperaccumulators, in hyperaccumulators even the classical phytochelatin-inducing metal, cadmium, is predominantly not bound by such sulfur ligands, but only by weak oxygen ligands. This applies to all hyperaccumulated metals investigated so far, as well as hyperaccumulation of the metalloid arsenic. Stronger ligands, as they have been shown to complex metals in non-hyperaccumulators, are in hyperaccumulators used for transient binding during transport to the storage sites. This confirmed that enhanced active metal transport, and not metal complexation, is the key mechanism of hyperaccumulation. Hyperaccumulators tolerate the high amount of accumulated heavy metals by sequestering them into vacuoles, usually in large storage cells of the epidermis. This is mediated by strongly elevated expression of specific transport proteins in various tissues from metal uptake in the shoots up to the storage sites in the leaf epidermis. However, this mechanism seems to be very metal specific. Non-hyperaccumulated metals in hyperaccumulators seem to be dealt with like in non-hyperaccumulator plants, i.e. detoxified by binding to strong ligands such as metallothioneins.
Polydeoxyribonucleotide improves wound healing of fractional laser resurfacing in rat model.
Yu, Mi; Lee, Jun Young
2017-02-01
Polydeoxyribonucleotide (PDRN) is an active compound that can promote wound healing. PDRN stimulates wound healing by enhancing angiogenesis and increasing fibroblast growth rates. Laser skin resurfacing is a popular cosmetic procedure for skin rejuvenation. Despite excellent improvement of photo-damaged skin and acne scarring, it is accompanied with drawbacks, such as prolonged erythema and crusting. This study was designed to assess the effect of PDRN on wounds induced by fractional laser resurfacing. Twelve male rats aged 8 weeks were randomly assigned to the PDRN treatment group and the control group. Wounds were induced using a fractional ablative CO 2 laser. The treatment group received daily injections of PDRN and the control group received injections of the vehicle. Wound healing assessed by clinical features and histopathologic findings. The process of wound healing was faster in the treatment group than in the control group. In the histopathological examination, the granulation tissue thickness score of the treatment group was significantly higher than that of the control group. Results of immunohistochemical staining showed a marked increase of VEGF-positive cells and PECAM-1/CD31-positive microvessels in the treatment group. PDRN may be a beneficial option to promote wound healing after laser treatment.
Diffusion with space memory modelled with distributed order space fractional differential equations
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M. Caputo
2003-06-01
Full Text Available Distributed order fractional differential equations (Caputo, 1995, 2001; Bagley and Torvik, 2000a,b were fi rst used in the time domain; they are here considered in the space domain and introduced in the constitutive equation of diffusion. The solution of the classic problems are obtained, with closed form formulae. In general, the Green functions act as low pass fi lters in the frequency domain. The major difference with the case when a single space fractional derivative is present in the constitutive equations of diffusion (Caputo and Plastino, 2002 is that the solutions found here are potentially more fl exible to represent more complex media (Caputo, 2001a. The difference between the space memory medium and that with the time memory is that the former is more fl exible to represent local phenomena while the latter is more fl exible to represent variations in space. Concerning the boundary value problem, the difference with the solution of the classic diffusion medium, in the case when a constant boundary pressure is assigned and in the medium the pressure is initially nil, is that one also needs to assign the fi rst order space derivative at the boundary.
FRACTIONAL CRYSTALLIZATION OF HANFORD SINGLE-SHELL TANK WASTES. A MODELING APPROACH
International Nuclear Information System (INIS)
HAMILTON, D.W.
2006-01-01
The Hanford site has 149 underground single-shell tanks (SST) storing mostly soluble, multi-salt, mixed wastes resulting from Cold War era weapons material production. These wastes must be retrieved and the salts immobilized before the tanks can be closed to comply with an overall site closure consent order entered into by the U.S. Department of Energy (DOE), the Environmental Protection Agency, and Washington State. Water will be used to retrieve the wastes and the resulting solution will be pumped to the proposed treatment process where a high curie (primarily 137 Cs) waste fraction will be separated from the other waste constituents. The separated waste streams will then be vitrified to allow for safe storage as an immobilized high level waste, or low level waste, borosilicate glass. Fractional crystallization, a common unit operation for production of industrial chemicals and pharmaceuticals, was proposed as the method to separate the salt wastes; it works by evaporating excess water until the solubilities of various species in the solution are exceeded (the solubility of a particular species depends on its concentration, temperature of the solution, and the presence of other ionic species in the solution). By establishing the proper conditions, selected pure salts can be crystallized and separated from the radioactive liquid phase
Heterogeneity and compartmental properties of insulin storage and secretion in rat islets
International Nuclear Information System (INIS)
Gold, G.; Landahl, H.D.; Gishizky, M.L.; Grodsky, G.M.
