An evaluation of mathematical models for predicting skin permeability.
Lian, Guoping; Chen, Longjian; Han, Lujia
2008-01-01
A number of mathematical models have been proposed for predicting skin permeability, mostly empirical and very few are deterministic. Early empirical models use simple lipophilicity parameters. The recent trend is to use more complicated molecular structure descriptors. There has been much debate on which models best predict skin permeability. This article evaluates various mathematical models using a comprehensive experimental dataset of skin permeability for 124 chemical compounds compiled from various sources. Of the seven models compared, the deterministic model of Mitragotri gives the best prediction. The simple quantitative structure permeability relationships (QSPR) model of Potts and Guy gives the second best prediction. The two models have many features in common. Both assume the lipid matrix as the pathway of transdermal permeation. Both use octanol-water partition coefficient and molecular size. Even the mathematical formulae are similar. All other empirical QSPR models that use more complicated molecular structure descriptors fail to provide satisfactory prediction. The molecular structure descriptors in the more complicated QSPR models are empirically related to skin permeation. The mechanism on how these descriptors affect transdermal permeation is not clear. Mathematically it is an ill-defined approach to use many colinearly related parameters rather than fewer independent parameters in multi-linear regression.
A mathematical look at a physical power prediction model
DEFF Research Database (Denmark)
Landberg, L.
1998-01-01
This article takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations and to give guidelines as to where simplifications can be made and where they cannot....... The article shows that there is a linear dependence between the geostrophic wind and the local wind at the surface, but also that great care must be taken in the selection of the simple mathematical models, since physical dependences play a very important role, e.g. through the dependence of the turning...
Predictive control applied to an evaporator mathematical model
Directory of Open Access Journals (Sweden)
Daniel Alonso Giraldo Giraldo
2010-07-01
Full Text Available This paper outlines designing a predictive control model (PCM applied to a mathematical model of a falling film evaporator with mechanical steam compression like those used in the dairy industry. The controller was designed using the Connoisseur software package and data gathered from the simulation of a non-linear mathematical model. A control law was obtained from minimising a cost function sublect to dynamic system constraints, using a quadratic programme (QP algorithm. A linear programming (LP algorithm was used for finding a sub-optimal operation point for the process in stationary state.
A mathematical look at a physical power prediction model
Energy Technology Data Exchange (ETDEWEB)
Landberg, L. [Riso National Lab., Roskilde (Denmark)
1997-12-31
This paper takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations, and to give guidelines as to where the simplifications can be made and where they can not. This paper shows that there is a linear dependence between the geostrophic wind and the wind at the surface, but also that great care must be taken in the selection of the models since physical dependencies play a very important role, e.g. through the dependence of the turning of the wind on the wind speed.
Mathematical models for predicting indoor air quality from smoking activity.
Ott, W R
1999-01-01
Much progress has been made over four decades in developing, testing, and evaluating the performance of mathematical models for predicting pollutant concentrations from smoking in indoor settings. Although largely overlooked by the regulatory community, these models provide regulators and risk assessors with practical tools for quantitatively estimating the exposure level that people receive indoors for a given level of smoking activity. This article reviews the development of the mass balanc...
Mathematical models for predicting indoor air quality from smoking activity.
Ott, W R
1999-05-01
Much progress has been made over four decades in developing, testing, and evaluating the performance of mathematical models for predicting pollutant concentrations from smoking in indoor settings. Although largely overlooked by the regulatory community, these models provide regulators and risk assessors with practical tools for quantitatively estimating the exposure level that people receive indoors for a given level of smoking activity. This article reviews the development of the mass balance model and its application to predicting indoor pollutant concentrations from cigarette smoke and derives the time-averaged version of the model from the basic laws of conservation of mass. A simple table is provided of computed respirable particulate concentrations for any indoor location for which the active smoking count, volume, and concentration decay rate (deposition rate combined with air exchange rate) are known. Using the indoor ventilatory air exchange rate causes slightly higher indoor concentrations and therefore errs on the side of protecting health, since it excludes particle deposition effects, whereas using the observed particle decay rate gives a more accurate prediction of indoor concentrations. This table permits easy comparisons of indoor concentrations with air quality guidelines and indoor standards for different combinations of active smoking counts and air exchange rates. The published literature on mathematical models of environmental tobacco smoke also is reviewed and indicates that these models generally give good agreement between predicted concentrations and actual indoor measurements.
Outcome Prediction in Mathematical Models of Immune Response to Infection.
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Manuel Mai
Full Text Available Clinicians need to predict patient outcomes with high accuracy as early as possible after disease inception. In this manuscript, we show that patient-to-patient variability sets a fundamental limit on outcome prediction accuracy for a general class of mathematical models for the immune response to infection. However, accuracy can be increased at the expense of delayed prognosis. We investigate several systems of ordinary differential equations (ODEs that model the host immune response to a pathogen load. Advantages of systems of ODEs for investigating the immune response to infection include the ability to collect data on large numbers of 'virtual patients', each with a given set of model parameters, and obtain many time points during the course of the infection. We implement patient-to-patient variability v in the ODE models by randomly selecting the model parameters from distributions with coefficients of variation v that are centered on physiological values. We use logistic regression with one-versus-all classification to predict the discrete steady-state outcomes of the system. We find that the prediction algorithm achieves near 100% accuracy for v = 0, and the accuracy decreases with increasing v for all ODE models studied. The fact that multiple steady-state outcomes can be obtained for a given initial condition, i.e. the basins of attraction overlap in the space of initial conditions, limits the prediction accuracy for v > 0. Increasing the elapsed time of the variables used to train and test the classifier, increases the prediction accuracy, while adding explicit external noise to the ODE models decreases the prediction accuracy. Our results quantify the competition between early prognosis and high prediction accuracy that is frequently encountered by clinicians.
Simple Mathematical Models Do Not Accurately Predict Early SIV Dynamics
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Cecilia Noecker
2015-03-01
Full Text Available Upon infection of a new host, human immunodeficiency virus (HIV replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the “standard” mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV. First, we found that the mode of virus production by infected cells (budding vs. bursting has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral
Mathematical modelling methodologies in predictive food microbiology: a SWOT analysis.
Ferrer, Jordi; Prats, Clara; López, Daniel; Vives-Rego, Josep
2009-08-31
Predictive microbiology is the area of food microbiology that attempts to forecast the quantitative evolution of microbial populations over time. This is achieved to a great extent through models that include the mechanisms governing population dynamics. Traditionally, the models used in predictive microbiology are whole-system continuous models that describe population dynamics by means of equations applied to extensive or averaged variables of the whole system. Many existing models can be classified by specific criteria. We can distinguish between survival and growth models by seeing whether they tackle mortality or cell duplication. We can distinguish between empirical (phenomenological) models, which mathematically describe specific behaviour, and theoretical (mechanistic) models with a biological basis, which search for the underlying mechanisms driving already observed phenomena. We can also distinguish between primary, secondary and tertiary models, by examining their treatment of the effects of external factors and constraints on the microbial community. Recently, the use of spatially explicit Individual-based Models (IbMs) has spread through predictive microbiology, due to the current technological capacity of performing measurements on single individual cells and thanks to the consolidation of computational modelling. Spatially explicit IbMs are bottom-up approaches to microbial communities that build bridges between the description of micro-organisms at the cell level and macroscopic observations at the population level. They provide greater insight into the mesoscale phenomena that link unicellular and population levels. Every model is built in response to a particular question and with different aims. Even so, in this research we conducted a SWOT (Strength, Weaknesses, Opportunities and Threats) analysis of the different approaches (population continuous modelling and Individual-based Modelling), which we hope will be helpful for current and future
Mathematical model predicts the elastic behavior of composite materials
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Zoroastro de Miranda Boari
2005-03-01
Full Text Available Several studies have found that the non-uniform distribution of reinforcing elements in a composite material can markedly influence its characteristics of elastic and plastic deformation and that a composite's overall response is influenced by the physical and geometrical properties of its reinforcing phases. The finite element method, Eshelby's method and dislocation mechanisms are usually employed in formulating a composite's constitutive response. This paper discusses a composite material containing SiC particles in an aluminum matrix. The purpose of this study was to find the correlation between a composite material's particle distribution and its resistance, and to come up with a mathematical model to predict the material's elastic behavior. The proposed formulation was applied to establish the thermal stress field in the aluminum-SiC composite resulting from its fabrication process, whereby the mixture is prepared at 600 °C and the composite material is used at room temperature. The analytical results, which are presented as stress probabilities, were obtained from the mathematical model proposed herein. These results were compared with the numerical ones obtained by the FEM method. A comparison of the results of the two methods, analytical and numerical, reveals very similar average thermal stress values. It is also shown that Maxwell-Boltzmann's distribution law can be applied to identify the correlation between the material's particle distribution and its resistance, using Eshelby's thermal stresses.
Eck, Christof; Knabner, Peter
2017-01-01
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
Iyer, Shivkumar Venkatraman; Wu, Bin; Li, Yunwei; Singh, Birendra
2015-12-01
This paper proposes a simplified mathematical model to predict the impact of connection of Distributed Generators (DGs) to the ac grid. The model allows the user to examine the fluctuations in the magnitude of voltages at different nodes in the distribution system. In order to use the model, the user does not require a commercial simulation software making it a handy tool for a practicing engineer. Analysis has been presented to describe how the detailed mathematical model of the system is reduced using elementary matrix manipulation techniques to obtain the final simplified mathematical model. Simulation results are presented to verify the mathematical model with a ring distribution system with three DGs connected to it and the results validate those attained from the mathematical model.
ECONOMIC AND MATHEMATICAL MODEL OF PREDICTION OF DEVIATION IN MOSCOW SUBURBAN RAILWAY COMPLEX
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Dmitry I. Valdman
2013-01-01
Full Text Available The article deals with the theoretical aspects of mathematical modeling and forecasting. Additionally, it describes a mathematical model for forecasting the number of incidents, depending on the number of different types of planned works with one and the same subject in service facilities, validation of the model via substituting of the data and comparing the predicted values calculated by the model and the actual values for the same periods.
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...
Directory of Open Access Journals (Sweden)
Timothy Heazlewood
2006-12-01
Full Text Available A number of studies have attempted to predict future Olympic performances in athletics and swimming based on trends displayed in previous Olympic Games. Some have utilised linear models to plot and predict change, whereas others have utilised multiple curve estimation methods based on inverse, sigmoidal, quadratic, cubic, compound, logistic, growth and exponential functions. The non linear models displayed closer fits to the actual data and were used to predict performance changes 10's, 100's and 1000's of years into the future. Some models predicted that in some events male and female times and distances would crossover and females would eventually display superior performance to males. Predictions using mathematical models based on pre-1996 athletics and pre-1998 swimming performances were evaluated based on how closely they predicted sprints and jumps, and freestyle swimming performances for both male and females at the 2000 and 2004 Olympic Games. The analyses revealed predictions were closer for the shorter swimming events where men's 50m and women's 50m and 100m actual times were almost identical to predicted times. For both men and women, as the swim distances increased the accuracy of the predictive model decreased, where predicted times were 4.5-7% faster than actual times achieved. The real trends in some events currently displaying performance declines were not foreseen by the mathematical models, which predicted consistent improvements across all athletic and swimming events selected for in this study
2016-01-01
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
A Mathematical Model for the Prediction of Fluid Responsiveness
Lansdorp, B.; Putten, van M.J.A.M.; Keijzer, de A.; Pickkers, P.; Oostrom, van J.
2013-01-01
Fluid therapy is commonly used to improve cardiac output in hemodynamically instable patients in the intensive care unit. However, to predict whether patients will benefit from this intervention (i. e. are volume responsive), is difficult. Dynamic indices, that rely on heart-lung interactions, have
Taylor, Kate; Appuhamy, J.A.D.R.N.; Dijkstra, J.; Kebreab, E.
2016-01-01
The aim of this study was to develop and evaluate mathematical models that predict mineral excretion, particularly calcium (Ca), magnesium (Mg) and selenium (Se), from lactating dairy cows. Mineral excretion can be affected by several dietary factors. A deficiency in Ca or Mg application to pasture,
Burlatsky, S F; O'Neill, J; Atrazhev, V V; Varyukhin, A N; Dmitriev, D V; Erikhman, N S
2013-01-01
Under typical PEM fuel cell operating conditions, part of membrane electrode assembly is subjected to humidity cycling due to variation of inlet gas RH and/or flow rate. Cyclic membrane hydration/dehydration would cause cyclic swelling/shrinking of the unconstrained membrane. In a constrained membrane, it causes cyclic stress resulting in mechanical failure in the area adjacent to the gas inlet. A mathematical modeling framework for prediction of the lifetime of a PEM FC membrane subjected to hydration cycling is developed in this paper. The model predicts membrane lifetime as a function of RH cycling amplitude and membrane mechanical properties. The modeling framework consists of three model components: a fuel cell RH distribution model, a hydration/dehydration induced stress model that predicts stress distribution in the membrane, and a damage accrual model that predicts membrane life-time. Short descriptions of the model components along with overall framework are presented in the paper. The model was used...
Agata, Yasuyoshi; Iwao, Yasunori; Miyagishima, Atsuo; Itai, Shigeru
2010-04-01
A mechanistic mathematical model was designed to predict dissolution patterns under non-sink conditions. Sulfamethoxazole was used as a model drug, and its physico-chemical properties such as solubility, density, and intrinsic dissolution rate constant etc., were investigated in order to apply these experimental values to the proposed model. Dissolution tests were employed as a way of validating the mathematical model, and it was found that the predictions given by the model were surprisingly accurate for all particle sizes. In addition, a simulation focused on forecasting the fraction of the drug that was dissolved at a certain time point when various initial particle diameters were used was also particularly valuable. Therefore, these results demonstrated that the model enables dissolution profiles to be analyzed under non-sink conditions.
Development of mathematical model to predict the mechanical properties of friction stir
Directory of Open Access Journals (Sweden)
R. Palanivel
2011-01-01
Full Text Available This paper presents a systematic approach to develop the mathematical model for predicting the ultimate tensile strength,yield strength, and percentage of elongation of AA6351 aluminum alloy which is widely used in automotive, aircraft anddefense Industries by incorporating (FSW friction stir welding process parameter such as tool rotational speed, weldingspeed, and axial force. FSW has been carried out based on three factors five level central composite rotatable design withfull replications technique. Response surface methodology (RSM is employed to develop the mathematical model. Analysisof variance (ANOVA Technique is used to check the adequacy of the developed mathematical model. The developedmathematical model can be used effectively at 95% confidence level. The effect of FSW process parameter on mechanicalproperties of AA6351 aluminum alloy has been analyzed in detail.
Classical mathematical models for description and prediction of experimental tumor growth.
Directory of Open Access Journals (Sweden)
Sébastien Benzekry
2014-08-01
Full Text Available Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1 to determine a statistical model for description of the measurement error, 2 to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3 to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80% extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70% beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.
Pragmatism, mathematical models, and the scientific ideal of prediction and control.
Moore, J
2015-05-01
Mathematical models are often held to be valuable, if not necessary, for theories and explanations in the quantitative analysis of behavior. The present review suggests that mathematical models primarily derived from the observation of functional relations do indeed contribute to the scientific value of theories and explanations, even though the final form of the models appears to be highly abstract. However, mathematical models not primarily so derived risk being essentialist in character, based on a particular view of formal causation. Such models invite less effective and frequently mentalistic theories and explanations of behavior. Models may be evaluated in terms of both (a) the verbal processes responsible for their origin and development and (b) the prediction and control engendered by the theories and explanations that incorporate the models, however indirect or abstract that prediction and control may be. Overall, the present review suggests that technological application and theoretical contemplation may be usefully viewed as continuous and overlapping forms of scientific activity, rather than dichotomous and mutually exclusive.
Mendel's use of mathematical modelling: ratios, predictions and the appeal to tradition.
Teicher, Amir
2014-01-01
The seventh section of Gregor Mendel's famous 1866 paper contained a peculiar mathematical model, which predicted the expected ratios between the number of constant and hybrid types, assuming self-pollination continued throughout further generations. This model was significant for Mendel's argumentation and was perceived as inseparable from his entire theory at the time. A close examination of this model reveals that it has several perplexing aspects which have not yet been systematically scrutinized. The paper analyzes those aspects, dispels some common misconceptions regarding the interpretation of the model, and re-evaluates the role of this model for Mendel himself. In light of the resulting analysis, Mendel's position between nineteenth-century hybridist tradition and twentieth-century population genetics is reassessed, and his sophisticated use of mathematics to legitimize his innovative theory is uncovered.
How Good Can We Get? Using mathematical models to predict the future of athletics
Mureika, J R
1998-01-01
Track and field world records have risen and fallen throughout the history of the sport. A recent rash of record-breaking performances has prompted the question: "How good can we get?". This article offers a review of several attempts to answer this question, based on mathematical modeling of key physiological processes. The predictions are compared with present-day world records, and a discussion of the future of athletics ensues...
Mathematical Model of Load Pass and Prediction of Fatigue Life on Bolt Threads with Reduced Lead
Asayama, Yukiteru
A mathematical model is proposed in order to elucidate the mechanism that the fatigue strength of external threads increases by reducing the lead on a thread system such as a bolt and nut. The model is constructed from the concept that a local strain proportional to the reducing degree of the lead, although the local strain is at first produced in the bolt thread farthest from the bearing surface of the nut, is induced in each thread root with an increase of applied load. The fatigue life predicted from the mathematical model shows good agreement with the experimental fatigue life of cadmium-plated external threads with the reduced lead on the material having strength as high as 1270MPa. The model can provide useful suggestions for the design of fasteners for aerospace, which are required to satisfy severe requirements of fatigue strengths and dimensions.
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Edori, E. S
2016-08-01
Full Text Available A model for predicting the corrosion rates in the furnace internal wall tubes of the refinery boiler was resolved, using the first order differential equation derived from the material balance equation of the system. The mathematical model was able to predict the metal loss recorded by ultrasonic thickness scanning technique (UTS, and the results shows an agreement. The results from both the model and UTS shows that in the various tubes of the furnace, internal wall of the refinery boiler were between the same range. The percentage deviation which was calculated to ascertain the acceptability of the model result as compared to that from UTS proved that the model is effective. The inhibitor model result show that corrosion will drastically reduce in the presence of corrosion inhibitors under proper chemical treatment and management. The model developed can be used to monitor furnace internal wall corrosion even when the system is in operation by extrapolating the result to further years.
Mathematical Modeling and Pure Mathematics
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
A mathematical model to predict the release of water-soluble drugs from HPMC matrices.
Fu, X C; Wang, G P; Fu, C Y; Liang, W Q
2004-09-01
A mathematical model to predict the fraction of water-soluble drug released as a function of release time (t, h), HPMC concentration (CH, w/w), and volume of drug molecule (V, nm3) was derived with ranitidine hydrochloride, diltiazem hydrochloride, and ribavirin as model drugs. The model is log (M(t)/M(infinity)) = 0.5 log t-0.3322CH-0.2222V-0.2988 (n = 140, r = 0.9848), where M(t) is the amount of drug released at time t, M(infinity) is the amount of drug released over a very long time, which corresponds in principle to the initial loading, n is the number of samples, and r is the correlation coefficient. The model was validated using isoniazid and satisfactory results were obtained. The model can be used to predict the release fraction of various soluble drugs from HPMC matrices having different polymer levels.
Lee, Dongchul; Hershey, Brad; Bradley, Kerry; Yearwood, Thomas
2011-07-01
To understand the theoretical effects of pulse width (PW) programming in spinal cord stimulation (SCS), we implemented a mathematical model of electrical fields and neural activation in SCS to gain insight into the effects of PW programming. The computational model was composed of a finite element model for structure and electrical properties, coupled with a nonlinear double-cable axon model to predict nerve excitation for different myelinated fiber sizes. Mathematical modeling suggested that mediolateral lead position may affect chronaxie and rheobase values, as well as predict greater activation of medial dorsal column fibers with increased PW. These modeling results were validated by a companion clinical study. Thus, variable PW programming in SCS appears to have theoretical value, demonstrated by the ability to increase and even 'steer' spatial selectivity of dorsal column fiber recruitment. It is concluded that the computational SCS model is a valuable tool to understand basic mechanisms of nerve fiber excitation modulated by stimulation parameters such as PW and electric fields.
Energy Technology Data Exchange (ETDEWEB)
Rockne, R; Alvord, E C Jr; Swanson, K R [Department of Pathology, University of Washington, 1959 NE Pacific St, Seattle, WA 98195 (United States); Rockhill, J K; Kalet, I; Hendrickson, K [Department of Radiation Oncology, University of Washington, 1959 NE Pacific St, Seattle, WA 98195 (United States); Mrugala, M; Spence, A M [Department of Neurology, University of Washington, 1959 NE Pacific St, Seattle, WA 98195 (United States); Lai, A; Cloughesy, T, E-mail: krae@uw.ed [Department of Neurology, University of California, 710 Westwood Plaza, Los Angeles, CA 90095 (United States)
2010-06-21
Glioblastoma multiforme (GBM) is the most malignant form of primary brain tumors known as gliomas. They proliferate and invade extensively and yield short life expectancies despite aggressive treatment. Response to treatment is usually measured in terms of the survival of groups of patients treated similarly, but this statistical approach misses the subgroups that may have responded to or may have been injured by treatment. Such statistics offer scant reassurance to individual patients who have suffered through these treatments. Furthermore, current imaging-based treatment response metrics in individual patients ignore patient-specific differences in tumor growth kinetics, which have been shown to vary widely across patients even within the same histological diagnosis and, unfortunately, these metrics have shown only minimal success in predicting patient outcome. We consider nine newly diagnosed GBM patients receiving diagnostic biopsy followed by standard-of-care external beam radiation therapy (XRT). We present and apply a patient-specific, biologically based mathematical model for glioma growth that quantifies response to XRT in individual patients in vivo. The mathematical model uses net rates of proliferation and migration of malignant tumor cells to characterize the tumor's growth and invasion along with the linear-quadratic model for the response to radiation therapy. Using only routinely available pre-treatment MRIs to inform the patient-specific bio-mathematical model simulations, we find that radiation response in these patients, quantified by both clinical and model-generated measures, could have been predicted prior to treatment with high accuracy. Specifically, we find that the net proliferation rate is correlated with the radiation response parameter (r = 0.89, p = 0.0007), resulting in a predictive relationship that is tested with a leave-one-out cross-validation technique. This relationship predicts the tumor size post-therapy to within inter
A New Mathematical Model for Flank Wear Prediction Using Functional Data Analysis Methodology
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Sonja Jozić
2014-01-01
Full Text Available This paper presents a new approach improving the reliability of flank wear prediction during the end milling process. In the present work, prediction of flank wear has been achieved by using cutting parameters and force signals as the sensitive carriers of information about the machining process. A series of experiments were conducted to establish the relationship between flank wear and cutting force components as well as the cutting parameters such as cutting speed, feed per tooth, and radial depth of cut. In order to be able to predict flank wear a new linear regression mathematical model has been developed by utilizing functional data analysis methodology. Regression coefficients of the model are in the form of time dependent functions that have been determined through the use of functional data analysis methodology. The mathematical model has been developed by means of applied cutting parameters and measured cutting forces components during the end milling of workpiece made of 42CrMo4 steel. The efficiency and flexibility of the developed model have been verified by comparing it with the separate experimental data set.
Roll paper pilot. [mathematical model for predicting pilot rating of aircraft in roll task
Naylor, F. R.; Dillow, J. D.; Hannen, R. A.
1973-01-01
A mathematical model for predicting the pilot rating of an aircraft in a roll task is described. The model includes: (1) the lateral-directional aircraft equations of motion; (2) a stochastic gust model; (3) a pilot model with two free parameters; and (4) a pilot rating expression that is a function of rms roll angle and the pilot lead time constant. The pilot gain and lead time constant are selected to minimize the pilot rating expression. The pilot parameters are then adjusted to provide a 20% stability margin and the adjusted pilot parameters are used to compute a roll paper pilot rating of the aircraft/gust configuration. The roll paper pilot rating was computed for 25 aircraft/gust configurations. A range of actual ratings from 2 to 9 were encountered and the roll paper pilot ratings agree quite well with the actual ratings. In addition there is good correlation between predicted and measured rms roll angle.
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Solomon Ndubuisi Eluozo
2012-11-01
Full Text Available Development of mathematical model to predict the transport of dissolved arsenic in groundwater influenced by seepage velocity has been carried out. This model was developed to monitor the rate of concentration at different period and depths. High and low concentrations were observed at different periods and depth as presented in the figures. These conditions can be attributed to soil stratification deposition in the study location and the influence of man-made activities. Based on these facts, it is recommended that risk assessment should be thoroughly done for soil and water and the predicted model should be applied in design and construction of groundwater system in the study area.
Energy Technology Data Exchange (ETDEWEB)
Goldsby, Michael E.; Mayo, Jackson R.; Bhattacharyya, Arnab (Massachusetts Institute of Technology, Cambridge, MA); Armstrong, Robert C.; Vanderveen, Keith
2008-09-01
The goal of this research was to examine foundational methods, both computational and theoretical, that can improve the veracity of entity-based complex system models and increase confidence in their predictions for emergent behavior. The strategy was to seek insight and guidance from simplified yet realistic models, such as cellular automata and Boolean networks, whose properties can be generalized to production entity-based simulations. We have explored the usefulness of renormalization-group methods for finding reduced models of such idealized complex systems. We have prototyped representative models that are both tractable and relevant to Sandia mission applications, and quantified the effect of computational renormalization on the predictive accuracy of these models, finding good predictivity from renormalized versions of cellular automata and Boolean networks. Furthermore, we have theoretically analyzed the robustness properties of certain Boolean networks, relevant for characterizing organic behavior, and obtained precise mathematical constraints on systems that are robust to failures. In combination, our results provide important guidance for more rigorous construction of entity-based models, which currently are often devised in an ad-hoc manner. Our results can also help in designing complex systems with the goal of predictable behavior, e.g., for cybersecurity.
Mathematical Models of Pluripotent Stem Cells: At the Dawn of Predictive Regenerative Medicine.
Pir, Pınar; Le Novère, Nicolas
2016-01-01
Regenerative medicine, ranging from stem cell therapy to organ regeneration, is promising to revolutionize treatments of diseases and aging. These approaches require a perfect understanding of cell reprogramming and differentiation. Predictive modeling of cellular systems has the potential to provide insights about the dynamics of cellular processes, and guide their control. Moreover in many cases, it provides alternative to experimental tests, difficult to perform for practical or ethical reasons. The variety and accuracy of biological processes represented in mathematical models grew in-line with the discovery of underlying molecular mechanisms. High-throughput data generation led to the development of models based on data analysis, as an alternative to more established modeling based on prior mechanistic knowledge. In this chapter, we give an overview of existing mathematical models of pluripotency and cell fate, to illustrate the variety of methods and questions. We conclude that current approaches are yet to overcome a number of limitations: Most of the computational models have so far focused solely on understanding the regulation of pluripotency, and the differentiation of selected cell lineages. In addition, models generally interrogate only a few biological processes. However, a better understanding of the reprogramming process leading to ESCs and iPSCs is required to improve stem-cell therapies. One also needs to understand the links between signaling, metabolism, regulation of gene expression, and the epigenetics machinery.
Mathematical modeling for prediction and optimization of TIG welding pool geometry
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U. Esme
2009-04-01
Full Text Available In this work, nonlinear and multi-objective mathematical models were developed to determine the process parameters corresponding to optimum weld pool geometry. The objectives of the developed mathematical models are to maximize tensile load (TL, penetration (P, area of penetration (AP and/or minimize heat affected zone (HAZ, upper width (UW and upper height (UH depending upon the requirements.
Yamamoto, Kimiyo N.; Ishii, Masatsugu; Inoue, Yoshihiro; Hirokawa, Fumitoshi; MacArthur, Ben D.; Nakamura, Akira; Haeno, Hiroshi; Uchiyama, Kazuhisa
2016-10-01
Although the capacity of the liver to recover its size after resection has enabled extensive liver resection, post-hepatectomy liver failure remains one of the most lethal complications of liver resection. Therefore, it is clinically important to discover reliable predictive factors after resection. In this study, we established a novel mathematical framework which described post-hepatectomy liver regeneration in each patient by incorporating quantitative clinical data. Using the model fitting to the liver volumes in series of computed tomography of 123 patients, we estimated liver regeneration rates. From the estimation, we found patients were divided into two groups: i) patients restored the liver to its original size (Group 1, n = 99) and ii) patients experienced a significant reduction in size (Group 2, n = 24). From discriminant analysis in 103 patients with full clinical variables, the prognosis of patients in terms of liver recovery was successfully predicted in 85–90% of patients. We further validated the accuracy of our model prediction using a validation cohort (prediction = 84–87%, n = 39). Our interdisciplinary approach provides qualitative and quantitative insights into the dynamics of liver regeneration. A key strength is to provide better prediction in patients who had been judged as acceptable for resection by current pragmatic criteria.
Yamamoto, Kimiyo N.; Ishii, Masatsugu; Inoue, Yoshihiro; Hirokawa, Fumitoshi; MacArthur, Ben D.; Nakamura, Akira; Haeno, Hiroshi; Uchiyama, Kazuhisa
2016-01-01
Although the capacity of the liver to recover its size after resection has enabled extensive liver resection, post-hepatectomy liver failure remains one of the most lethal complications of liver resection. Therefore, it is clinically important to discover reliable predictive factors after resection. In this study, we established a novel mathematical framework which described post-hepatectomy liver regeneration in each patient by incorporating quantitative clinical data. Using the model fitting to the liver volumes in series of computed tomography of 123 patients, we estimated liver regeneration rates. From the estimation, we found patients were divided into two groups: i) patients restored the liver to its original size (Group 1, n = 99); and ii) patients experienced a significant reduction in size (Group 2, n = 24). From discriminant analysis in 103 patients with full clinical variables, the prognosis of patients in terms of liver recovery was successfully predicted in 85–90% of patients. We further validated the accuracy of our model prediction using a validation cohort (prediction = 84–87%, n = 39). Our interdisciplinary approach provides qualitative and quantitative insights into the dynamics of liver regeneration. A key strength is to provide better prediction in patients who had been judged as acceptable for resection by current pragmatic criteria. PMID:27694914
Energy Technology Data Exchange (ETDEWEB)
Handy, B.J.; Greene, J.C. [NNC Solutions Ltd, Warrington (United Kingdom)
2004-09-01
NNC limited provides an ion exchange resin technology facility, which includes a resin testing service. A range of ion exchange resin properties is measured and this includes ion exchange capacity, resin bead particle sizes and anion kinetic performance in terms of mass transfer coefficients. It has long been considered by the authors that the experimental data for resins taken from operating condensate polishing plant (CPP) could be used to predict the expected plant performance. This has now been realised with the development of a mathematical model which predicts CPP behaviour using appropriate experimentally derived parameters and plant design data. Modelling methods for the separate anion and cation components of a mixed bed were initially developed before the mixed bed as a whole was addressed. Initially, an analytical approach was adopted, which proved successful for simple cases. For more complex examples a numerical approach was developed and found to be more suitable. The paper describes the development of anion and cation bed models, and a mixed bed model. In the latter model, the anion and cation components modelled earlier are combined, and used to model simultaneously typical concentrations of ammonia, sodium, chloride and sulphate. Examples of operation are given, and observations and points of interest are discussed with respect to the calculated concentration profiles. The experimental behaviour of a number of resin samples taken from operating plant was examined in a purpose-built ultrapure water recirculation loop equipped with a range of analytical instruments. This has permitted the observed experimental results to be compared with model predictions. The next stage of the model development is to identify plants suitable for testing the model against real plant performance and the authors are now seeking to identify plant managers interested in collaborating in this venture. (orig.)
Mathematical modelling to predict the roughness average in micro milling process
Burlacu, C.; Iordan, O.
2016-08-01
Surface roughness plays a very important role in micro milling process and in any machining process, because indicates the state of the machined surface. Many surface roughness parameters that can be used to analyse a surface, but the most common surface roughness parameter used is the average roughness (Ra). This paper presents the experimental results obtained at micro milling of the C45W steel and the ways to determine the Ra parameter with respect to the working conditions. The chemical characteristics of the material were determined from a spectral analysis, chemical composition was measured at one point and two points, graphical and tabular. A profilometer Surtronic 3+ was used to examine the surface roughness profiles; the effect of independent parameters can be investigated and can get a proper relationship between the Ra parameter and the process variables. The mathematical model were developed, using multiple regression method with four independent variables D, v, ap, fz; the analysis was done using statistical software SPSS. The ANOVA analysis of variance and the F- test was used to justify the accuracy of the mathematical model. The multiple regression method was used to determine the correlation between a criterion variable and the predictor variables. The prediction model can be used for micro milling process optimization.
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Aitziber Ojanguren
2013-06-01
Full Text Available Industrial processes that apply high temperatures in the presence of oxygen may compromise the stability of conjugated linoleic acid (CLA bioactive isomers. Statistical techniques are used in this study to model and predict, on a laboratory scale, the oxidative behaviour of oil with high CLA content, controlling the limiting factors of food processing. This modelling aims to estimate the impact of an industrial frying process (140 °C, 7 L/h air on the oxidation of CLA oil for use as frying oil instead of sunflower oil. A factorial design was constructed within a temperature (80–200 °C and air flow (7–20 L/h range. Oil stability index (Rancimat method was used as a measure of oxidation. Three-level full factorial design was used to obtain a quadratic model for CLA oil, enabling the oxidative behaviour to be predicted under predetermined process conditions (temperature and air flow. It is deduced that temperatures applied in food processes affect the oxidation of CLA to a greater extent than air flow. As a result, it is estimated that the oxidative stability of CLA oil is less resistant to industrial frying than sunflower oil. In conclusion, thanks to the mathematical model, a good choice of the appropriate industrial food process can be selected to avoid the oxidation of the bioactive isomers of CLA, ensuring its functionality in novel applications.
The epidemiological impact of antiretroviral use predicted by mathematical models: a review
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Ferguson Neil M
2005-09-01
Full Text Available Abstract This review summarises theoretical studies attempting to assess the population impact of antiretroviral therapy (ART use on mortality and HIV incidence. We describe the key parameters that determine the impact of therapy, and argue that mathematical models of disease transmission are the natural framework within which to explore the interaction between antiviral use and the dynamics of an HIV epidemic. Our review focuses on the potential effects of ART in resource-poor settings. We discuss choice of model type and structure, the potential for risk behaviour change following widespread introduction of ART, the importance of the stage of HIV infection at which treatment is initiated, and the potential for spread of drug resistance. These issues are illustrated with results from models of HIV transmission. We demonstrate that HIV transmission models predicting the impact of ART use should incorporate a realistic progression through stages of HIV infection in order to capture the effect of the timing of treatment initiation on disease spread. The realism of existing models falls short of properly reproducing patterns of diagnosis timing, incorporating heterogeneity in sexual behaviour, and describing the evolution and transmission of drug resistance. The uncertainty surrounding certain effects of ART, such as changes in sexual behaviour and transmission of ART-resistant HIV strains, demands exploration of best and worst case scenarios in modelling, but this must be complemented by surveillance and behavioural surveys to quantify such effects in settings where ART is implemented.
Tsuruyama, Tatsuaki
2014-01-01
A biological signal is transmitted by interactions between signaling molecules in the cell. To date, there have been extensive studies regarding signaling pathways using numerical simulation of kinetic equations that are based on equations of continuity and Fick's law. To obtain a mathematical formulation of cell signaling, we propose a stability kinetic model of cell biological signaling of a simple two-parameter model based on the kinetics of the diffusion-limiting step. In the present model, the signaling is regulated by the binding of a cofactor, such as ATP. Non-linearity of the kinetics is given by the diffusion fluctuation in the interaction between signaling molecules, which is different from previous works that hypothesized autocatalytic reactions. Numerical simulations showed the presence of a critical concentration of the cofactor beyond which the cell signaling molecule concentration is altered in a chaos-like oscillation with frequency, which is similar to a discontinuous phase transition in physics. Notably, we found that the frequency is given by the logarithm function of the difference of the outside cofactor concentration from the critical concentration. This implies that the outside alteration of the cofactor concentration is transformed into the oscillatory alteration of cell inner signaling. Further, mathematical stability kinetic analysis predicted a discontinuous dynamic phase transition in the critical state at which the cofactor concentration is equivalent to the critical concentration. In conclusion, the present model illustrates a unique feature of cell signaling, and the stability analysis may provide an analytical framework of the cell signaling system and a novel formulation of biological signaling.
Mathematical modeling of herpes simplex virus-2 suppression with pritelivir predicts trial outcomes
Schiffer, Joshua T.; Swan, David A.; Magaret, Amalia; Corey, Lawrence; Wald, Anna; Ossig, Joachim; Ruebsamen-Schaeff, Helga; Stoelben, Susanne; Timmler, Burkhard; Zimmermann, Holger; Melhem, Murad R.; Van Wart, Scott A.; Rubino, Christopher M.; Birkmann, Alexander
2016-01-01
Pharmacokinetic and pharmacodynamic models estimate the potency of antiviral agents but do not capture viral and immunologic factors that drive the natural dynamics of infection. We designed a mathematical model that synthesizes pharmacokinetics, pharmacodynamics and viral pathogenesis concepts to simulate the activity of pritelivir, a DNA helicase-primase inhibitor that targets herpes simplex virus. Our simulations recapitulate detailed viral kinetic shedding features in five dosage arms of a phase 2 clinical trial. We identify that in vitro estimates of EC50 are lower than in vivo values for the drug. Nevertheless, pritelivir potently decreases shedding at appropriate doses based on its mode of action and long half-life. While pritelivir directly inhibits replication in epithelial cells, our model indicates that pritelivir also indirectly limits downstream viral spread from neurons to genital keratinocytes, within genital ulcers, and from ulcer to new mucosal sites of infection. We validate our model based on its ability to predict outcomes in a subsequent trial with a higher dose. The model can therefore be employed to optimize dose selection in clinical practice. PMID:26843190
A mathematical outcome prediction model in severe head injury : a pilot study.
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Mukherjee K
2000-01-01
Full Text Available 103 patients of head injury, with a Glasgow coma scale (GCS score of 8 or less, were studied prospectively. GCS score, brain stem reflexes, motor score, reaction level scale, and Glasgow Liege scale were evaluated as prognostic variables. Linear logistic regression analysis was used to obtain coefficients of these variables and mathematical formulae developed to predict outcome in individual patients.
W.A. Stolk (Wilma); S.J. de Vlas (Sake); J.D.F. Habbema (Dik)
2006-01-01
textabstractMathematical simulation models for transmission and control of lymphatic filariasis are useful tools for studying the prospects of lymphatic filariasis elimination. Two simulation models are currently being used. The first, EPIFIL, is a population-based, deterministic model that simulate
Mathematical problems in meteorological modelling
Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella
2016-01-01
This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...
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Leonardo H. D. Messias, Homero G. Ferrari, Ivan G. M. Reis, Pedro P. M. Scariot, Fúlvia B. Manchado-Gobatto
2015-03-01
Full Text Available The purpose of this study was to analyze if different combinations of trials as well as mathematical models can modify the aerobic and anaerobic estimates from critical velocity protocol applied in canoe slalom. Fourteen male elite slalom kayakers from Brazilian canoe slalom team (K1 were evaluated. Athletes were submitted to four predictive trials of 150, 300, 450 and 600 meters in a lake and the time to complete each trial was recorded. Critical velocity (CV-aerobic parameter and anaerobic paddling capacity (APC-anaerobic parameter were obtained by three mathematical models (Linear1=distance-time; Linear 2=velocity-1/time and Non-Linear = time-velocity. Linear 1 was chosen for comparison of predictive trials combinations. Standard combination (SC was considered as the four trials (150, 300, 450 and 600 m. High fits of regression were obtained from all mathematical models (range - R² = 0.96-1.00. Repeated measures ANOVA pointed out differences of all mathematical models for CV (p = 0.006 and APC (p = 0.016 as well as R² (p = 0.033. Estimates obtained from the first (1 and the fourth (4 predictive trials (150 m = lowest; and 600 m = highest, respectively were similar and highly correlated (r=0.98 for CV and r = 0.96 for APC with the SC. In summary, methodological aspects must be considered in critical velocity application in canoe slalom, since different combinations of trials as well as mathematical models resulted in different aerobic and anaerobic estimates.