1982-01-01
To investigate compartmental properties of insulin storage and secretion, isolated rat islets were used for pulse-labeling experiments, after which proinsulin and insulin were purified rigorously. Processing of proinsulin to insulin neared completion by 3 h without additional loss of either radioactive peptide by cellular or extracellular proteolysis. The amount of labeled hormone rapidly diminished in islets; it was secreted at a higher fractional rate than immunoreactive insulin, resulting in secreted insulin's having a higher specific activity than the average cellular insulin. Newly synthesized insulin, therefore, was secreted preferentially. Changes in the specific activity of secreted and cellular insulin with time were consistent with changes predicted for islets containing 33% of their total insulin in a glucose-labile compartment. Predictions were based on steady-state analysis of a simple storage-limited representation of B cell function. Islets from either the dorsal or ventral part of the pancreas also contained 33% of their total insulin in a glucose-labile compartment. The same compartment was mobilized by 20 mM glucose, 50 mM potassium + 2 mM glucose, or 20 MM glucose + 1 mM 3-isobutylmethylxanthine as indicated by the specific activity ratio of secreted vs. cellular insulin, even though average secretion rates with these stimuli differed by more than threefold. In the absence of calcium, the effectiveness of 20 mM glucose as a secretagogue declined markedly, and the older stored insulin was preferentially mobilized because secreted insulin had a lower rather than a higher specific activity than cellular insulin. Results provide insight into the mechanisms of nonrandom mobilization and secretion of insulin form the B cell
Merola, Alberto; Murphy, Kevin; Stone, Alan J; Germuska, Michael A; Griffeth, Valerie E M; Blockley, Nicholas P; Buxton, Richard B; Wise, Richard G
2016-04-01
Several techniques have been proposed to estimate relative changes in cerebral metabolic rate of oxygen consumption (CMRO2) by exploiting combined BOLD fMRI and cerebral blood flow data in conjunction with hypercapnic or hyperoxic respiratory challenges. More recently, methods based on respiratory challenges that include both hypercapnia and hyperoxia have been developed to assess absolute CMRO2, an important parameter for understanding brain energetics. In this paper, we empirically optimize a previously presented "original calibration model" relating BOLD and blood flow signals specifically for the estimation of oxygen extraction fraction (OEF) and absolute CMRO2. To do so, we have created a set of synthetic BOLD signals using a detailed BOLD signal model to reproduce experiments incorporating hypercapnic and hyperoxic respiratory challenges at 3T. A wide range of physiological conditions was simulated by varying input parameter values (baseline cerebral blood volume (CBV0), baseline cerebral blood flow (CBF0), baseline oxygen extraction fraction (OEF0) and hematocrit (Hct)). From the optimization of the calibration model for estimation of OEF and practical considerations of hypercapnic and hyperoxic respiratory challenges, a new "simplified calibration model" is established which reduces the complexity of the original calibration model by substituting the standard parameters α and β with a single parameter θ. The optimal value of θ is determined (θ=0.06) across a range of experimental respiratory challenges. The simplified calibration model gives estimates of OEF0 and absolute CMRO2 closer to the true values used to simulate the experimental data compared to those estimated using the original model incorporating literature values of α and β. Finally, an error propagation analysis demonstrates the susceptibility of the original and simplified calibration models to measurement errors and potential violations in the underlying assumptions of isometabolism
Directory of Open Access Journals (Sweden)
Luiza G. Ungarova
2016-12-01
Full Text Available We considere and analyze the uniaxial phenomenological models of viscoelastic deformation based on fractional analogues of Scott Blair, Voigt, Maxwell, Kelvin and Zener rheological models. Analytical solutions of the corresponding differential equations are obtained with fractional Riemann–Liouville operators under constant stress with further unloading, that are written by the generalized (two-parameter fractional exponential function and contains from two to four parameters depending on the type of model. A method for identifying the model parameters based on the background information for the experimental creep curves with constant stresses was developed. Nonlinear problem of parametric identification is solved by two-step iterative method. The first stage uses the characteristic data points diagrams and features in the behavior of the models under unrestricted growth of time and the initial approximation of parameters are determined. At the second stage, the refinement of these parameters by coordinate descent (the Hooke–Jeeves's method and minimizing the functional standard deviation for calculated and experimental values is made. Method of identification is realized for all the considered models on the basis of the known experimental data uniaxial viscoelastic deformation of Polyvinylchloride Elastron at a temperature of 20∘C and five the tensile stress levels. Table-valued parameters for all models are given. The errors analysis of constructed phenomenological models is made to experimental data over the entire ensemble of curves viscoelastic deformation. It was found that the approximation errors for the Scott Blair fractional model is 14.17 %, for the Voigt fractional model is 11.13 %, for the Maxvell fractional model is 13.02 %, for the Kelvin fractional model 10.56 %, for the Zener fractional model is 11.06 %. The graphs of the calculated and experimental dependences of viscoelastic deformation of Polyvinylchloride
Flow of magnetic particles in blood with isothermal heating: A fractional model for two-phase flow
Ali, Farhad; Imtiaz, Anees; Khan, Ilyas; Sheikh, Nadeem Ahmad
2018-06-01
In the sixteenth century, medical specialists were of the conclusion that magnet can be utilized for the treatment or wipe out the illnesses from the body. On this basis, the research on magnet advances day by day for the treatment of different types of diseases in mankind. This study aims to investigate the effect of magnetic field and their applications in human body specifically in blood. Blood is a non-Newtonian fluid because its viscosity depends strongly on the fraction of volume occupied by red cells also called the hematocrit. Therefore, in this paper blood is considered as an example of non-Newtonian Casson fluid. The blood flow is considered in a vertical cylinder together with heat transfer due to mixed conviction caused by buoyancy force and the external pressure gradient. Effect of magnetic field on the velocities of blood and magnetic particles is also considered. The problem is modelled using the Caputo-Fabrizio derivative approach. The governing fractional partial differential equations are solved using Laplace and Hankel transformation techniques and exact solutions are obtained. Effects of different parameters such as Grashof number, Prandtl number, Casson fluid parameter and fractional parameters, and magnetic field are shown graphically. Both velocity profiles increase with the increase of Grashoff number and Casson fluid parameter and reduce with the increase of magnetic field.
International Nuclear Information System (INIS)
Li, Huizhen; Wei, Yanli; Lydy, Michael J.; You, Jing
2014-01-01
The dynamic flux of an organophosphate and four pyrethroid pesticides was determined in an air-(soil)-water-sediment system based on monitoring data from Guangzhou, China. The total air–water flux, including air–water gaseous exchange and atmospheric deposition, showed deposition from air to water for chlorpyrifos, bifenthrin and cypermethrin, but volatilization for lambda-cyhalothrin and permethrin. The transport of the pesticides from overlying water to sediment suggested that sediment acted as a sink for the pesticides. Additionally, distinct annual atmospheric depositional fluxes between legacy and current-use pesticides suggested the role of consumer usage in their transport throughout the system. Finally, pesticide toxicity was estimated from annual air–water-sediment flux within an urban stream in Guangzhou. A dynamic flux-based risk assessment indicated that inter-compartmental transport of chlorpyrifos decreased its atmospheric exposure, but had little influence on its aquatic toxicity. Instead, water-to-sediment transport of pyrethroids increased their sediment toxicity, which was supported by previously reported toxicity data. - Highlights: • Transport fluxes of chlorpyrifos and pyrethroids were assessed in Guangzhou, China. • Sediment acted as a sink for chlorpyrifos and pyrethroids. • Air-to-water transport decreased the exposure risk of atmospheric chlorpyrifos. • Dynamic transport might increase the risk of pyrethroids in air and sediment. • Flux-based pesticide concentrations provide a way to estimate sediment toxicity. - Regional risk assessment could be improved by integrating dynamic flux information derived from inter-compartmental models
DEFF Research Database (Denmark)
Jin, Biao; Rolle, Massimo
: dichlorobenzamide (BAM), isoproturon (IPU) and diclofenac (DCF). The model successfully reproduces the multi-element isotope data, and precisely captures the dual element isotope trends, characterizing the different degradation pathways. Besides illustrating the model capability of mechanistic evaluation...