Time estimation predicts mathematical intelligence.
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Peter Kramer
Full Text Available BACKGROUND: Performing mental subtractions affects time (duration estimates, and making time estimates disrupts mental subtractions. This interaction has been attributed to the concurrent involvement of time estimation and arithmetic with general intelligence and working memory. Given the extant evidence of a relationship between time and number, here we test the stronger hypothesis that time estimation correlates specifically with mathematical intelligence, and not with general intelligence or working-memory capacity. METHODOLOGY/PRINCIPAL FINDINGS: Participants performed a (prospective time estimation experiment, completed several subtests of the WAIS intelligence test, and self-rated their mathematical skill. For five different durations, we found that time estimation correlated with both arithmetic ability and self-rated mathematical skill. Controlling for non-mathematical intelligence (including working memory capacity did not change the results. Conversely, correlations between time estimation and non-mathematical intelligence either were nonsignificant, or disappeared after controlling for mathematical intelligence. CONCLUSIONS/SIGNIFICANCE: We conclude that time estimation specifically predicts mathematical intelligence. On the basis of the relevant literature, we furthermore conclude that the relationship between time estimation and mathematical intelligence is likely due to a common reliance on spatial ability.
Messias, Leonardo H D; Ferrari, Homero G; Reis, Ivan G M; Scariot, Pedro P M; Manchado-Gobatto, Fúlvia B
2015-03-01
The purpose of this study was to analyze if different combinations of trials as well as mathematical models can modify the aerobic and anaerobic estimates from critical velocity protocol applied in canoe slalom. Fourteen male elite slalom kayakers from Brazilian canoe slalom team (K1) were evaluated. Athletes were submitted to four predictive trials of 150, 300, 450 and 600 meters in a lake and the time to complete each trial was recorded. Critical velocity (CV-aerobic parameter) and anaerobic paddling capacity (APC-anaerobic parameter) were obtained by three mathematical models (Linear1=distance-time; Linear 2=velocity-1/time and Non-Linear = time-velocity). Linear 1 was chosen for comparison of predictive trials combinations. Standard combination (SC) was considered as the four trials (150, 300, 450 and 600 m). High fits of regression were obtained from all mathematical models (range - R² = 0.96-1.00). Repeated measures ANOVA pointed out differences of all mathematical models for CV (p = 0.006) and APC (p = 0.016) as well as R² (p = 0.033). Estimates obtained from the first (1) and the fourth (4) predictive trials (150 m = lowest; and 600 m = highest, respectively) were similar and highly correlated (r=0.98 for CV and r = 0.96 for APC) with the SC. In summary, methodological aspects must be considered in critical velocity application in canoe slalom, since different combinations of trials as well as mathematical models resulted in different aerobic and anaerobic estimates. Key pointsGreat attention must be given for methodological concerns regarding critical velocity protocol applied on canoe slalom, since different estimates were obtained depending on the mathematical model and the predictive trials used.Linear 1 showed the best fits of regression. Furthermore, to the best of our knowledge and considering practical applications, this model is the easiest one to calculate the estimates from critical velocity protocol. Considering this, the abyss between science
Ramakrishnan, Sridhar; Lu, Wei; Laxminarayan, Srinivas; Wesensten, Nancy J; Rupp, Tracy L; Balkin, Thomas J; Reifman, Jaques
2015-06-01
Humans display a trait-like response to sleep loss. However, it is not known whether this trait-like response can be captured by a mathematical model from only one sleep-loss condition to facilitate neurobehavioural performance prediction of the same individual during a different sleep-loss condition. In this paper, we investigated the extent to which the recently developed unified mathematical model of performance (UMP) captured such trait-like features for different sleep-loss conditions. We used the UMP to develop two sets of individual-specific models for 15 healthy adults who underwent two different sleep-loss challenges (order counterbalanced; separated by 2-4 weeks): (i) 64 h of total sleep deprivation (TSD) and (ii) chronic sleep restriction (CSR) of 7 days of 3 h nightly time in bed. We then quantified the extent to which models developed using psychomotor vigilance task data under TSD predicted performance data under CSR, and vice versa. The results showed that the models customized to an individual under one sleep-loss condition accurately predicted performance of the same individual under the other condition, yielding, on average, up to 50% improvement over non-individualized, group-average model predictions. This finding supports the notion that the UMP captures an individual's trait-like response to different sleep-loss conditions. © 2014 European Sleep Research Society.
MATHEMATICAL MODELS FOR THE PREDICTION OF THE ENCAPSULATION BEHAVIOR IN FOOD SYSTEMS
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Iuliana Vinitila
2010-07-01
Full Text Available The simulation of the encapsulation behavior in the multiphase complex system such food structure is based on the mathematical models constructed in respect with the Non-equilibrium thermodynamics Theory, Flory-Huggins Free Volume Theory (FHFV and Complex Dispersed Systems (CDS.The present research paper presents the differential equations describing the evolution in time of the multiphase dividing surfaces and the excess quantities such as surface density, surface momentum, surface energy and surface entropy associated with the dividing surfaces. The new completed theory of bio-polymers phase transitions co-jointed from Interfacial Transport Phenomena (ITP, FHFV and CDS will be validated with the inverse analysis method.
Longhi, Daniel Angelo; Dalcanton, Francieli; Falcão de Aragão, Gláucia Maria; Carciofi, Bruno Augusto Mattar; Laurindo, João Borges
2013-10-21
Mathematical models taking temperature variations into account are useful in predicting microbial growth in foods, like meat products, for which Lactobacillus plantarum is a mesophilic and one of the main spoiling bacterium. The current study assessed the ability of the main primary models and their non-isothermal versions to predict L. plantarum growth under constant and variable temperature. Experimental data of microbial growth were obtained in MRS medium under isothermal conditions (4, 8, 12, 16, 20, and 30°C) which were used to obtain the secondary models. The experimental data under non-isothermal conditions (periodically oscillating temperature between the plateaus 4-12, 5-15, and 20-30°C) were used to validate the non-isothermal models. The bias factors indicated that all assessed models provided safe predictions of the microorganism growth at the non-isothermal conditions. Overall, despite the very good performance of the primary models (isothermal), none of the models was able to predict with accuracy the L. plantarum growth under temperature variations, mainly when the temperature range was close to refrigeration temperature. Incorporating the complex microbial adaptation mechanisms into the predictive models is a challenge to be overcome.
Teaching Mathematical Modeling in Mathematics Education
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
Ebben, Matthew R.; Krieger, Ana C.
2016-03-01
The intent of this study is to develop a predictive model to convert an oxygen desaturation index (ODI) to an apnea-hypopnea index (AHI). This model will then be compared to actual AHI to determine its precision. One thousand four hundred and sixty-seven subjects given polysomnograms with concurrent pulse oximetry between April 14, 2010, and February 7, 2012, were divided into model development (n=733) and verification groups (n=734) in order to develop a predictive model of AHI using ODI. Quadratic regression was used for model development. The coefficient of determination (r2) between the actual AHI and the predicted AHI (PredAHI) was 0.80 (r=0.90), which was significant at a papnea.
Quality Prediction and Control of Reducing Pipe Based on EOS-ELM-RPLS Mathematics Modeling Method
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Dong Xiao
2014-01-01
Full Text Available The inspection of inhomogeneous transverse and longitudinal wall thicknesses, which determines the quality of reducing pipe during the production of seamless steel reducing pipe, is lags and difficult to establish its mechanism model. Aiming at the problems, we proposed the quality prediction model of reducing pipe based on EOS-ELM-RPLS algorithm, which taking into account the production characteristics of its time-varying, nonlinearity, rapid intermission, and data echelon distribution. Key contents such as analysis of data time interval, solving of mean value, establishment of regression model, and model online prediction were introduced and the established prediction model was used in the quality prediction and iteration control of reducing pipe. It is shown through experiment and simulation that the prediction and iteration control method based on EOS-ELM-RPLS model can effectively improve the quality of steel reducing pipe, and, moreover, its maintenance cost was low and it has good characteristics of real time, reliability, and high accuracy.
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Tsang-Pai Liu
2012-03-01
Conclusion: In summary, the greater predictive accuracy and precision made the application of BIA with the BP–ANN mathematical model more feasible for the clinical measurement of FM and FFM in the lower limbs of elderly people.
Energy Technology Data Exchange (ETDEWEB)
Ge, Y.T.; Tassou, S.A. [Brunel Univ., Dept. of Mechanical Engineering, Uxbridge (United Kingdom)
2000-04-01
This paper describes a mathematical model developed to simulate the performance of supermarket refrigeration systems. Such a model can be used for the comparison of different systems and control strategies in terms of their energy and total equivalent warming impact. The model is based on a larger number of component models which have been linked together within the TRNSYS environment. Major component models include the compressor, air-cooled condenser, thermostatic expansion valve, display cabinet and control. The overall system model has been validated against monitored data obtained from both a laboratory-based system and a full-scale system in a supermarket in Scotland. The value of the model is illustrated by determining and comparing the effectiveness of head pressure and variable-speed control against fixed head pressure and constant speed control. It is shown that even at summer ambient conditions the system can be operated without problems at much lower head pressures than is done in practice under fixed-pressure control strategies. The use of variable-speed control on one of the compressors can also provide better control of the suction pressure and a substantial (up to 23 per cent) energy savings compared to on-off control. (Author)
Mathematical model for prediction of pyrolysis and ignition of wood under external heat flux
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The pyrolysis and ignition of combustible materials is an important aspect of the processes taking place in an unwanted fire. A prediction model presented in this paper is to study pyrolysis and ignition time of wood under external heat flux. The solution of the model provides the temperature at each point of the solid and the local solid conversion. And the time to ignition of the wood is predicted with the solution of surface temperature. In general, a good agreement between experimental and theoretical results is obtained.
Panayidou, Klea; Gsteiger, Sandro; Egger, Matthias; Kilcher, Gablu; Carreras, Máximo; Efthimiou, Orestis; Debray, Thomas P A; Trelle, Sven; Hummel, Noemi
2016-09-01
The performance of a drug in a clinical trial setting often does not reflect its effect in daily clinical practice. In this third of three reviews, we examine the applications that have been used in the literature to predict real-world effectiveness from randomized controlled trial efficacy data. We searched MEDLINE, EMBASE from inception to March 2014, the Cochrane Methodology Register, and websites of key journals and organisations and reference lists. We extracted data on the type of model and predictions, data sources, validation and sensitivity analyses, disease area and software. We identified 12 articles in which four approaches were used: multi-state models, discrete event simulation models, physiology-based models and survival and generalized linear models. Studies predicted outcomes over longer time periods in different patient populations, including patients with lower levels of adherence or persistence to treatment or examined doses not tested in trials. Eight studies included individual patient data. Seven examined cardiovascular and metabolic diseases and three neurological conditions. Most studies included sensitivity analyses, but external validation was performed in only three studies. We conclude that mathematical modelling to predict real-world effectiveness of drug interventions is not widely used at present and not well validated. © 2016 The Authors Research Synthesis Methods Published by John Wiley & Sons Ltd.
A Predictive Mathematical Model of Muscle Forces for Children with Cerebral Palsy
Lee, Samuel C. K.; Ding, Jun; Prosser, Laura A.; Wexler, Anthony S.; Binder-Macleod, Stuart A.
2009-01-01
Aim: The purpose of this study was to determine if our previously developed muscle model could be used to predict forces of the quadriceps femoris and triceps surae muscles of children with spastic diplegic cerebral palsy (CP). Method: Twenty-two children with CP (12 males, 10 females; mean age 10y, SD 2y, range 7-13y; Gross Motor Function…
2015-01-01
captures an individual???s trait-like response to different sleep -loss conditions. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION...seven consecutive nights of 3 h nightly TIB. Both challenges were preceded by a sleep -satiation stage of 7 in-laboratory nights with 10 h TIB and...Can a mathematical model predict an individual’s trait-like response to both total and partial sleep loss? SR IDHAR RAMAKR I SHNAN 1 , WE I LU 1 , SR
Mathematical Model for Predicting the Resistivity of an Electroconductive Woven Structure
Tokarska, Magdalena
2017-03-01
Highly conductive woven fabrics (WF) can be used as electronic components. Resistivity is an intrinsic physical property of the conductive textile materials (CTM). The McLachlan model that describes the resistivity of a two-component macroscopic composite (TCMC) subjected to a constant external electric field was proposed to predict the resistivity of fabrics. The volume fraction of voids in material, the voids dimension, and a single morphology parameter were taken into account. The resistivity of a chosen WF was determined based on the model. Verification of the received results was carried out. In the case of four samples, the verification was confirmed by the high level of prediction being in the range of 83-88%. In the case of one sample, the verification was negative (26%). This allowed one to pay attention to the influence of compactness and irregularity of the woven structure on results received using the model.
Cheboyina, Sreekhar; O'Haver, John; Wyandt, Christy M
2006-01-01
A mathematical model was developed based on the theory of drop formation to predict the size of the pellets formed in the freeze pelletization process. Further the model was validated by studying the effect of various parameters on the pellet size such as viscosity of the pellet forming and column liquids, surface/interfacial tension, density difference between pellet forming and column liquids; size, shape, and material of construction of the needle tips and temperatures maintained in the columns. In this study, pellets were prepared from different matrices including polyethylene glycols and waxes. The column liquids studied were silicone oils and aqueous glycerol solutions. The surface/interfacial tension, density difference between pellet forming and column liquids and needle tip size were found to be the most important factors affecting pellet size. The viscosity of the column liquid was not found to significantly affect the size of the pellets. The size of the pellets was also not affected by the pellet forming liquids of low viscosities. An increase in the initial column temperature slightly decreased the pellet size. The mathematical model developed was found to successfully predict the size of the pellets with an average error of 3.32% for different matrices that were studied.
Developing mathematical modelling competence
DEFF Research Database (Denmark)
Blomhøj, Morten; Jensen, Tomas Højgaard
2003-01-01
In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....
Teaching Mathematical Modelling.
Jones, Mark S.
1997-01-01
Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…
Predictive mathematical modeling of knee static laxity after ACL reconstruction: in vivo analysis.
Signorelli, C; Bonanzinga, T; Grassi, A; Lopomo, N; Zaffagnini, S; Marcacci, M
2016-11-01
Previous studies did not take into consideration such large variety of surgery variables which describe the performed anterior cruciate ligament (ACL) reconstruction and the interaction among them in the definition of postoperative outcome. Seventeen patients who underwent navigated Single Bundle plus Lateral Plasty ACL reconstruction were enrolled in the study. Static laxity was evaluated as the value of anterior/posterior displacement at 30° and at 90° of flexion, internal/external rotation at 30° and 90° of knee flexion, varus/valgus test at 0° and 30° of flexion. The evaluated surgical variables were analyzed through a multivariate analysis defining the following models: AP30estimate, AP90estimate, IE30estimate, IE90estimate, VV0estimate, VV30estimate. Surgical variables has been defined as the angles between the tibial tunnel and the three planes, the lengths of the tunnel and the relationship between native footprints and tunnels. An analogous characterization was performed for the femoral side. Performance and significance of the defined models have been quantified by the correlation ratio (η(2)) and the corresponding p-value (*p static laxity values. The only exception was the AP90estimate model. The η(2) ranged from 0.568 (IE90estimate) to 0.995 (IE30estimate). The orientation of the tibial tunnel resulted to be the most important surgical variable for the performed laxity estimation. Mathematical models for postoperative knee laxity is a useful tool to evaluate the effects of different surgical variables on the postoperative outcome.
Three-dimensional transient mathematical model to predict the heat transfer rate of a heat pipe
Directory of Open Access Journals (Sweden)
S Boothaisong
2015-02-01
Full Text Available A three-dimensional model was developed to simulate the heat transfer rate on a heat pipe in a transient condition. This article presents the details of a calculation domain consisting of a wall, a wick, and a vapor core. The governing equation based on the shape of the pipe was numerically simulated using the finite element method. The developed three-dimensional model attempted to predict the transient temperature, the velocity, and the heat transfer rate profiles at any domain. The values obtained from the model calculation were then compared with the actual results from the experiments. The experiment showed that the time required to attain a steady state (where transient temperature is constant was reasonably consistent with the model. The working fluid r134a (tetrafluoroethane was the quickest to reach the steady state and transferred the greatest amount of heat.
Mathematical modelling techniques
Aris, Rutherford
1995-01-01
""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode
A Mathematical Prediction of Standing Waves
Higgins, Jon
1970-01-01
Presents a problem in standing waves that provides an example of the mathematics used by theoretical physicists to generate predictions of new phenomena from fundamental background knowledge. Mathematical analysis required to solve problem is accomplished by simple graphical processes. (BR)
Applied impulsive mathematical models
Stamova, Ivanka
2016-01-01
Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.
Wang, Yao; Bronshtein, Tomer; Sarig, Udi; Nguyen, Evelyne Bao-Vi; Boey, Freddy Yin Chiang; Venkatraman, Subbu S; Machluf, Marcelle
2013-05-01
In most tissue engineering applications, understanding the factors affecting the growth dynamics of coculture systems is crucial for directing the population toward a desirable regenerative process. Yet, no comprehensive analysis method exists to quantify coculture population dynamics, let alone, a unifying model addressing the "environmental" factors influencing cell growth, all together. Here we suggest a modification of the Lotka-Volterra model to analyze the population dynamics of cocultured cells and predict their growth profiles for tissue engineering applications. This model, commonly used to describe the population dynamics of a prey and predator sharing a closed ecological niche, was found to fit our empirical data on cocultures of endothelial cells (ECs) and mesenchymal stem cells (MSCs) that have been widely investigated for their regenerative potential. Applying this model to cocultures of this sort allows us to quantify the effect that culturing conditions have on the way cell growth is affected by the same cells or by the other cells in the coculture. We found that in most cases, EC growth was inhibited by the same cells but promoted by MSCs. The principles resulting from this analysis can be used in various applications to guide the population toward a desired direction while shedding new light on the fundamental interactions between ECs and MSCs. Similar results were also demonstrated on complex substrates made from decellularized porcine cardiac extracellular matrix, where growth occurred only after coculturing ECs and MSCs together. Finally, this unique implementation of the Lotka-Volterra model may also be regarded as a roadmap for using such models with other potentially regenerative cocultures in various applications.
Wang, Yao; Bronshtein, Tomer; Sarig, Udi; Nguyen, Evelyne Bao-Vi; Boey, Freddy Yin Chiang; Venkatraman, Subbu S.
2013-01-01
In most tissue engineering applications, understanding the factors affecting the growth dynamics of coculture systems is crucial for directing the population toward a desirable regenerative process. Yet, no comprehensive analysis method exists to quantify coculture population dynamics, let alone, a unifying model addressing the “environmental” factors influencing cell growth, all together. Here we suggest a modification of the Lotka-Volterra model to analyze the population dynamics of cocultured cells and predict their growth profiles for tissue engineering applications. This model, commonly used to describe the population dynamics of a prey and predator sharing a closed ecological niche, was found to fit our empirical data on cocultures of endothelial cells (ECs) and mesenchymal stem cells (MSCs) that have been widely investigated for their regenerative potential. Applying this model to cocultures of this sort allows us to quantify the effect that culturing conditions have on the way cell growth is affected by the same cells or by the other cells in the coculture. We found that in most cases, EC growth was inhibited by the same cells but promoted by MSCs. The principles resulting from this analysis can be used in various applications to guide the population toward a desired direction while shedding new light on the fundamental interactions between ECs and MSCs. Similar results were also demonstrated on complex substrates made from decellularized porcine cardiac extracellular matrix, where growth occurred only after coculturing ECs and MSCs together. Finally, this unique implementation of the Lotka-Volterra model may also be regarded as a roadmap for using such models with other potentially regenerative cocultures in various applications. PMID:23216214
Sikka, M P; Ghosh, S; Mukhopadhyay, A
2016-09-01
The effectiveness of the compression treatment by a medical compression bandage is dependent on the pressure generated at the interface between the bandage and the skin. This pressure is called interface pressure or sub-bandage pressure. The performance of a bandage depends upon the level of interface pressure applied by the bandage and the sustenance of this pressure over time. The interface pressure exerted by the bandage depends on several other factors like limb shape or size, application technique, physical and structural properties of the bandage, physical activities taken by the patient, etc. The current understanding of how bandages apply pressure to a limb is based on the Law of Laplace, which states that tension in the walls of a container is dependent on both the pressure of the container's content and its radius. This concept was translated mathematically into equation relating pressure to tension and radius by Thomas. In addition, a modified equation was generated by multiplying the model with a constant that represents the number of bandage layers in order to use the model to estimate the pressure applied by multi-layer bandages. This simple multiplication adjustment was questioned by researchers. They had doubts about the model validity and whether it can be used to predict the sub-bandage pressure applied by pressure garments. One of the questions that were raised regarding the bandage thickness affecting the sub-bandage pressure has been recently explored by Al Khaburi where he used the thin and thick cylinder shell theory to study the effect of Multi Component Bandage's (MCB) thickness on the sub-bandage pressure. The model by Al Khaburi and the earlier models developed for pressure prediction are all based on calculations considering the cylindrical limb shapes although the human limb normally is wider at the calf and reduces in circumference towards the ankle. So in our approach, the bandage is assumed to take a conical shape during application
Garcia-Arias, A.; Pons, C.; Frances, F.
2013-12-01
The vegetation of the riversides is a main part of the complex riparian ecosystems and has an important role maintaining the fluvial ecosystems. Biotic and abiotic interactions between the river and the riverbank are essential for the subsistence and the development of both ecosystems. In semi-arid Mediterranean areas, the riparian vegetation growth and distribution is especially controlled by the water accessibility, determining the limit between the lush riparian bands and the sparse upland. Human intervention can alter the river hydrology determining the riparian vegetation wellbeing and its distribution and, in consequence, affecting both riparian and fluvial ecosystems. Predictive models are necessary decision support tools for adequate river management and restoration initiatives. In this context, the RibAV model is useful to predict the impact of water demand and river flow regulation on the riparian vegetation. RibAV is able to reproduce the vegetation performance on the riverside allowing the scenarios analysis in terms of vegetation distribution and wellbeing. In this research several flow regulation and water demand scenarios are proposed and the impacts over three plant functional types (PFTs) are analyzed. The PFTs group the herbaceous riparian plants, the woody riparian plants and the terrestrial vegetation. The study site is the Terde reach at the Mijares River, a 539m length reach located in a semi-arid Mediterranean area in Spain. The scenarios represent river flow alterations required to attend different human demands. These demands encompass different seasonality, magnitude and location. The seasonality is represented as hydroelectric (constant all over the year), urban (increased during the summer period) and agricultural demands (monthly seasonality). The magnitude is varied considering the 20%, the 40% and the 80% of the mean daily flow. Two locations are considered, upstream or downstream the study site. To attend the demands located
Why Do Spatial Abilities Predict Mathematical Performance?
Tosto, Maria Grazia; Hanscombe, Ken B.; Haworth, Claire M. A.; Davis, Oliver S. P.; Petrill, Stephen A.; Dale, Philip S.; Malykh, Sergey; Plomin, Robert; Kovas, Yulia
2014-01-01
Spatial ability predicts performance in mathematics and eventual expertise in science, technology and engineering. Spatial skills have also been shown to rely on neuronal networks partially shared with mathematics. Understanding the nature of this association can inform educational practices and intervention for mathematical underperformance.…
Mathematical Modeling of the Expert System Predicting the Severity of Acute Pancreatitis
Directory of Open Access Journals (Sweden)
Maria A. Ivanchuk
2014-01-01
Full Text Available The method of building the hyperplane which separates the convex hulls in the Euclidean space Rn is proposed. The algorithm of prediction of the presence of severity in patients based on this method is developed and applied in practice to predict the presence of severity in patients with acute pancreatitis.
Nitanai, Yuta; Agata, Yasuyoshi; Iwao, Yasunori; Itai, Shigeru
2012-05-30
From wax matrix dosage forms, drug and water-soluble polymer are released into the external solvent over time. As a consequence, the pore volume inside the wax matrix particles is increased and the diffusion coefficient of the drug is altered. In the present study, we attempted to derive a novel empirical mathematical model, namely, a time-dependent diffusivity (TDD) model, that assumes the change in the drug's diffusion coefficient can be used to predict the drug release from spherical wax matrix particles. Wax matrix particles were prepared by using acetaminophen (APAP), a model drug; glyceryl monostearate (GM), a wax base; and aminoalkyl methacrylate copolymer E (AMCE), a functional polymer that dissolves below pH 5.0 and swells over pH 5.0. A three-factor, three-level (3(3)) Box-Behnken design was used to evaluate the effects of several of the variables in the model formulation, and the release of APAP from wax matrix particles was evaluated by the paddle method at pH 4.0 and pH 6.5. When comparing the goodness of fit to the experimental data between the proposed TDD model and the conventional pure diffusion model, a better correspondence was observed for the TDD model in all cases. Multiple regression analysis revealed that an increase in AMCE loading enhanced the diffusion coefficient with time, and that this increase also had a significant effect on drug release behavior. Furthermore, from the results of the multiple regression analysis, a formulation with desired drug release behavior was found to satisfy the criteria of the bitter taste masking of APAP without lowering the bioavailability. That is to say, the amount of APAP released remains below 15% for 10 min at pH 6.5 and exceeds 90% within 30 min at pH 4.0. The predicted formulation was 15% APAP loading, 8.25% AMCE loading, and 400 μm mean particle diameter. When wax matrix dosage forms were prepared accordingly, the predicted drug release behavior agreed well with experimental values at each pH level
Classification and disease prediction via mathematical programming
Lee, Eva K.; Wu, Tsung-Lin
2007-11-01
In this chapter, we present classification models based on mathematical programming approaches. We first provide an overview on various mathematical programming approaches, including linear programming, mixed integer programming, nonlinear programming and support vector machines. Next, we present our effort of novel optimization-based classification models that are general purpose and suitable for developing predictive rules for large heterogeneous biological and medical data sets. Our predictive model simultaneously incorporates (1) the ability to classify any number of distinct groups; (2) the ability to incorporate heterogeneous types of attributes as input; (3) a high-dimensional data transformation that eliminates noise and errors in biological data; (4) the ability to incorporate constraints to limit the rate of misclassification, and a reserved-judgment region that provides a safeguard against over-training (which tends to lead to high misclassification rates from the resulting predictive rule) and (5) successive multi-stage classification capability to handle data points placed in the reserved judgment region. To illustrate the power and flexibility of the classification model and solution engine, and its multigroup prediction capability, application of the predictive model to a broad class of biological and medical problems is described. Applications include: the differential diagnosis of the type of erythemato-squamous diseases; predicting presence/absence of heart disease; genomic analysis and prediction of aberrant CpG island meythlation in human cancer; discriminant analysis of motility and morphology data in human lung carcinoma; prediction of ultrasonic cell disruption for drug delivery; identification of tumor shape and volume in treatment of sarcoma; multistage discriminant analysis of biomarkers for prediction of early atherosclerois; fingerprinting of native and angiogenic microvascular networks for early diagnosis of diabetes, aging, macular
Mathematical models of morphogenesis
Directory of Open Access Journals (Sweden)
Dilão Rui
2015-01-01
Full Text Available Morphogenesis is the ensemble of phenomena that generates the form and shape of organisms. Organisms are classified according to some of its structural characteristics, to its metabolism and to its form. In particular, the empirical classification associated with the phylum concept is related with the form and shape of organisms. In the first part of this talk, we introduce the class of mathematical models associated the Turing approach to pattern formation. In the Turing approach, morphogenesis models are described by reaction-diffusion parabolic partial differential equations. Based on this formalism, we present a mathematical model describing the first two hours of development of the fruit fly Drosophila. In the second part of this talk, we present results on Pareto optimality to calibrate and validate mathematical models.
Mathematical modelling of metabolism
DEFF Research Database (Denmark)
Gombert, Andreas Karoly; Nielsen, Jens
2000-01-01
Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....
Principles of mathematical modeling
Dym, Clive
2004-01-01
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Carmona Benitez, R.B.; Lodewijiks, G.
2010-01-01
A mathematical model to estimate the average airlines operational costs and airports charges per route is important for airlines companies trying to open new routes and for data generation for other purpose such as transport modeling, simulation modeling, investment analyses for airlines and airport
Concepts of mathematical modeling
Meyer, Walter J
2004-01-01
Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec
A mathematical model for predicting glucose levels in critically-ill patients: the PIGnOLI model
Directory of Open Access Journals (Sweden)
Zhongheng Zhang
2015-06-01
Full Text Available Background and Objectives. Glycemic control is of paramount importance in the intensive care unit. Presently, several BG control algorithms have been developed for clinical trials, but they are mostly based on experts’ opinion and consensus. There are no validated models predicting how glucose levels will change after initiating of insulin infusion in critically ill patients. The study aimed to develop an equation for initial insulin dose setting.Methods. A large critical care database was employed for the study. Linear regression model fitting was employed. Retested blood glucose was used as the independent variable. Insulin rate was forced into the model. Multivariable fractional polynomials and interaction terms were used to explore the complex relationships among covariates. The overall fit of the model was examined by using residuals and adjusted R-squared values. Regression diagnostics were used to explore the influence of outliers on the model.Main Results. A total of 6,487 ICU admissions requiring insulin pump therapy were identified. The dataset was randomly split into two subsets at 7 to 3 ratio. The initial model comprised fractional polynomials and interactions terms. However, this model was not stable by excluding several outliers. I fitted a simple linear model without interaction. The selected prediction model (Predicting Glucose Levels in ICU, PIGnOLI included variables of initial blood glucose, insulin rate, PO volume, total parental nutrition, body mass index (BMI, lactate, congestive heart failure, renal failure, liver disease, time interval of BS recheck, dextrose rate. Insulin rate was significantly associated with blood glucose reduction (coefficient: −0.52, 95% CI [−1.03, −0.01]. The parsimonious model was well validated with the validation subset, with an adjusted R-squared value of 0.8259.Conclusion. The study developed the PIGnOLI model for the initial insulin dose setting. Furthermore, experimental study is
Mathematical Model to Predict Skin Concentration after Topical Application of Drugs
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Hiroaki Todo
2013-12-01
Full Text Available Skin permeation experiments have been broadly done since 1970s to 1980s as an evaluation method for transdermal drug delivery systems. In topically applied drug and cosmetic formulations, skin concentration of chemical compounds is more important than their skin permeations, because primary target site of the chemical compounds is skin surface or skin tissues. Furthermore, the direct pharmacological reaction of a metabolically stable drug that binds with specific receptors of known expression levels in an organ can be determined by Hill’s equation. Nevertheless, little investigation was carried out on the test method of skin concentration after topically application of chemical compounds. Recently we investigated an estimating method of skin concentration of the chemical compounds from their skin permeation profiles. In the study, we took care of “3Rs” issues for animal experiments. We have proposed an equation which was capable to estimate animal skin concentration from permeation profile through the artificial membrane (silicone membrane and animal skin. This new approach may allow the skin concentration of a drug to be predicted using Fick’s second law of diffusion. The silicone membrane was found to be useful as an alternative membrane to animal skin for predicting skin concentration of chemical compounds, because an extremely excellent extrapolation to animal skin concentration was attained by calculation using the silicone membrane permeation data. In this chapter, we aimed to establish an accurate and convenient method for predicting the concentration profiles of drugs in the skin based on the skin permeation parameters of topically active drugs derived from steady-state skin permeation experiments.
Directory of Open Access Journals (Sweden)
I. G. Bakulin
2016-01-01
Full Text Available Currently in the Russian Federation or chronic hepatitis C (CHC are still relevant Interferon-based regimens. The purpose of this study is to investigate the influence of baseline characteristics and prognosis of the patient HCV genotype 1 for the development of leukopenia (LP and neutropenia (NP. We investigated factors such as sex, age, body mass index (BMI, viral load, genotype of Interleukin-28 B (IL-28B, the initial level of leukocytes and neutrophils, alanine aminotransferase (ALT, fibrosis, duration of infection, presence of previous therapy. Absolute values of leukocytes and neutrophils were analyzed on 4, 12, 24, 48 weeks of therapy, and at 4, 12, 24 weeks after antiviral treatment with protease inhibitors (PI 1 and 2 generation. Prognostic criteria were identified, indicating the possible development of the LP and NP expressed during treatment with interferon: female gender, low initial load, TT-genotype of IL-28B, the initial level of white blood cells and neutrophils below 5,7×109/L and 3,4×109/L, respectively. Mathematical models predicting the onset of LP and NP, formalized in the form of decision trees were also constructed. These models have shown the greatest potential for practical use in view of highest accuracy and reliability.
Brown, David J.; Orelien, Jean; Gordon, John D.; Chu, Andrew C.; Chu, Michael D.; Nakamura, Masafumi; Handa, Hiroshi; Kayama, Fujio; Denison, Michael S.; Clark, George C.
2010-01-01
Remediation of hazardous waste sites requires efficient and cost-effective methods to assess the extent of contamination by toxic substances including dioxin-like chemicals. Traditionally, dioxin-like contamination has been assessed by gas chromatography/high-resolution mass spectrometry (GC/MS) analysis for specific polychlorinated dibenzo-p-dioxins, dibenzofurans, and biphenyl congeners. Toxic equivalency factors for these congeners are then used to estimate the overall dioxin toxic equivalency (TEQ) of complex mixtures found in samples. The XDS-CALUX bioassay estimates contamination by dioxin-like chemicals in a sample extract by measuring expression of a sensitive reporter gene in genetically engineered cells. The output of the XDS-CALUX assay is a CALUX-TEQ value, calibrated based on TCDD standards. Soil samples taken from a variety of hazardous waste sites were measured using the XDS-CALUX bioassay and GC/MS. TEQ and CALUX-TEQ from these methods were compared, and a mathematical model was developed describing the relationship between these two data sets: log(TEQ) = 0.654 × log(CALUX-TEQ) + 0.058-(log(CALUX-TEQ))2. Applying this equation to these samples showed that predicted and GC/MS measured TEQ values strongly correlate (R2 = 0.876) and that TEQ values predicted from CALUX-TEQ were on average nearly identical to the GC/MS-TEQ. The ability of XDS-CALUX bioassay data to predict GC/MS-derived TEQ data should make this procedure useful in risk assessment and management decisions. PMID:17626436
Mathematical modeling of biological processes
Friedman, Avner
2014-01-01
This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.
Two mathematical models for predicting dispersion of particles in the human lung.
Ganser, G H; Christie, I; McCawley, M A
2007-02-01
The dispersion of particles in the human lung is modeled as a series of virtual mixing tanks. Using the experimental results of Scherer et al. (1975, J. Appl. Physiol., 38(4), pp. 719-723) for a five-generation glass lung model, it is shown that each generation of the glass lung behaves like an independent virtual mixing tank. The corresponding resident time distribution is shown to have a variance approximately equal to the square of the average time a particle spends in the generation. By assuming that each generation of the human lung behaves as an independent virtual mixing tank, the realistic lung data provided by Weibel (1963, Morphometry of the Human Lung, Spinger-Verlag, New York) are used to validate this assumption in two ways. First, the half-width of the exhaled particle concentration profile is obtained. Second, a system of differential equations, with the concentration of particles in each mixing tank as its solution, is derived and solved numerically. This gives the exhaled concentration profile. Both techniques yield similar results to each other, and both give excellent agreement with the experimental data. The virtual mixing tank approach allows the complex mixing that occurs in the branching pathways of the lung to be more simply modeled. The model, thereby derived, is simple to change and could lead to enhancements in the understanding of the underlying processes contributing to the ventilation of the lung in health and disease.
Mathematical modeling in psychological researches
Directory of Open Access Journals (Sweden)
Aleksandra Zyolko
2013-04-01
Full Text Available The author considers the nature of mathematical modeling and its significance in psychological researches. The author distinguishes the types of mathematical models: deterministic, stochastic models and synergetic models. The system approach is proposed as an instrument of implementation of mathematical modelling in psychological research.
Mathematical models of hysteresis
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-08-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.
Pereira, André; Conde, Daniel; Ferreira, Carla S. S.; Walsh, Rory; Ferreira, Rui M. L.
2017-04-01
Deforestation and urbanization generally lead to increased soil erosion andthrough the indirect effect of increased overland flow and peak flood discharges. Mathematical modelling tools can be helpful for predicting the spatial distribution of erosion and the morphological changes on the channel network. This is especially useful to predict the impacts of land-use changes in parts of the watershed, namely due to urbanization. However, given the size of the computational domain (normally the watershed itself), the need for high spatial resolution data to model accurately sediment transport processes and possible need to model transcritical flows, the computational cost is high and requires high-performance computing techniques. The aim of this work is to present the latest developments of the hydrodynamic and morphological model STAV2D and its applicability to predict runoff and erosion at watershed scale. STAV2D was developed at CEris - Instituto Superior Técnico, Universidade de Lisboa - as a tool particularly appropriated to model strong transient flows in complex and dynamic geometries. It is based on an explicit, first-order 2DH finite-volume discretization scheme for unstructured triangular meshes, in which a flux-splitting technique is paired with a reviewed Roe-Riemann solver, yielding a model applicable to discontinuous flows over time-evolving geometries. STAV2D features solid transport in both Euleran and Lagrangian forms, with the aim of describing the transport of fine natural sediments and then the large individual debris. The model has been validated with theoretical solutions and laboratory experiments (Canelas et al., 2013 & Conde et al., 2015). STAV-2D now supports fully distributed and heterogeneous simulations where multiple different hardware devices can be used to accelerate computation time within a unified Object-Oriented approach: the source code for CPU and GPU has the same compilation units and requires no device specific branches, like
Mathematical models for prediction of rheological parameters in vinasses derived from sugar cane
Chacua, Leidy M.; Ayala, Germán; Rojas, Hernán; Agudelo, Ana C.
2016-04-01
The rheological behaviour of vinasses derived from sugar cane was studied as a function of time (0 and 600 s), soluble solids content (44 and 60 °Brix), temperature (10 and 50°C), and shear rate (0.33 and 1.0 s-1). The results indicated that vinasses were time-independent at 25°C, where shear stress values ranged between 0.01 and 0.08 Pa. Flow curves showed a shear-thinning rheological behaviour in vinasses with a flow behaviour index between 0.69 and 0.89, for temperature between 10 and 20°C. With increasing temperature, the flow behaviour index was modified, reaching values close to 1.0. The Arrhenius model described well the thermal activation of shear stress and the consistency coefficient as a function of temperature. Activation energy from the Arrhenius model ranged between 31 and 45 kJ mol-1. Finally, the consistency coefficient as a function of the soluble solids content and temperature was well fitted using an exponential model (R2 = 0.951), showing that the soluble solids content and temperature have an opposite effect on consistency coefficient values.
Huang, Lu; Jiang, Yuyang; Chen, Yuzong
2017-01-01
Synergistic drug combinations enable enhanced therapeutics. Their discovery typically involves the measurement and assessment of drug combination index (CI), which can be facilitated by the development and applications of in-silico CI predictive tools. In this work, we developed and tested the ability of a mathematical model of drug-targeted EGFR-ERK pathway in predicting CIs and in analyzing multiple synergistic drug combinations against observations. Our mathematical model was validated against the literature reported signaling, drug response dynamics, and EGFR-MEK drug combination effect. The predicted CIs and combination therapeutic effects of the EGFR-BRaf, BRaf-MEK, FTI-MEK, and FTI-BRaf inhibitor combinations showed consistent synergism. Our results suggest that existing pathway models may be potentially extended for developing drug-targeted pathway models to predict drug combination CI values, isobolograms, and drug-response surfaces as well as to analyze the dynamics of individual and combinations of drugs. With our model, the efficacy of potential drug combinations can be predicted. Our method complements the developed in-silico methods (e.g. the chemogenomic profile and the statistically-inferenced network models) by predicting drug combination effects from the perspectives of pathway dynamics using experimental or validated molecular kinetic constants, thereby facilitating the collective prediction of drug combination effects in diverse ranges of disease systems.