Feingold, Graham; Balsells, Joseph; Glassmeier, Franziska; Yamaguchi, Takanobu; Kazil, Jan; McComiskey, Allison
2017-07-01
The relationship between the albedo of a cloudy scene A and cloud fraction fc is studied with the aid of heuristic models of stratocumulus and cumulus clouds. Existing work has shown that scene albedo increases monotonically with increasing cloud fraction but that the relationship varies from linear to superlinear. The reasons for these differences in functional dependence are traced to the relationship between cloud deepening and cloud widening. When clouds deepen with no significant increase in fc (e.g., in solid stratocumulus), the relationship between A and fc is linear. When clouds widen as they deepen, as in cumulus cloud fields, the relationship is superlinear. A simple heuristic model of a cumulus cloud field with a power law size distribution shows that the superlinear A-fc behavior is traced out either through random variation in cloud size distribution parameters or as the cloud field oscillates between a relative abundance of small clouds (steep slopes on a log-log plot) and a relative abundance of large clouds (flat slopes). Oscillations of this kind manifest in large eddy simulation of trade wind cumulus where the slope and intercept of the power law fit to the cloud size distribution are highly correlated. Further analysis of the large eddy model-generated cloud fields suggests that cumulus clouds grow larger and deeper as their underlying plumes aggregate; this is followed by breakup of large plumes and a tendency to smaller clouds. The cloud and thermal size distributions oscillate back and forth approximately in unison.
International Nuclear Information System (INIS)
Nilsson, P.; Joiner, M.C.
1990-01-01
A generalized equation for cell survival or tissue effects after fractionated low dose-rate irradiations, when there is incomplete repair between fractions and significant repair during fractions, is derived in terms of the h- and g-functions of the 'incomplete-repair' (IR) model. The model is critically dependent on α/β, repair half-time, treatment time and interfraction interval, and should therefore be regarded primarily as a tool for the analysis of fractionation and dose-rate effects in carefully designed radiobiological experiments, although it should also be useful in exploring, in a general way, the feasibility of clinical treatment protocols using fractionated low dose-rate treatments. (author)
Binder, Harald; Sauerbrei, Willi; Royston, Patrick
2013-06-15
In observational studies, many continuous or categorical covariates may be related to an outcome. Various spline-based procedures or the multivariable fractional polynomial (MFP) procedure can be used to identify important variables and functional forms for continuous covariates. This is the main aim of an explanatory model, as opposed to a model only for prediction. The type of analysis often guides the complexity of the final model. Spline-based procedures and MFP have tuning parameters for choosing the required complexity. To compare model selection approaches, we perform a simulation study in the linear regression context based on a data structure intended to reflect realistic biomedical data. We vary the sample size, variance explained and complexity parameters for model selection. We consider 15 variables. A sample size of 200 (1000) and R(2) = 0.2 (0.8) is the scenario with the smallest (largest) amount of information. For assessing performance, we consider prediction error, correct and incorrect inclusion of covariates, qualitative measures for judging selected functional forms and further novel criteria. From limited information, a suitable explanatory model cannot be obtained. Prediction performance from all types of models is similar. With a medium amount of information, MFP performs better than splines on several criteria. MFP better recovers simpler functions, whereas splines better recover more complex functions. For a large amount of information and no local structure, MFP and the spline procedures often select similar explanatory models. Copyright © 2012 John Wiley & Sons, Ltd.
International Nuclear Information System (INIS)
Tyapkin, A.A.
1976-01-01
The problem is raised on the interpretation of quarks having fractional quantum numbers as structural quasi-particles. A new composite model is proposed on the basis of the fundamental triplet representation of fermions having integral quantum numbers