Energy Technology Data Exchange (ETDEWEB)
Biswas, J.; Chowdhury, R.; Bhattacharya, P. [Chemical Engineering Department, Jadavpur University, Kolkata 700 032 (India)
2007-01-15
An anaerobic digester of 10L capacity has been operated in batch mode at an optimum temperature of 40{sup o}C and at a pH of 6.8 using vegetable/food residues as the feed material. The effect of slurry concentration and that of the concentration of carbohydrate, protein and fat in the slurry on the biogas production rate and methane concentration in the biogas have been studied. The slurry concentration has been varied in the range of 72.0-700kgm{sup -3}. At a slurry concentration of 67.7kgm{sup -3} the effect of carbohydrate concentration has been studied by varying the ratios of carbohydrate, protein and fat in the range of 6.9:4.3:1-12.1:4.3:1 by using a sole carbohydrate source, namely sucrose. The effect of protein concentration has been studied by varying the ratios of carbohydrate, protein and fat in the range of 5.6:7.0:1-5.6:13.0:1 by using a sole protein source, namely papain and that of fat concentration has been studied by varying the ratios of carbohydrate, protein and fat in the range of 7.2:10:1.6-7.2:10:5 by using a fat source, namely vanaspati. A deterministic mathematical model using differential system equations have been developed and it is capable of predicting the behaviour of the digester satisfactorily. (author)
1994-11-01
NewEngl d U.S. Art RAYo WAERAYaEPRIENCSATO Incudebilio grapicr•efe "M ( p prgam) 3dCOeTt L -E nv i Eroa BORpR of E. Nw Y ri.ARm E er Wter...constant = 8.206 x 10.5 atm m3/(gmole-kelvins) T = absolute temperature, kelvins. A temperature of 298K (25 °C) is assumed in the model. The parameter...bottom sediment material are shown in Table 3. Table 2 Concentrations of DDE and Lindane In Water Column Sampling Day DDE, ppt, X ± SD Undane, ppt, X
Energy Technology Data Exchange (ETDEWEB)
Rabi, Jose A. [Pontificia Univ. Catolica de Minas Gerais, Pocos de Caldas, MG (Brazil). Faculdade de Engenharia Civil]. E-mail: jrabi@pucpcaldas.br; Mohamad, Abdulmajeed A. [The University of Calgary, Alberta (Canada). Faculty of Engineering. Dept. of Mechanical and Manufacturing Engineering]. E-mail: amohamad@enme.ucalgary.ca
2004-07-01
Radon-222 is a radionuclide exhaled from phosphogypsum by-produced at phosphate fertilizer industries. Alternative large-scale application of this waste may indicate a material substitute for civil engineering provided that environmental issues concerning its disposal and management are overcome. The first part of this paper outlines a steady-state two-dimensional model for {sup 222}Rn transport through porous media, inside which emanation (source term) and decay (sink term) exist. Boussinesq approach is evoked for the laminar buoyancy-driven interstitial air flow, which is also modeled according to Darcy-Brinkman formulation. In order to account for simultaneous effects of entailed physical parameters, governing equations are cast into dimensionless form. Apart from usual controlling parameters like Reynolds, Prandtl, Schmidt, Grashof and Darcy numbers, three unconventional dimensionless groups are put forward. Having in mind {sup 222}Rn transport in phosphogypsum-bearing porous media, the physical meaning of those newly introduced parameters and representative values for the involved physical parameters are presented. A limiting diffusion-dominated scenario is addressed, for which an analytical solution is deduced for boundary conditions including an impermeable phosphogypsum stack base and a non-zero fixed concentration activity at the stack top. Accordingly, an expression for the average Sherwood number corresponding to the normalized {sup 222}Rn exhalation rate is presented.
Finite mathematics models and applications
Morris, Carla C
2015-01-01
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
Using "Prediction" to Promote Mathematical Reasoning
Kim, Ok-Kyeong; Kasmer, Lisa
2007-01-01
This article introduces prediction as a useful tool to promote mathematical reasoning. First, the article addresses prediction expectations in state standards and gives examples. It also provides a classroom example and activities to illustrate what prediction can look like and how it can serve as a building block for the development of students'…
Mathematical modeling predicts enhanced growth of X-ray irradiated pigmented fungi.
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Igor Shuryak
Full Text Available Ionizing radiation is known for its cytotoxic and mutagenic properties. However, recent evidence suggests that chronic sub-lethal irradiation stimulates the growth of melanin-pigmented (melanized fungi, supporting the hypothesis that interactions between melanin and ionizing photons generate energy useful for fungal growth, and/or regulate growth-promoting genes. There are no quantitative models of how fungal proliferation is affected by ionizing photon energy, dose rate, and presence versus absence of melanin on the same genetic background. Here we present such a model, which we test using experimental data on melanin-modulated radiation-induced proliferation enhancement in the fungus Cryptococcus neoformans, exposed to two different peak energies (150 and 320 kVp over a wide range of X-ray dose rates. Our analysis demonstrates that radiation-induced proliferation enhancement in C. neoformans behaves as a binary "on/off" phenomenon, which is triggered by dose rates 5000 mGy/h. Proliferation enhancement of irradiated cells compared with unirradiated controls occurs at both X-ray peak energies, but its magnitude is modulated by X-ray peak energy and cell melanization. At dose rates <5000 mGy/h, both melanized and non-melanized cells exposed to 150 kVp X-rays, and non-melanized cells exposed to 320 kVp X-rays, all exhibit the same proliferation enhancement: on average, chronic irradiation stimulates each founder cell to produce 100 (95% CI: 83, 116 extra descendants over 48 hours. Interactions between melanin and 320 kVp X-rays result in a significant (2-tailed p-value = 4.8 × 10(-5 additional increase in the number of radiation-induced descendants per founder cell: by 55 (95% CI: 29, 81. These results show that both melanin-dependent and melanin-independent mechanisms are involved in radiation-induced fungal growth enhancement, and implicate direct and/or indirect interactions of melanin with high energy ionizing photons as an important pro
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Maria eArepeva
2015-04-01
Full Text Available Acquired bacterial resistance is one of the causes of mortality and morbidity from infectious diseases. Mathematical modeling allows us to predict the spread of resistance and to some extent to control its dynamics. The purpose of this review was to examine existing mathematical models in order to understand pros and cons of currently used approaches and to build our own model. During the analysis, seven articles about the mathematical approaches to studying resistance that satisfied the inclusion / exclusion criteria were selected. All models were classified according to the approach used to study resistance in the presence of antibiotic and were analyzed in terms of our research. Some models require modifications associated with the specific of the research. Further work plan of model building is as follows: modify some models, according to our research, check all obtained models on our data, and select the optimal model or several models with the best quality of prediction. After that we would be able to build a model for the development of resistance using the obtained results.
Authenticity of Mathematical Modeling
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Dermol, Janja; Miklavčič, Damijan
2014-12-01
High voltage electric pulses cause electroporation of the cell membrane. Consequently, flow of the molecules across the membrane increases. In our study we investigated possibility to predict the percentage of the electroporated cells in an inhomogeneous electric field on the basis of the experimental results obtained when cells were exposed to a homogeneous electric field. We compared and evaluated different mathematical models previously suggested by other authors for interpolation of the results (symmetric sigmoid, asymmetric sigmoid, hyperbolic tangent and Gompertz curve). We investigated the density of the cells and observed that it has the most significant effect on the electroporation of the cells while all four of the mathematical models yielded similar results. We were able to predict electroporation of cells exposed to an inhomogeneous electric field based on mathematical modeling and using mathematical formulations of electroporation probability obtained experimentally using exposure to the homogeneous field of the same density of cells. Models describing cell electroporation probability can be useful for development and presentation of treatment planning for electrochemotherapy and non-thermal irreversible electroporation.
Examples of Mathematical Modeling
Johnston, Matthew D.; Edwards, Carina M.; Bodmer, Walter F.; Maini, Philip K.; Chapman, S. Jonathan
2008-01-01
Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al.5 to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters. PMID:17873520
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived......, thereby implying that interactions between spreading processes are driving forces of attention dynamics. Overall, the thesis contributes to a quantitative understanding of a wide range of different human behaviors by applying mathematical modeling to behavioral data. There can be no doubt......During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...
Okamoto, Etsuji
2013-11-19
The Japanese Government settled a class litigation case with hepatitis B virus (HBV) carriers who claim to have been infected through needle/syringe sharing in childhood mass vaccination with a blanket compensation agreement. However, it is difficult to estimate how many of the present HBV carriers were infected horizontally from mass vaccination and how many were infected vertically from mothers. A mathematical model to predict the risk of infection through needle/syringe sharing in mass vaccination was proposed and a formula was developed. The formula was presented in a logarithmic graph enabling users to estimate how many people will be infected if a needle/syringe is shared by how many people for how many times under certain probability of infection. The formula was then applied to the historical data of mass tuberculin skin tests (TSTs) and BCG inoculation, from which a best estimate of how much needle/syringe sharing was practiced in different birth cohorts was determined. For the oldest cohort born between 1951 and 1955, the prevalence of HBV carriers-0.65% at birth through vertical transmission-more than doubled in 1995 (1.46%) through horizontal transmission. If the probability of infection through needle/syringe sharing is assumed to be 10%, it is theoretically likely that an average of five or more people shared a needle/syringe four times to achieve the prevalence of HBV carriers in 1995. However, for the youngest cohort born between 1981 and 1985, the effects of needle/syringe sharing were negligible because the later prevalence of HBV carriers was lower than the prevalence at birth. More than half of the HBV carriers born in the early 1950s might have contracted the disease by mass vaccinations. Japan's experience needs to be shared with other countries as a caution in conducting mass vaccination programs under scarce needle/syringe supply (291 words).
Mathematical Modelling in European Education
Ferri, Rita Borromeo
2013-01-01
Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…
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Walcher Sebastian
2011-06-01
Full Text Available Abstract Background 7D-cadherins like LI-cadherin are cell adhesion molecules and represent exceptional members of the cadherin superfamily. Although LI-cadherin was shown to act as a functional Ca2+-dependent adhesion molecule, linking neighboring cells together, and to be dysregulated in a variety of diseases, the physiological role is still enigmatic. Interestingly 7D-cadherins occur only in the lateral plasma membranes of cells from epithelia of water transporting tissues like the gut, the liver or the kidney. Furthermore LI-cadherin was shown to exhibit a highly cooperative Ca2+-dependency of the binding activity. Thus it is tempting to assume that LI-cadherin regulates the water transport through the epithelium in a passive fashion by changing its binding activity in dependence on the extracellular Ca2+. Results We developed a simple mathematical model describing the epithelial lining of a lumen with a content of variable osmolarity covering an interstitium of constant osmolarity. The width of the lateral intercellular cleft was found to influence the water transport significantly. In the case of hypertonic luminal content a narrow cleft is necessary to further increase concentration of the luminal content. If the cleft is too wide, the water flux will change direction and water is transported into the lumen. Electron microscopic images show that in fact areas of the gut can be found where the lateral intercellular cleft is narrow throughout the lateral cell border whereas in other areas the lateral intercellular cleft is widened. Conclusions Our simple model clearly predicts that changes of the width of the lateral intercellular cleft can regulate the direction and efficiency of water transport through a simple epithelium. In a narrow cleft the cells can increase the concentration of osmotic active substances easily by active transport whereas if the cleft is wide, friction is reduced but the cells can hardly build up high osmotic
The mathematics of cancer: integrating quantitative models.
Altrock, Philipp M; Liu, Lin L; Michor, Franziska
2015-12-01
Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.
Mathematical modeling with multidisciplinary applications
Yang, Xin-She
2013-01-01
Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the
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Shannon R Moore
2014-06-01
Full Text Available The link between mechanics and biology in the generation and the adaptation of bone has been well studied in context of skeletal development and fracture healing. Yet, the prediction of tissue genesis within - and the spatiotemporal healing of - postnatal defects, necessitates a quantitative evaluation of mechano-biological interactions using experimental and clinical parameters. To address this current gap in knowledge, this study aims to develop a mechanistic mathematical model of tissue genesis using bone morphogenetic protein (BMP to represent of a class of factors that may coordinate bone healing. Specifically, we developed a mechanistic, mathematical model to predict the dynamics of tissue genesis by periosteal progenitor cells within a long bone defect surrounded by periosteum and stabilized via an intramedullary nail. The emergent material properties and mechanical environment associated with nascent tissue genesis influence the strain stimulus sensed by progenitor cells within the periosteum. Using a mechanical finite element model, periosteal surface strains are predicted as a function of emergent, nascent tissue properties. Strains are then input to a mechanistic mathematical model, where mechanical regulation of BMP-2 production mediates rates of cellular proliferation, differentiation and tissue production, to predict healing outcomes. A parametric approach enables the spatial and temporal prediction of endochondral tissue regeneration, assessed as areas of cartilage and mineralized bone, as functions of radial distance from the periosteum and time. Comparing model results to histological outcomes from two previous studies of periosteum-mediated bone regeneration in a common ovine model, it was shown that mechanistic models incorporating mechanical feedback successfully predict patterns (spatial and trends (temporal of bone tissue regeneration. The novel model framework presented here integrates a mechanistic feedback system based
Mathematical modeling in chronobiology.
Bordyugov, G; Westermark, P O; Korenčič, A; Bernard, S; Herzel, H
2013-01-01
Circadian clocks are autonomous oscillators entrained by external Zeitgebers such as light-dark and temperature cycles. On the cellular level, rhythms are generated by negative transcriptional feedback loops. In mammals, the suprachiasmatic nucleus (SCN) in the anterior part of the hypothalamus plays the role of the central circadian pacemaker. Coupling between individual neurons in the SCN leads to precise self-sustained oscillations even in the absence of external signals. These neuronal rhythms orchestrate the phasing of circadian oscillations in peripheral organs. Altogether, the mammalian circadian system can be regarded as a network of coupled oscillators. In order to understand the dynamic complexity of these rhythms, mathematical models successfully complement experimental investigations. Here we discuss basic ideas of modeling on three different levels (1) rhythm generation in single cells by delayed negative feedbacks, (2) synchronization of cells via external stimuli or cell-cell coupling, and (3) optimization of chronotherapy.
Energy Technology Data Exchange (ETDEWEB)
Filipy, R.E.; Borst, F.J.; Cross, F.T.; Park, J.F.; Moss, O.R.; Roswell, R.L.; Stevens, D.L.
1980-05-01
A mathematical model was constructed for the purpose of predicting the fraction of human population which would die within 1 year of an accidental exposure to airborne radionuclides. The model is based on data from laboratory experiments with rats, dogs and baboons, and from human epidemiological data. Doses from external, whole-body irradiation and from inhaled, alpha- and beta-emitting radionuclides are calculated for several organs. The probabilities of death from radiation pneumonitis and from bone marrow irradiation are predicted from doses accumulated within 30 days of exposure to the radioactive aerosol. The model is compared with existing similar models under hypothetical exposure conditions. Suggestions for further experiments with inhaled radionuclides are included. 25 refs., 16 figs., 13 tabs.
Mathematical Modeling and Computational Thinking
Sanford, John F.; Naidu, Jaideep T.
2017-01-01
The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…
Directory of Open Access Journals (Sweden)
Edmar Clemente
2011-09-01
Full Text Available Solid mixtures for refreshment are already totally integrated to the Brazilian consumers' daily routine, because of their quick preparation method, yield and reasonable price - quite lower if compared to 'ready-to-drink' products or products for prompt consumption, what makes them economically more accessible to low-income populations. Within such a context, the aim of this work was to evaluate the physicochemical and mineral composition, as well as the hygroscopic behavior of four different brands of solid mixture for mango refreshment. The BET, GAB, Oswim and Henderson mathematical models were built through the adjustment of experimental data to the isotherms of adsorption. Results from the physiochemical evaluation showed that the solid mixtures for refreshments are considerable sources of ascorbic acid and reductor sugar; and regarding mineral compounds, they are significant sources of calcium, sodium and potassium. It was also verified that the solid mixtures for refreshments of the four studied brands are considered highly hygroscopic.
Pitzer, Virginia E.; Bowles, Cayley C.; Baker, Stephen; Kang, Gagandeep; Balaji, Veeraraghavan; Farrar, Jeremy J.; Grenfell, Bryan T.
2014-01-01
Background Modeling of the transmission dynamics of typhoid allows for an evaluation of the potential direct and indirect effects of vaccination; however, relevant typhoid models rooted in data have rarely been deployed. Methodology/Principal Findings We developed a parsimonious age-structured model describing the natural history and immunity to typhoid infection. The model was fit to data on culture-confirmed cases of typhoid fever presenting to Christian Medical College hospital in Vellore, India from 2000–2012. The model was then used to evaluate the potential impact of school-based vaccination strategies using live oral, Vi-polysaccharide, and Vi-conjugate vaccines. The model was able to reproduce the incidence and age distribution of typhoid cases in Vellore. The basic reproductive number (R0) of typhoid was estimated to be 2.8 in this setting. Vaccination was predicted to confer substantial indirect protection leading to a decrease in the incidence of typhoid in the short term, but (intuitively) typhoid incidence was predicted to rebound 5–15 years following a one-time campaign. Conclusions/Significance We found that model predictions for the overall and indirect effects of vaccination depend strongly on the role of chronic carriers in transmission. Carrier transmissibility was tentatively estimated to be low, consistent with recent studies, but was identified as a pivotal area for future research. It is unlikely that typhoid can be eliminated from endemic settings through vaccination alone. PMID:24416466
Directory of Open Access Journals (Sweden)
Virginia E Pitzer
Full Text Available BACKGROUND: Modeling of the transmission dynamics of typhoid allows for an evaluation of the potential direct and indirect effects of vaccination; however, relevant typhoid models rooted in data have rarely been deployed. METHODOLOGY/PRINCIPAL FINDINGS: We developed a parsimonious age-structured model describing the natural history and immunity to typhoid infection. The model was fit to data on culture-confirmed cases of typhoid fever presenting to Christian Medical College hospital in Vellore, India from 2000-2012. The model was then used to evaluate the potential impact of school-based vaccination strategies using live oral, Vi-polysaccharide, and Vi-conjugate vaccines. The model was able to reproduce the incidence and age distribution of typhoid cases in Vellore. The basic reproductive number (R 0 of typhoid was estimated to be 2.8 in this setting. Vaccination was predicted to confer substantial indirect protection leading to a decrease in the incidence of typhoid in the short term, but (intuitively typhoid incidence was predicted to rebound 5-15 years following a one-time campaign. CONCLUSIONS/SIGNIFICANCE: We found that model predictions for the overall and indirect effects of vaccination depend strongly on the role of chronic carriers in transmission. Carrier transmissibility was tentatively estimated to be low, consistent with recent studies, but was identified as a pivotal area for future research. It is unlikely that typhoid can be eliminated from endemic settings through vaccination alone.
Mathematical modelling of cucumber (cucumis sativus) drying
Shahari, N.; Hussein, S. M.; Nursabrina, M.; Hibberd, S.
2014-07-01
This paper investigates the applicability of using an experiment based mathematical model (empirical model) and a single phase mathematical model with shrinkage to describe the drying curve of cucumis sativus (cucumber). Drying experiments were conducted using conventional air drying and data obtained from these experiments were fitted to seven empirical models using non-linear least square regression based on the Levenberg Marquardt algorithm. The empirical models were compared according to their root mean square error (RMSE), sum of square error (SSE) and coefficient of determination (R2). A logarithmic model was found to be the best empirical model to describe the drying curve of cucumber. The numerical result of a single phase mathematical model with shrinkage was also compared with experiment data for cucumber drying. A good agreement was obtained between the model predictions and the experimental data.
Nyati, H
2000-06-01
Survival and growth of Listeria monocytogenes isolates during sous vide processing and storage, and the applicability of predictive modelling in determining the potential for growth of L. monocytogenes in broth models and in sous vide products was investigated. L. monocytogenes grew in anaerobic tryptose phosphate broth and in chicken and beef samples by 2 log cycles in 8 days at 3 degrees C and 4-5 log cycles in 6 days at 8 degrees C. However, heating to an internal temperature of 70 degrees C resulted in a 4-5 log reduction and 70 degrees C/2 min resulted in a reduction greater than 7 log cycles. Lowering the product pH to 5.0 was effective in inhibiting L. monocytogenes growth, whereas a sodium chloride concentration of 2% had a negligible effect on growth rates. The square root model (Ratkowsky et al., 1983) predicted L. monocytogenes growth rates at 0-25 degrees C with a coefficient of determination (R2 value) of 98.36-99.63% and a bias factor of 1.08 to 1.21 in beef, chicken and broth substrates of unmodified pH. In addition, the Response Surface Polynomial Model (Version 3.1, Buchanan et al., 1989) predicted generation times at 5-25 degrees C with a 0-17.4% difference between observed and expected generation times in tryptose phosphate broth at pH 7.3. There were however, large differences (25.5 vs. 5.3 h) between observed generation times at pH 5.6 (8 degrees C) and those predicted by the Pathogen Modelling Program in tryptose phosphate broth. A divergence from predicted values was also noted at lower temperatures (0-3.5 degrees C) in the square root model.
Darby, S C; Pike, M. C.
1988-01-01
Epidemiological studies of active smokers have shown that the duration of smoking has a much greater effect on lung cancer risk than the amount smoked. This observation suggests that passive smoking might be much more harmful than would be predicted from measures of the level of exposure alone, as it is often of very long duration frequently beginning in early childhood. In this paper we have investigated this using a multistage model with five stages. The model is shown to provide an excelle...
DEFF Research Database (Denmark)
Krøll, Annette Elisabeth; Marcussen, Lis
1997-01-01
An equilibrium equation for pure component adsorption is compared to experiments and to the vacancy solution theory. The investigated equilibrium equation is a special case of a model for prediction of multicomponent adsorption equilibria.The vacancy solution theory for multicomponent systems req...
Mathematical model for bone mineralization
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Svetlana V Komarova
2015-08-01
Full Text Available Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly non-linear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology.
Mathematical Models of Tuberculosis Reactivation and Relapse
Directory of Open Access Journals (Sweden)
Robert Steven Wallis
2016-05-01
Full Text Available The natural history of human infection with Mycobacterium tuberculosis (Mtb is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiology of tuberculosis in patients treated with tumor necrosis factor antagonists, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic.
Mathematical Model for Hit Phenomena
Ishii, Akira; Hayashi, Takefumi; Matsuda, Naoya; Nakagawa, Takeshi; Arakaki, Hisashi; Yoshida, Narihiko
2010-01-01
The mathematical model for hit phenomena in entertainments is presented as a nonlinear, dynamical and non-equilibrium phenomena. The purchase intention for each person is introduced and direct and indirect communications are expressed as two-body and three-body interaction in our model. The mathematical model is expressed as coupled nonlinear differential equations. The important factor in the model is the decay time of rumor for the hit. The calculated results agree very well with revenues of recent 25 movies.
An introduction to mathematical modeling
Bender, Edward A
2000-01-01
Employing a practical, ""learn by doing"" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields - including science, engineering, and operations research - to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The
Directory of Open Access Journals (Sweden)
M Taki
2017-05-01
Full Text Available Introduction Controlling greenhouse microclimate not only influences the growth of plants, but also is critical in the spread of diseases inside the greenhouse. The microclimate parameters were inside air, greenhouse roof and soil temperature, relative humidity and solar radiation intensity. Predicting the microclimate conditions inside a greenhouse and enabling the use of automatic control systems are the two main objectives of greenhouse climate model. The microclimate inside a greenhouse can be predicted by conducting experiments or by using simulation. Static and dynamic models are used for this purpose as a function of the metrological conditions and the parameters of the greenhouse components. Some works were done in past to 2015 year to simulation and predict the inside variables in different greenhouse structures. Usually simulation has a lot of problems to predict the inside climate of greenhouse and the error of simulation is higher in literature. The main objective of this paper is comparison between heat transfer and regression models to evaluate them to predict inside air and roof temperature in a semi-solar greenhouse in Tabriz University. Materials and Methods In this study, a semi-solar greenhouse was designed and constructed at the North-West of Iran in Azerbaijan Province (geographical location of 38°10′ N and 46°18′ E with elevation of 1364 m above the sea level. In this research, shape and orientation of the greenhouse, selected between some greenhouses common shapes and according to receive maximum solar radiation whole the year. Also internal thermal screen and cement north wall was used to store and prevent of heat lost during the cold period of year. So we called this structure, ‘semi-solar’ greenhouse. It was covered with glass (4 mm thickness. It occupies a surface of approximately 15.36 m2 and 26.4 m3. The orientation of this greenhouse was East–West and perpendicular to the direction of the wind prevailing
Jaime-Pérez, José Carlos; Jiménez-Castillo, Raúl Alberto; Vázquez-Hernández, Karina Elizabeth; Salazar-Riojas, Rosario; Méndez-Ramírez, Nereida; Gómez-Almaguer, David
2017-10-01
Advances in automated cell separators have improved the efficiency of plateletpheresis and the possibility of obtaining double products (DP). We assessed cell processor accuracy of predicted platelet (PLT) yields with the goal of a better prediction of DP collections. This retrospective proof-of-concept study included 302 plateletpheresis procedures performed on a Trima Accel v6.0 at the apheresis unit of a hematology department. Donor variables, software predicted yield and actual PLT yield were statistically evaluated. Software prediction was optimized by linear regression analysis and its optimal cut-off to obtain a DP assessed by receiver operating characteristic curve (ROC) modeling. Three hundred and two plateletpheresis procedures were performed; in 271 (89.7%) occasions, donors were men and in 31 (10.3%) women. Pre-donation PLT count had the best direct correlation with actual PLT yield (r = 0.486. P linear regression analysis accurately corrected this underestimation and ROC analysis identified a precise cut-off to reliably predict a DP. © 2016 Wiley Periodicals, Inc.
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...... studies have considered data sets with just one behavioral variable such as email communication. The Social Fabric interdisciplinary research project is an attempt to collect a more complete data set on human behavior by providing 1000 smartphones with pre-installed data collection software to students...... data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived...
Study on mathematical model of steam coal blending
Institute of Scientific and Technical Information of China (English)
高洪阁; 李白英; 刘泽常; 尹增德
2002-01-01
It is necessary to set up a new mathematical model of steam coal blending instead of the old model. Indexes such as moisture content, ash content, volatile matter, sulfur content and heating value in the new mathematical model have linear relation. The new mathematical model can also predict ash-fusion temperature precisely by considering coal ash ratio in steam coal blending, therefore it is possible to obtain linear relation of ash-fusion temperature between single coal and steam coal blending. The new mathematical model can improve precision of steam coal blending and perfect the old mathematical model of steam coal blending.
Mathematical Models of Biochemical Oscillations
Conrad, Emery David
1999-01-01
The goal of this paper is to explain the mathematics involved in modeling biochemical oscillations. We first discuss several important biochemical concepts fundamental to the construction of descriptive mathematical models. We review the basic theory of differential equations and stability analysis as it relates to two-variable models exhibiting oscillatory behavior. The importance of the Hopf Bifurcation will be discussed in detail for the central role it plays in limit cycle behavior and...
Institute of Scientific and Technical Information of China (English)
M. Peer; M. Mahdyarfar; T. Mohammadi
2008-01-01
In recent times, membranes have found wide applications in gas separation processes. As most of the industrial membrane separation units use hollow fiber modules, having a proper model for simulating this type of membrane module is very useful in achieving guidelines for design and characterization of membrane separation units. In this study, a model based on Coker, Freeman, and Fleming's study was used for estimating the required membrane area. This model could simulate a multicomponent gas mixture separation by solving the governing differential mass balance equations with numerical methods. Results of the model were validated using some binary and multicomponent experimental data from the literature. Also, the artificial neural network (ANN) technique was applied to predict membrane gas separation behavior and the results of the ANN simulation were compared with the simulation results of the model and the experimental data. Good consistency between these results shows that ANN method can be successfully used for prediction of the separation behavior after suitable training of the network.
Rateitschak, Katja; Karger, Anna; Fitzner, Brit; Lange, Falko; Wolkenhauer, Olaf; Jaster, Robert
2010-01-01
Signal transducer and activator of transcription (STAT) 1 is essentially involved in the mediation of antifibrotic interferon-gamma (IFN gamma) effects in pancreatic stellate cells (PSC). Here, we have further analysed the activation of the STAT1 pathway in a PSC line by combining quantitative data generation with mathematical modelling. At saturating concentrations of IFN gamma, a triphasic pattern of STAT1 activation was observed. An initial, rapid induction of phospho-STAT1 was followed by a plateau phase and another, long-lasting phase of further increase. The late increase occurred despite enhanced expression of the feedback inhibitor (SOCS1), and corresponded to increased levels of total STAT1 protein. If IFN gamma was applied at non-saturating concentrations, phospho-STAT1 and SOCS1 levels peaked and declined again over a 12 hour period, while STAT1 protein levels remained high. The mathematical model, based on a system of ordinary differential equations, describes temporal changes of the network components as a function of interactions and transport processes. The model reproduced activation profiles of all components of the STAT1 pathway that were experimentally analysed. Furthermore, it successfully predicted the dynamics of network components in additional experimental studies. Based on experimental findings and the results obtained from modelling, we suggest exhaustion of applied IFN gamma and STAT1 dephosphorylation by tyrosine phosphatases as limiting factors of STAT1 activation in PSC. In contrast, we did not obtain compelling evidence that SOCS1 acts as an efficient feedback inhibitor in our experimental system. We believe that further investigations into mathematical modelling of the STAT1 pathway will improve the understanding of the antifibrotic interferon action.
Mathematical Models of Waiting Time.
Gordon, Sheldon P.; Gordon, Florence S.
1990-01-01
Considered are several mathematical models that can be used to study different waiting situations. Problems involving waiting at a red light, bank, restaurant, and supermarket are discussed. A computer program which may be used with these problems is provided. (CW)
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
2016-01-01
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
Energy Technology Data Exchange (ETDEWEB)
Lopez, E.; Hernandez, J. B.; Solorio, G.; Vergara, H. J.; Vazquez, O.; Garnica, F.
2013-06-01
The heat transfer coefficient was estimated at the bottom surface at Jominy bar end quench specimen by solution of the heat inverse conduction problem. A mathematical model based on the finite-difference method was developed to predict thermal paths and volume fraction of transformed phases. The mathematical model was codified in the commercial package Microsoft Visual Basic v. 6. The calculated thermal path and final phase distribution were used to evaluate the hardness distribution along the AISI 4140 Jominy bar. (Author)
The Spectrum of Mathematical Models.
Karplus, Walter J.
1983-01-01
Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…
Murthy, Thirupathihalli Pandurangappa Krishna; Manohar, Balaraman
2014-12-01
Mango ginger (Curcuma amada) was dried in a through-flow dryer system at different temperatures (40-70 °C) and air velocities (0.84 - 2.25 m/s) to determine the effect of drying on drying rate and effective diffusivity. As the temperature and air velocity increased, drying time significantly decreased. Among the ten different thin layer drying models considered to determine the kinetic drying parameters, semi empirical Midilli et al., model gave the best fit for all drying conditions. Effective moisture diffusivity varied from 3.7 × 10(-10) m(2)/s to 12.5 × 10(-10) m(2)/s over the temperature and air velocity range of study. Effective moisture diffusivity regressed well with Arrhenius model and activation energy of the model was found to be 32.6 kJ/mol. Artificial neural network modeling was also employed to predict the drying behaviour and found suitable to describe the drying kinetics with very high correlation coefficient of 0.998.
Mathematical modeling prediction deviation and meaning%数学建模预测的偏差与意义
Institute of Scientific and Technical Information of China (English)
于佳彤
2015-01-01
In this paper, the influence of tourism of Shanghai expo as an example, analyzed the grey model GM (1, 1) in world expo for the next five years the number of domestic tourists and tourism revenue forecast. Of 2010-2014 in combination with the actual number of domestic tourists and tourist il ustrate modeling evaluation prediction error causes and improvement, analyses the modeling for students and the practical significance of the real life.%本文以世博会对上海旅游业的影响为例，分析了灰色模型GM(1，1)等在世博对未来5年国内游客人数及旅游收入的预测值。结合实际2010—2014年的国内游客人数及旅游收入阐明建模评估预测的误差起因及改进，分析了建模对学生以及现实生活的实际意义。
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
Representations used by mathematics student teachers in mathematical modeling process
Directory of Open Access Journals (Sweden)
Aytuğ Özaltun
2014-02-01
Full Text Available The purpose of this study is to determine representations used by mathematics student teachers in steps of mathematical modeling process based on their solutions of problems formed in the context of different classification of modeling. The study was conducted with fifteen secondary mathematics student teachers given a Mathematical Modeling course. The participants were separated into five collaboration groups of three students. Data were collected with the detailed written papers given by the groups for the problems and GeoGebra solution files. The groups benefited from verbal, algebraic, figural, tabular and dynamic representations while they were solving the problems. Considering all steps of the process, groups at most used verbal and algebraic representations. While they used only verbal representation in analyzing the problem, they benefited from at most verbal representation and then figural representation in establishing the systematic structure. The most used is algebraic and then verbal representations in the steps of mathematization, meta-mathematization, and mathematical analysis. In the steps of interpretation/evaluation and the model verification, the groups mainly benefited from verbal and then algebraic representations. Further researches towards why representations are preferred in the specific steps of the mathematical modeling process are suggested.Key Words: Mathematical modeling, modeling problems, mathematics student teachers, representations.
The 24-Hour Mathematical Modeling Challenge
Galluzzo, Benjamin J.; Wendt, Theodore J.
2015-01-01
Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…
Generalized Mathematical Model for Hot Rolling Process of Plate
Institute of Scientific and Technical Information of China (English)
Zhenshan CUI; Bingye XU
2003-01-01
A generalized mathematical model is developed to predict the changes of temperature, rolling pressure, strain,strain rate, and austenite grain size for plate hot rolling and cooling processes. The model is established mainly by incorporating analytical an
Modeling interdisciplinary activities involving Mathematics
DEFF Research Database (Denmark)
Iversen, Steffen Møllegaard
2006-01-01
In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...
Energy Technology Data Exchange (ETDEWEB)
Zambrano, Lorenzo [Instituto de Investigaciones Electricas, Cuernavaca (Mexico)
1986-12-31
There is an abundant, reliable, free, source of energy whose use can be planned and besides, practicably inexhaustible: the solar energy. In Mexico it constitutes an important resource, because of its geographical position; for this reason it is fundamental to know it well, either by means of measurements conducted for several years or by mathematical models. These last ones predict with meteorological variables, the values of the solar radiation with acceptable precision. At the Instituto de Investigaciones Electricas (IIE) a model is studied for the prediction of the solar radiation to be adapted to the local conditions of Mexico. It is used in simulation studies of the solar plants functioning and other solar systems. [Espanol] Existe una fuente de energia abundante, confiable, gratuita, cuyo uso puede planearse y, ademas, es practicamente inagotable: la solar. En Mexico constituye un recurso importante, por la posicion geografica del pais; por eso es fundamental conocerlo bien, ya mediante mediciones realizadas durante algunos anos, ya mediante modelos matematicos. Estos ultimos predicen, con datos de variables meteorologicas, los valores de la radiacion solar con precision aceptable. En el Instituto de Investigaciones Electricas (IIE) se estudia un modelo de prediccion de radiacion solar para adaptarlo a las condiciones locales de Mexico. Se usa en estudios de simulacion del funcionamiento de plantas helioelectricas y otros sistemas solares.
Mathematical modelling of membrane separation
DEFF Research Database (Denmark)
Vinther, Frank
This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate....... It is found that the probability of entering the pore is highest when the largest of the radii in the ellipse is equal to half the radius of the pore, in case of molecules with circular radius less than the pore radius. The results are directly related to the macroscopic distribution coefficient...
Mathematical modeling of the flash converting process
Energy Technology Data Exchange (ETDEWEB)
Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)
1996-12-31
An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)
Competence with Fractions Predicts Gains in Mathematics Achievement
Bailey, Drew H.; Hoard, Mary K.; Nugent, Lara; Geary, David C.
2012-01-01
Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth…
Why Do Early Mathematics Skills Predict Later Reading? The Role of Mathematical Language
Purpura, David J.; Logan, Jessica A. R.; Hassinger-Das, Brenna; Napoli, Amy R.
2017-01-01
A growing body of evidence indicates that the development of mathematics and literacy skills is highly related. The importance of literacy skills--specifically language--for mathematics development has been well rationalized. However, despite several prominent studies indicating that mathematics skills are highly predictive of literacy…
Mathematical models for therapeutic approaches to control HIV disease transmission
Roy, Priti Kumar
2015-01-01
The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...
Sugibayashi, Kenji; Todo, Hiroaki; Oshizaka, Takeshi; Owada, Yoko
2010-01-01
To calculate the skin concentration of active ingredients in cosmetics and topical pharmaceuticals using silicone membrane permeation. A series of parabens were used as model ingredients. Skin concentration of parabens was calculated using silicone membrane permeability. Their partition coefficient from formulations to the silicone membrane was determined by the membrane permeation profiles, and used to calculate their silicone membrane concentration, under an assumption that the membrane is one homogenous diffusion layer. The same procedure was applied for hairless rat skin. The calculated concentration of parabens in silicone membrane was very close to their observed values. However, the skin concentration calculated by skin permeability was not similar to the observed concentration. Re-calculation was performed under the assumption that the skin consists of two diffusion layers. This modification using permeation data through full-thickness and stripped skin enabled precise prediction of the skin concentration of parabens. In addition, the partition coefficient to the silicone membrane was useful to estimate their skin concentration. Ingredient concentration in skin can be precisely predicted using diffusion equations and partition coefficients through permeation experiments using a silicone membrane. The calculated in-skin concentration is useful for formulation studies of cosmetics and topical pharmaceuticals.
Modeling life the mathematics of biological systems
Garfinkel, Alan; Guo, Yina
2017-01-01
From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. This book develops the mathematical tools essential for students in the life sciences to describe these interacting systems and to understand and predict their behavior. Complex feedback relations and counter-intuitive responses are common in dynamical systems in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models ...
Yilmaz, Suha; Tekin-Dede, Ayse
2016-01-01
Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…
Competence with fractions predicts gains in mathematics achievement.
Bailey, Drew H; Hoard, Mary K; Nugent, Lara; Geary, David C
2012-11-01
Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, pmathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.
Panayidou, Klea; Gsteiger, Sandro; Egger, Matthias; Kilcher, Gablu; Carreras, Máximo; Efthimiou, Orestis; Debray, Thomas P A; Trelle, Sven; Hummel, Noemi
2016-01-01
The performance of a drug in a clinical trial setting often does not reflect its effect in daily clinical practice. In this third of three reviews, we examine the applications that have been used in the literature to predict real-world effectiveness from randomized controlled trial efficacy data. We
Modeling interdisciplinary activities involving Mathematics
DEFF Research Database (Denmark)
Iversen, Steffen Møllegaard
2006-01-01
In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...
Mathematical modeling of microbial growth in milk
Directory of Open Access Journals (Sweden)
Jhony Tiago Teleken
2011-12-01
Full Text Available A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.
Competence with Fractions Predicts Gains in Mathematics Achievement
Drew H. Bailey; Hoard, Mary K.; Nugent, Lara; David C Geary
2012-01-01
Competence with fractions predicts later mathematics achievement, but the co-developmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this co-development through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grade (n = 212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted one year...
Using Prediction to Promote Mathematical Understanding and Reasoning
Kasmer, Lisa; Kim, Ok-Kyeong
2011-01-01
Research has shown that prediction has the potential to promote the teaching and learning of mathematics because it can be used to enhance students' thinking and reasoning at all grade levels in various topics. This article addresses the effectiveness of using prediction on students' understanding and reasoning of mathematical concepts in a middle…
Mathematical modelling in solid mechanics
Sofonea, Mircea; Steigmann, David
2017-01-01
This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...
Casha, Aaron R; Camilleri, Liberato; Manché, Alexander; Gatt, Ruben; Attard, Daphne; Gauci, Marilyn; Camilleri-Podesta, Marie-Therese; Mcdonald, Stuart; Grima, Joseph N
2015-11-01
The human rib cage resembles a masonry dome in shape. Masonry domes have a particular construction that mimics stress distribution. Rib cortical thickness and bone density were analyzed to determine whether the morphology of the rib cage is sufficiently similar to a shell dome for internal rib structure to be predicted mathematically. A finite element analysis (FEA) simulation was used to measure stresses on the internal and external surfaces of a chest-shaped dome. Inner and outer rib cortical thickness and bone density were measured in the mid-axillary lines of seven cadaveric rib cages using computerized tomography scanning. Paired t tests and Pearson correlation were used to relate cortical thickness and bone density to stress. FEA modeling showed that the stress was 82% higher on the internal than the external surface, with a gradual decrease in internal and external wall stresses from the base to the apex. The inner cortex was more radio-dense, P rib level. The internal anatomical features of ribs, including the inner and outer cortical thicknesses and bone densities, are similar to the stress distribution in dome-shaped structures modeled using FEA computer simulations of a thick-walled dome pressure vessel. Fixation of rib fractures should include the stronger internal cortex. © 2015 Wiley Periodicals, Inc.
mathematical model for direct evaporative space cooling systems
African Journals Online (AJOL)
eobe
MATHEMATICAL MODEL FOR DIRECT EVAPORATIVE SPACE COOLING. SYSTEMS ... Water is the working fluid in evaporative cooling thus it is ..... co o lin g efficien cy (%. ) Time (hrs) predicted experimental. 0. 10. 20. 30. 40. 50. 60. 70. 80.
2015-08-24
dislocations in RDX - family of crystallographic planes on which slip occurs- The (010)[100] screw configuration was found to be unstable. Structure of the (010...Peierls stress (critical stress for dislocation motion), c) we discovered a family of point defects which are rotated and distorted molecules...result needed in crystal plasticity models of hot spot formation, e) we developed a family of coarse grained models for the RDX crystal in which the
Opinions of Secondary School Mathematics Teachers on Mathematical Modelling
Tutak, Tayfun; Güder, Yunus
2013-01-01
The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…
Opinions of Secondary School Mathematics Teachers on Mathematical Modelling
Tutak, Tayfun; Güder, Yunus
2013-01-01
The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…
Continuum mechanics the birthplace of mathematical models
Allen, Myron B
2015-01-01
Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer. This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe
Mathematical models of granular matter
Mariano, Paolo; Giovine, Pasquale
2008-01-01
Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.
Tessone, Ariel; Nava, Maurizio; Blondeel, Phillip; Spano, Andrea
2016-02-01
Ever since its introduction, the transverse rectus abdominis myocutaneous flap has become the mainstay of autologous breast reconstruction. However, concerns regarding donor site morbidity due to the breach of abdominal wall musculature integrity soon followed. Muscle-sparing techniques, eventually eliminating the muscle from the flap all-together with the deep inferior epigastric artery perforator flap, did not eliminate the problem of abdominal wall weakness. This led to the conclusion that motor innervation might be at fault. Studies have shown that even in the presence of an intact rectus abdominis muscle, and an intact anterior rectus sheath, denervation of the rectus abdominis muscle results in significant abdominal wall weakness leading to superior and inferior abdominal bulges, and abdominal herniation. Our aim was to establish a mathematical model to predict the location of the motor innervation to the rectus abdominis muscle, and thus provide surgeons with a tool that will allow them to reduce abdominal morbidity during deep inferior epigastric artery perforator and free muscle-sparing transverse rectus abdominis myocutaneous surgery. We dissected 42 cadaveric hemiabdomens and mapped the course of the thoracolumbar nerves. We then standardized and analyzed our findings and presented them as a relative map which can be adjusted to body type and dimensions. Our dissections show that the motor innervation is closely related to the lateral vascular supply. Thus, when possible, we support the preferred utilization of the medial vascular supply, and the preservation of the lateral supply and motor innervation.
Mathematical modeling of laser lipolysis
Directory of Open Access Journals (Sweden)
Reynaud Jean
2008-02-01
Full Text Available Abstract Background and Objectives Liposuction continues to be one of the most popular procedures performed in cosmetic surgery. As the public's demand for body contouring continues, laser lipolysis has been proposed to improve results, minimize risk, optimize patient comfort, and reduce the recovery period. Mathematical modeling of laser lipolysis could provide a better understanding of the laser lipolysis process and could determine the optimal dosage as a function of fat volume to be removed. Study design/Materials and Methods An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc. The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer with a nonlinear air-tissue boundary condition including free convection. Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature. Results In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s give similar skin surface temperature (max: 41°C. These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction
Mathematical modeling of kidney transport.
Layton, Anita T
2013-01-01
In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease.
Mathematical Modeling in Combustion Science
Takeno, Tadao
1988-01-01
An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.
A mathematical model of inheritance
Institute of Scientific and Technical Information of China (English)
瞿裕忠; 王志坚; 徐家福
1996-01-01
Inheritance is regarded as the hallmark of object-oriented programming languages.A mathematical model of inheritance is presented.In this model,the graph-sorted signature is introduced to represent the algebraic structure of the program,and an extension function on the graph-sorted signatures is used to formally describe the semantics of inheritance.The program’s algebraic structure reflects the syntactic constraints of the language and the corresponding extension function exposes the character of the language’s inheritance.
Application of Mathematical Modeling Activities in Costarican High School Education
Directory of Open Access Journals (Sweden)
Karen Porras-Lizano
2015-01-01
Full Text Available This paper describes the experience gained in implementing mathematical modeling activities as a methodological strategy in teaching issues such as proportions, with a group of eighth year of an academic-day-school, located in the province of San Jose, Costa Rica in 2012. Different techniques for gathering information were applied, such as participant observation and questionnaires. Among the relevant results are the cyclical development of mathematical thinking of students in the stages of mathematical modeling (description, manipulation, prediction and validation for solving the problem; developing of teamwork skills; and appreciation of mathematics as a useful and effective discipline. To resolve the activities proposed in this study, social interactions such as sharing information, thoughts and ideas, were generated, stimulating the zone of proximal development of the participating students. Likewise, the mathematical modeling activities allowed students to have a positive role in mathematics classes, stimulating, in turn, a different attitude compared to regular classes.
Levpuscek, Melita Puklek; Zupancic, Maja; Socan, Gregor
2013-01-01
The study examined individual factors and social factors that influence adolescent students' achievement in mathematics. The predictive model suggested direct positive effects of student intelligence, self-rated openness and parental education on achievement in mathematics, whereas direct effects of extraversion on measures of achievement were…
A Mathematical Model of Mechanotransduction
Roth, Bradley J
2016-01-01
This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between intracellular and extracellular displacements drive mechanotransduction. A one-dimensional example illustrates the model, which is then extended to two dimensions. In several cases the equations are solved analytically, illustrating how displacements divide into two parts: monodomain displacements are identical in both spaces and therefore do not contribute to mechanotransduction, whereas bidomain displacements cause mechanotransduction. A new length constant depends on the intracellular and extracellular shear moduli and the integrin spring constant, and bidomain effects often occur within a few length constants of the tissue edge. Numerical methods for solving the model equations are being developed. Precursors to the model and potential applications are discussed. The bidomain model...
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular analysis tools within the neuroimaging community. Such methods...... attempt to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical...... influence of model regularization parameter choices on the model generalization, the reliability of the spatial brain patterns extracted from the analysis model, and the ability of the model to identify relevant brain networks defining the underlying neural encoding of the experiment. We show that known...
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular within the neuroimaging community. Such methods attempt...... to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical neuroimaging data...... of model regularization parameter choices on the model generalization, the reliability of the spatial brain patterns extracted from the analysis model, and the ability of the resulting model to identify relevant brain networks defining the underlying neural encoding of the experiment. We show that known...
Designing Prediction Tasks in a Mathematics Software Environment
Brunström, Mats; Fahlgren, Maria
2015-01-01
There is a recognised need in mathematics teaching for new kinds of tasks which exploit the affordances provided by new technology. This paper focuses on the design of prediction tasks to foster student reasoning about exponential functions in a mathematics software environment. It draws on the first iteration of a design based research study…
A mathematical model of aortic aneurysm formation
Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R.; Friedman, Avner; Zhu, Dai
2017-01-01
Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient’s aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient’s abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material. PMID:28212412
Why do early mathematics skills predict later reading? The role of mathematical language.
Purpura, David J; Logan, Jessica A R; Hassinger-Das, Brenna; Napoli, Amy R
2017-09-01
A growing body of evidence indicates that the development of mathematics and literacy skills is highly related. The importance of literacy skills-specifically language-for mathematics development has been well rationalized. However, despite several prominent studies indicating that mathematics skills are highly predictive of literacy development, the reason for this relation is not well understood. The purpose of this study was to identify how and why early mathematics is predictive of early literacy development. Participants included 125 preschool children 3-5 years old (M = 4 years 3 months). Participants were assessed on mathematics, literacy, and cognitive measures in both the fall and spring of their preschool year. Mediation analyses indicated that the relation between early mathematics and literacy skills is mediated by children's mathematical language skills. These findings suggest that, in prior research identifying mathematical performance as a significant predictor of later literacy skills, mathematical performance may have acted only as a proxy measure for more complex language skills such as those assessed on a mathematical language measure. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Explorations in Elementary Mathematical Modeling
Directory of Open Access Journals (Sweden)
Mazen Shahin
2010-06-01
Full Text Available In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and cooperative learning into this inquiry-based learning course where students work in small groups on carefully designed activities and utilize available software to support problem solving and understanding of real life situations. We emphasize the use of graphical and numerical techniques, rather than theoretical techniques, to investigate and analyze the behavior of the solutions of the difference equations.As an illustration of our approach, we will show a nontraditional and efficient way of introducing models from finance and economics. We will also present an interesting model of supply and demand with a lag time, which is called the cobweb theorem in economics. We introduce a sample of a research project on a technique of removing chaotic behavior from a chaotic system.
Mathematical Modelling Plant Signalling Networks
Muraro, D.
2013-01-01
During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.
Santos, Guido; Díaz, Mario; Torres, Néstor V
2016-01-01
A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease.
A mathematical model of a computational problem solving system
Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan
2015-05-01
This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.
Mathematical modelling of leprosy and its control.
Blok, David J; de Vlas, Sake J; Fischer, Egil A J; Richardus, Jan Hendrik
2015-03-01
Leprosy or Hansen's disease is an infectious disease caused by the bacterium Mycobacterium leprae. The annual number of new leprosy cases registered worldwide has remained stable over the past years at over 200,000. Early case finding and multidrug therapy have not been able interrupt transmission completely. Elimination requires innovation in control and sustained commitment. Mathematical models can be used to predict the course of leprosy incidence and the effect of intervention strategies. Two compartmental models and one individual-based model have been described in the literature. Both compartmental models investigate the course of leprosy in populations and the long-term impact of control strategies. The individual-based model focusses on transmission within households and the impact of case finding among contacts of new leprosy patients. Major improvement of these models should result from a better understanding of individual differences in exposure to infection and developing leprosy after exposure. Most relevant are contact heterogeneity, heterogeneity in susceptibility and spatial heterogeneity. Furthermore, the existing models have only been applied to a limited number of countries. Parameterization of the models for other areas, in particular those with high incidence, is essential to support current initiatives for the global elimination of leprosy. Many challenges remain in understanding and dealing with leprosy. The support of mathematical models for understanding leprosy epidemiology and supporting policy decision making remains vital.
Mathematical model of induction heating
Rak, Josef
2017-07-01
One of mathematical models of induction heating can be described by a parabolic differential equation with the specific Joule looses in the body. Advantage of this method is that the detailed knowledge of the 3D-magnetic field is not necessary and move of the body or the inductor can be easily implemented. The specific Joule looses can computed by solving the Fredholm integral equation of the second kind for the eddy current of density by the Nyström method with the singularity subtraction.
Thermoregulation in premature infants: A mathematical model.
Pereira, Carina Barbosa; Heimann, Konrad; Czaplik, Michael; Blazek, Vladimir; Venema, Boudewijn; Leonhardt, Steffen
2016-12-01
In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37°C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25±0.21°C and that of skin temperature averaged 0.36±0.36°C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12±0.11°C and that of skin temperatures hovered around 0.30°C. The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions. Copyright Â© 2016 Elsevier Ltd. All rights reserved.
Mathematical models of human african trypanosomiasis epidemiology.
Rock, Kat S; Stone, Chris M; Hastings, Ian M; Keeling, Matt J; Torr, Steve J; Chitnis, Nakul
2015-03-01
Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT.
Mathematical models in marketing a collection of abstracts
Funke, Ursula H
1976-01-01
Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...
Mathematical modeling courses for Media technology students
DEFF Research Database (Denmark)
Timcenko, Olga
2009-01-01
This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematic...
A Generative Model of Mathematics Learning
Wittrock, M. C.
1974-01-01
The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…
Energy Technology Data Exchange (ETDEWEB)
Suehiro, M.; Oda, T.; Senuma, T.; Konishi, S. [Nippon Steel Corp., Tokyo (Japan)
1995-11-06
A mathematical model for predicting transformation of high carbon steel during cooling (transformation from austenite to pearlite, ferrite, and bainite) has been developed. The basic equation for this model is the Cahn`s transformation progress behavior indicating equation, from which an equation was introduced that represents transformation velocity for the case of generation and growth of nuclei and for the case of site saturation. Using these equations makes it possible to calculate transformation in arbitrary cooling processes. In addition, a prediction model for hot processing transformation that expresses the influence of the hot processing on transformation was coupled with the transformation equation to improve the accuracy of transformation prediction. Rise in steel plate temperature that takes place because of generation of transformation latent heat during cooling was calculated by using a two-dimensional heat conduction equation. Off-line applications of this model include prediction of steel plate temperatures on a hot-run table, improvement in productivity by increasing plate passing speed in a continuous hot rolling process, and correction of variation in finishing rolling temperature. On-line applications include controls in hot-run water injection facilities, and automation of an on-line control system. 13 refs., 18 figs., 1 tab.
Incorporating neurophysiological concepts in mathematical thermoregulation models
Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.
2014-01-01
Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.
Mathematical models in biological discovery
Walter, Charles
1977-01-01
When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medic...
A mathematical model of aerosol holding chambers
DEFF Research Database (Denmark)
Zak, M; Madsen, J; Berg, E
1999-01-01
A mathematical model of aerosol delivery from holding chambers (spacers) was developed incorporating tidal volume (VT), chamber volume (Vch), apparatus dead space (VD), effect of valve insufficiency and other leaks, loss of aerosol by immediate impact on the chamber wall, and fallout of aerosol...... in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London......, Ontario, Canada), NebuChamber (Astra, Södirtälje, Sweden) and Nebuhaler (Astra) adapted for babies. The dose of fluticasone proportionate delivered by the Babyhaler (Glaxco Wellcome, Oxbridge, Middlesex, UK) was 80% of that predicted, probably because of incomplete priming of this spacer. Of the above...
Economic-mathematical methods and models under uncertainty
Aliyev, A G
2013-01-01
Brief Information on Finite-Dimensional Vector Space and its Application in EconomicsBases of Piecewise-Linear Economic-Mathematical Models with Regard to Influence of Unaccounted Factors in Finite-Dimensional Vector SpacePiecewise Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence in Three-Dimensional Vector SpacePiecewise-Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence on a PlaneBases of Software for Computer Simulation and Multivariant Prediction of Economic Even at Uncertainty Conditions on the Base of N-Comp
Building fire zone model with symbolic mathematics
Institute of Scientific and Technical Information of China (English)
武红梅; 郜冶; 周允基
2009-01-01
To apply the fire modelling for the fire engineer with symbolic mathematics,the key equations of a zone model were demonstrated. There were thirteen variables with nine constraints,so only four ordinary differential equations (ODEs) were required to solve. A typical fire modelling with two-room structure was studied. Accordingly,the source terms included in the ODEs were simplified and modelled,and the fourth Runge-Kutta method was used to solve the ordinary differential equations (ODEs) with symbolic mathematics. Then a zone model could be used with symbolic mathematics. It is proposed that symbolic mathematics is possible for use by fire engineer.
Mathematical modeling in biomedical imaging
2012-01-01
This volume reports on recent mathematical and computational advances in optical, ultrasound, and opto-acoustic tomographies. It outlines the state-of-the-art and future directions in these fields and provides readers with the most recently developed mathematical and computational tools. It is particularly suitable for researchers and graduate students in applied mathematics and biomedical engineering.
Fluid reasoning predicts future mathematical performance among children and adolescents.
Green, Chloe T; Bunge, Silvia A; Briones Chiongbian, Victoria; Barrow, Maia; Ferrer, Emilio
2017-05-01
The aim of this longitudinal study was to determine whether fluid reasoning (FR) plays a significant role in the acquisition of mathematics skills above and beyond the effects of other cognitive and numerical abilities. Using a longitudinal cohort sequential design, we examined how FR measured at three assessment occasions, spaced approximately 1.5years apart, predicted math outcomes for a group of 69 participants between ages 6 and 21years across all three assessment occasions. We used structural equation modeling (SEM) to examine the direct and indirect relations between children's previous cognitive abilities and their future math achievement. A model including age, FR, vocabulary, and spatial skills accounted for 90% of the variance in future math achievement. In this model, FR was the only significant predictor of future math achievement; age, vocabulary, and spatial skills were not significant predictors. Thus, FR was the only predictor of future math achievement across a wide age range that spanned primary school and secondary school. These findings build on Cattell's conceptualization of FR as a scaffold for learning, showing that this domain-general ability supports the acquisition of rudimentary math skills as well as the ability to solve more complex mathematical problems.
Mathematical modeling of the Phoenix Rising pathway.
Directory of Open Access Journals (Sweden)
Chad Liu
2014-02-01
Full Text Available Apoptosis is a tightly controlled process in mammalian cells. It is important for embryogenesis, tissue homoeostasis, and cancer treatment. Apoptosis not only induces cell death, but also leads to the release of signals that promote rapid proliferation of surrounding cells through the Phoenix Rising (PR pathway. To quantitatively understand the kinetics of interactions of different molecules in this pathway, we developed a mathematical model to simulate the effects of various changes in the PR pathway on the secretion of prostaglandin E2 (PGE2, a key factor for promoting cell proliferation. These changes include activation of caspase 3 (C3, caspase 7 (C7, and nuclear factor κB (NFκB. In addition, we simulated the effects of cyclooxygenase-2 (COX2 inhibition and C3 knockout on the level of secreted PGE2. The model predictions on PGE2 in MEF and 4T1 cells at 48 hours after 10-Gray radiation were quantitatively consistent with the experimental data in the literature. Compared to C7, the model predicted that C3 activation was more critical for PGE2 production. The model also predicted that PGE2 production could be significantly reduced when COX2 expression was blocked via either NFκB inactivation or treatment of cells with exogenous COX2 inhibitors, which led to a decrease in the rate of conversion from arachidonic acid to prostaglandin H2 in the PR pathway. In conclusion, the mathematical model developed in this study yielded new insights into the process of tissue regrowth stimulated by signals from apoptotic cells. In future studies, the model can be used for experimental data analysis and assisting development of novel strategies/drugs for improving cancer treatment or normal tissue regeneration.
Mathematical models for plant-herbivore interactions
Feng, Zhilan; DeAngelis, Donald L.
2017-01-01
Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.
Computacional-representantional model of mathematics (crmmath)
Toro Carvajal, Luis Alberto
2016-01-01
This paper presents the so-called computational representational model of mathematics (MCRMATH), its theoretical importance for mathematics education and its relation with the use of technology tools in mathematics teaching. To do this, from a cognitive point of view, we conduct a research study of representations and we explain the computational-representational model of mind (CRMM).
A Mathematical Model for Cisplatin Cellular Pharmacodynamics
Directory of Open Access Journals (Sweden)
Ardith W. El-Kareh
2003-03-01
Full Text Available A simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (∼100 hours. The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy.
Mathematical Model for Photovoltaic Cells
Directory of Open Access Journals (Sweden)
Wafaa ABD EL-BASIT
2013-11-01
Full Text Available The study of photovoltaic systems in an efficient manner requires a precise knowledge of the (I-V and (P-V characteristic curves of photovoltaic modules. So, the aim of the present paper is to estimate such characteristics based on different operating conditions. In this concern, a simple one diode mathematical model was implemented using MATLAB script. The output characteristics of PV cell depend on the environmental conditions. For any solar cell, the model parameters are function of the irradiance and the temperature values of the site where the panel is placed. In this paper, the numerical values of the equivalent circuit parameters are generated by the program. As well, the dependence of the cells electrical parameters are analyzed under the influence of different irradiance and temperature levels. The variation of slopes of the (I–V curves of a cell at short-circuit and open-circuit conditions with intensity of illumination in small span of intensity and different temperature levels have been applied to determine the cell parameters, shunt resistance, series resistance. The results show that the efficiency of solar cells has an inverse relationship with temperature, irradiance levels are affected by the change of the photo-generation current and the series resistance in the single diode model.
Marcelino, Lilia; de Sousa, Óscar; Lopes, António
2017-01-01
Early numerical competencies (ENC) (counting, number relations, and basic arithmetic operations) have a central position in the initial learning of mathematics, and their assessment is useful for predicting later mathematics achievement. Using a regression model, this study aims to analyze the correlational and predictive evidence between ENC and mathematics achievement in first grade Portuguese children (n = 123). The children’s ENC were examined at the point of school entry. Three criterion groups (low, moderate, and high ENC) were formed based on the results of the early numerical brief screener and mathematics achievement measured at the end of first grade. The following hypotheses were tested: children who started first grade with low numerical competencies remained low mathematics achievement at the end of first grade; and children who started with high numerical competencies, finished the first grade with high mathematics achievement. The results showed that ENC contributed to a significant amount of explained variance in mathematics achievement at the end of the first grade. Children with low numerical competencies performed lower than children with moderate and high numerical competencies. Findings suggest that ENC are meaningful for predicting first-grade mathematics difficulties. PMID:28713308
Directory of Open Access Journals (Sweden)
Lilia Marcelino
2017-06-01
Full Text Available Early numerical competencies (ENC (counting, number relations, and basic arithmetic operations have a central position in the initial learning of mathematics, and their assessment is useful for predicting later mathematics achievement. Using a regression model, this study aims to analyze the correlational and predictive evidence between ENC and mathematics achievement in first grade Portuguese children (n = 123. The children’s ENC were examined at the point of school entry. Three criterion groups (low, moderate, and high ENC were formed based on the results of the early numerical brief screener and mathematics achievement measured at the end of first grade. The following hypotheses were tested: children who started first grade with low numerical competencies remained low mathematics achievement at the end of first grade; and children who started with high numerical competencies, finished the first grade with high mathematics achievement. The results showed that ENC contributed to a significant amount of explained variance in mathematics achievement at the end of the first grade. Children with low numerical competencies performed lower than children with moderate and high numerical competencies. Findings suggest that ENC are meaningful for predicting first-grade mathematics difficulties.
Modelling and Optimizing Mathematics Learning in Children
Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus
2013-01-01
This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…
Scaffolding Mathematical Modelling with a Solution Plan
Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner
2015-01-01
In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…
Mathematical Model of Gravitational and Electrostatic Forces
Krouglov, Alexei
2006-01-01
Author presents mathematical model for acting-on-a-distance attractive and repulsive forces based on propagation of energy waves that produces Newton expression for gravitational and Coulomb expression for electrostatic forces. Model uses mathematical observation that difference between two inverse exponential functions of the distance asymptotically converges to function proportional to reciprocal of distance squared.
Mathematical Modelling as a Professional Task
Frejd, Peter; Bergsten, Christer
2016-01-01
Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…
Mineral potential mapping with mathematical geological models
Porwal, A.K.
2006-01-01
Mathematical geological models are being increasingly used by natural resources delineation and planning agencies for mapping areas of mineral potential in order to optimize land use in accordance with socio-economic needs of the society. However, a key problem in spatial-mathematical-model-based mi
Mathematical Modeling of the Agriculture Crop Technology
Directory of Open Access Journals (Sweden)
D. Drucioc
1999-02-01
Full Text Available The organized structure of computer system for economic and ecological estimation of agriculture crop technologies is described. The system is composed of six interconnected blocks. The linear, non-linear and stochastic mathematical models for machinery sizing and selection in farm-level cropping system is presented in the mathematical model block of computer system.
Mineral potential mapping with mathematical geological models
Porwal, A.K.
2006-01-01
Mathematical geological models are being increasingly used by natural resources delineation and planning agencies for mapping areas of mineral potential in order to optimize land use in accordance with socio-economic needs of the society. However, a key problem in spatial-mathematical-model-based
Mathematical Modeling of the Induced Mutation Process in Bacterial Cells
Belov, Oleg V.; Krasavin, Evgeny A.; Parkhomenko, Alexander Yu.
2010-01-01
A mathematical model of the ultraviolet (UV) irradiation-induced mutation process in bacterial cells Escherichia coli is developed. Using mathematical approaches, the whole chain of events is tracked from a cell exposure to the damaging factor to mutation formation in the DNA chain. An account of the key special features of the regulation of this genetic network allows predicting the effects induced by the cell exposure to certain UV energy fluence.
Mathematical Modeling of Cellular Metabolism.
Berndt, Nikolaus; Holzhütter, Hermann-Georg
2016-01-01
Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.
Mathematical modelling of scour: A review
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2007-01-01
A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers/piles and pipeli......A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...
Predictive models of forest dynamics.
Purves, Drew; Pacala, Stephen
2008-06-13
Dynamic global vegetation models (DGVMs) have shown that forest dynamics could dramatically alter the response of the global climate system to increased atmospheric carbon dioxide over the next century. But there is little agreement between different DGVMs, making forest dynamics one of the greatest sources of uncertainty in predicting future climate. DGVM predictions could be strengthened by integrating the ecological realities of biodiversity and height-structured competition for light, facilitated by recent advances in the mathematics of forest modeling, ecological understanding of diverse forest communities, and the availability of forest inventory data.
Mathematical modeling in soil science
Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel
2015-04-01
Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.
Mathematical and computational modeling simulation of solar drying Systems
Mathematical modeling of solar drying systems has the primary aim of predicting the required drying time for a given commodity, dryer type, and environment. Both fundamental (Fickian diffusion) and semi-empirical drying models have been applied to the solar drying of a variety of agricultural commo...
A Mathematical Model of Cigarette Smoldering Process
Directory of Open Access Journals (Sweden)
Chen P
2014-12-01
Full Text Available A mathematical model for a smoldering cigarette has been proposed. In the analysis of the cigarette combustion and pyrolysis processes, a receding burning front is defined, which has a constant temperature (~450 °C and divides the cigarette into two zones, the burning zone and the pyrolysis zone. The char combustion processes in the burning zone and the pyrolysis of virgin tobacco and evaporation of water in the pyrolysis zone are included in the model. The hot gases flow from the burning zone, are assumed to go out as sidestream smoke during smoldering. The internal heat transport is characterized by effective thermal conductivities in each zone. Thermal conduction of cigarette paper and convective and radiative heat transfer at the outer surface were also considered. The governing partial differential equations were solved using an integral method. Model predictions of smoldering speed as well as temperature and density profiles in the pyrolysis zone for different kinds of cigarettes were found to agree with the experimental data. The model also predicts the coal length and the maximum coal temperatures during smoldering conditions. The model provides a relatively fast and efficient way to simulate the cigarette burning processes. It offers a practical tool for exploring important parameters for cigarette smoldering processes, such as tobacco components, properties of cigarette paper, and heat generation in the burning zone and its dependence on the mass burn rate.
Preschool executive functioning abilities predict early mathematics achievement.
Clark, Caron A C; Pritchard, Verena E; Woodward, Lianne J
2010-09-01
Impairments in executive function have been documented in school-age children with mathematical learning difficulties. However, the utility and specificity of preschool executive function abilities in predicting later mathematical achievement are poorly understood. This study examined linkages between children's developing executive function abilities at age 4 and children's subsequent achievement in mathematics at age 6, 1 year after school entry. The study sample consisted of a regionally representative cohort of 104 children followed prospectively from ages 2 to 6 years. At age 4, children completed a battery of executive function tasks that assessed planning, set shifting, and inhibitory control. Teachers completed the preschool version of the Behavior Rating Inventory of Executive Function. Clinical and classroom measures of children's mathematical achievement were collected at age 6. Results showed that children's performance on set shifting, inhibitory control, and general executive behavior measures during the preschool period accounted for substantial variability in children's early mathematical achievement at school. These associations persisted even after individual differences in general cognitive ability and reading achievement were taken into account. Findings suggest that early measures of executive function may be useful in identifying children who may experience difficulties learning mathematical skills and concepts. They also suggest that the scaffolding of these executive skills could potentially be a useful additional component in early mathematics education.
A Seminar in Mathematical Model-Building.
Smith, David A.
1979-01-01
A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)
Zephyr - the prediction models
DEFF Research Database (Denmark)
Nielsen, Torben Skov; Madsen, Henrik; Nielsen, Henrik Aalborg
2001-01-01
This paper briefly describes new models and methods for predicationg the wind power output from wind farms. The system is being developed in a project which has the research organization Risø and the department of Informatics and Mathematical Modelling (IMM) as the modelling team and all the Dani...
Children's visuospatial memory predicts mathematics achievement through early adolescence.
Li, Yaoran; Geary, David C
2017-01-01
A previous study showed that gains in visuospatial memory from first to fifth grade predicted end-of-fifth grade mathematics but not reading achievement, controlling other factors. In this follow up study, these relations were assessed from sixth to ninth grade, inclusive (n = 145). The results showed that growth in visuospatial memory across the elementary school years was related to growth in mathematics achievement after fifth grade, controlling intelligence, the central executive and phonological memory components of working memory, in-class attentive behavior, parental education, and fifth grade mathematics achievement. As found for fifth grade, this relation was not found for reading achievement after fifth grade. In total, the results suggest that visuospatial memory has a unique influence on ease of learning some types of mathematics and that this influence becomes more important across successive grades.
MATHEMATICAL MODEL OF GRAIN MICRONIZATION
Directory of Open Access Journals (Sweden)
V. A. Afanas’ev
2014-01-01
Full Text Available Summary. During micronisation grain moisture evaporates mainly in decreasing drying rate period. Grain layer located on the surface of the conveyor micronisers will be regarded as horizontal plate. Due to the fact that the micronisation process the surface of the grain evaporates little moisture (within 2-7 % is assumed constant plate thickness. Because in the process of micronization grain structure is changing, in order to achieve an exact solution of the equations necessary to take into account changes thermophysical, optical and others. Equation of heat transfer is necessary to add a term that is responsible for the infrared heating. Because of the small thickness of the grain, neglecting the processes occurring at the edge of the grain, that is actually consider the problem of an infinite plate. To check the adequacy of the mathematical model of the process of micronisation of wheat grain moisture content must be comparable to the function of time, obtained by solving the system of equations with the measured experimental data of experience. Numerical solution of a system of equations for the period of decreasing drying rate is feasible with the help of the Maple 14, substituting the values of the constants in the system. Calculation of the average relative error does not exceed 7- 10 %, and shows a good agreement between the calculated data and the experimental values.
Applications of mathematical models of road cycling
Dahmen, Thorsten; Saupe, Dietmar; Wolf, Stefan
2012-01-01
This contribution discusses several use cases of mathematical models for road cycling. A mechanical model for the pedaling forces is the basis for an accurate indoor ergometer simulation of road cycling on real-world tracks. Together with a simple physiological model for the exertion of the athlete as a function of his/her accumulated power output, an optimal riding strategy for time trials on mountain ascents is computed. A combination of the two models leads to a mathematical optimization p...
Mathematical model insights into arsenic detoxification
Directory of Open Access Journals (Sweden)
Nijhout H Frederik
2011-08-01
Full Text Available Abstract Background Arsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs, which then undergoes hepatic methylation to methylarsonic acid (MMAs and a second methylation to dimethylarsinic acid (DMAs. Although MMAs and DMAs are also known to be toxic, DMAs is more easily excreted in the urine and therefore methylation has generally been considered a detoxification pathway. A collaborative modeling project between epidemiologists, biologists, and mathematicians has the purpose of explaining existing data on methylation in human studies in Bangladesh and also testing, by mathematical modeling, effects of nutritional supplements that could increase As methylation. Methods We develop a whole body mathematical model of arsenic metabolism including arsenic absorption, storage, methylation, and excretion. The parameters for arsenic methylation in the liver were taken from the biochemical literature. The transport parameters between compartments are largely unknown, so we adjust them so that the model accurately predicts the urine excretion rates of time for the iAs, MMAs, and DMAs in single dose experiments on human subjects. Results We test the model by showing that, with no changes in parameters, it predicts accurately the time courses of urinary excretion in mutiple dose experiments conducted on human subjects. Our main purpose is to use the model to study and interpret the data on the effects of folate supplementation on arsenic methylation and excretion in clinical trials in Bangladesh. Folate supplementation of folate-deficient individuals resulted in a 14% decrease in arsenicals in the blood. This is confirmed by the model and the model predicts that arsenicals in the liver will decrease by 19% and arsenicals in other body stores by 26% in these same individuals. In addition, the model predicts that arsenic
Mathematical Programming Models in Educational Planning.
McNamara, James F.
This document begins by defining and discussing educational planning. A brief overview of mathematical programing with an explanation of the general linear programing model is then provided. Some recent applications of mathematical programing techniques to educational planning problems are reviewed, and their implications for educational research…
Mathematical models in biology bringing mathematics to life
Ferraro, Maria; Guarracino, Mario
2015-01-01
This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...
A mathematical model of symmetry based on mathematical definition
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.
A mathematical model of symmetry based on mathematical definition
Institute of Scientific and Technical Information of China (English)
刘玉生; 杨将新; 吴昭同; 高曙明
2002-01-01
Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disignd/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance beeanse of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: ( 1 ) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements ; after which, the mathematical models of syrmmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.
Study of Photovoltaic Cells Engineering Mathematical Model
Zhou, Jun; Yu, Zhengping; Lu, Zhengyi; Li, Chenhui; Zhang, Ruilan
2016-11-01
The characteristic curve of photovoltaic cells is the theoretical basis of PV Power, which simplifies the existing mathematical model, eventually, obtains a mathematical model used in engineering. The characteristic curve of photovoltaic cells contains both exponential and logarithmic calculation. The exponential and logarithmic spread out through Taylor series, which includes only four arithmetic and use single chip microcontroller as the control center. The result shows that: the use of single chip microcontroller for calculating exponential and logarithmic functions, simplifies mathematical model of PV curve, also can meet the specific conditions’ requirement for engineering applications.
Mathematical modeling a chemical engineer's perspective
Rutherford, Aris
1999-01-01
Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus
Developmental gains in visuospatial memory predict gains in mathematics achievement.
Li, Yaoran; Geary, David C
2013-01-01
Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4) were larger than gains in the capacity of the central executive (d = 1.6) that in turn were larger than gains in phonological memory span (d = 1.1). First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning.
Developmental gains in visuospatial memory predict gains in mathematics achievement.
Directory of Open Access Journals (Sweden)
Yaoran Li
Full Text Available Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4 were larger than gains in the capacity of the central executive (d = 1.6 that in turn were larger than gains in phonological memory span (d = 1.1. First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning.
Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms
Eric, Chan Chun Ming
2009-01-01
The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…
Mathematically modelling proportions of Japanese populations by industry
Hirata, Yoshito
2016-10-01
I propose a mathematical model for temporal changes of proportions for industrial sectors. I prove that the model keeps the proportions for the primary, the secondary, and the tertiary sectors between 0 and 100% and preserves their total as 100%. The model fits the Japanese historical data between 1950 and 2005 for the population proportions by industry very well. The model also predicts that the proportion for the secondary industry becomes negligible and becomes less than 1% at least around 2080.
Mathematical modelling of the calcination process | Olayiwola ...
African Journals Online (AJOL)
Mathematical modelling of the calcination process. ... High quality lime is an essential raw material for Electric Arc Furnaces and Basic Oxygen Furnaces ... From the numerical simulation, it is observed that the gas temperature increases as the ...
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...
Applied mathematics: Models, Discretizations, and Solvers
Institute of Scientific and Technical Information of China (English)
D.E. Keyes
2007-01-01
@@ Computational plasma physicists inherit decades of developments in mathematical models, numerical algorithms, computer architecture, and software engineering, whose recent coming together marks the beginning of a new era of large-scale simulation.
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...... are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues...
Cooking Potatoes: Experimentation and Mathematical Modeling.
Chen, Xiao Dong
2002-01-01
Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)
Mathematical Modeling of Chemical Stoichiometry
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
Mathematical modeling in biomedical imaging
2009-01-01
This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.
Mathematical Modeling of Chemical Stoichiometry
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
A Structural Equation Model Explaining 8th Grade Students' Mathematics Achievements
Yurt, Eyüp; Sünbül, Ali Murat
2014-01-01
The purpose of this study is to investigate, via a model, the explanatory and predictive relationships among the following variables: Mathematical Problem Solving and Reasoning Skills, Sources of Mathematics Self-Efficacy, Spatial Ability, and Mathematics Achievements of Secondary School 8th Grade Students. The sample group of the study, itself…
Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat
2017-01-01
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…
Yu, Chung-huang; Hung, Yu-Cheng; Lin, Yang-Hua; Chen, Guan-Xun; Wei, Shun-Hwa; Huang, Chang-Hung; Chen, Chen-Sheng
2014-09-01
A solid-ankle cushioned heel (SACH) foot is a non-joint foot without natural ankle function. Trans-tibial amputees may occur toe scuffing in the late swing phase due to a lack of active dorsiflexion. To address this problem, clinical guidelines suggests shortening the pylon to produce a smooth gait. However, this causes a leg length discrepancy, induces asymmetry in the hip joint, and causes an overload of L5/S1 joint force. Therefore, this study aimed to investigate the influence of different prosthesis pylons on the hip joint and L5/S1 joint forces. Ten subjects were recruited using leg length for normalisation. Four different pylon reductions (0%, 1%, 2%, and 3%) were used for gait analysis. A Vicon system and force plates were used to collect kinematic data and ground reaction force, respectively. The software package MATLAB was used to create a mathematical model for evaluating the symmetry and force of the hip joint and the low back force of the L5/S1 joint. The model was validated by the correlation coefficient (CC=0.947) and root mean square (RMS=0.028 BW). The model estimated that the 1% group had a symmetrical hip joint force and a lower L5/S1 joint force in the vertical direction. This study indicates that a 1% pylon shortening on a SACH prosthesis is appropriate for a trans-tibial amputee.
Students’ mathematical learning in modelling activities
DEFF Research Database (Denmark)
Kjeldsen, Tinne Hoff; Blomhøj, Morten
2013-01-01
Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts...... involved. We argue that progress in students’ conceptual learning needs to be conceptualised separately from that of progress in their modelling competency. Findings are that modelling activities open a window to the students’ images of the mathematical concepts involved; that modelling activities can...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....
Mathematical model of cylindrical form tolerance
Institute of Scientific and Technical Information of China (English)
蔡敏; 杨将新; 吴昭同
2004-01-01
Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and data transferring with computers. How to interpret its semantics is becoming a focus of relevant studies. This work based on the mathematical definition of form tolerance in ANSI Y 14.5.1 M-1994, established the mathematical model of form tolerance for cylindrical feature. First, each tolerance in the national standard was established by vector equation. Then on the foundation of toler-ance's mathematical definition theory, each tolerance zone's mathematical model was established by inequality based on degrees of feature. At last the variance area of each tolerance zone is derived. This model can interpret the semantics of form tolerance exactly and completely.
Mathematical model of cylindrical form tolerance
Institute of Scientific and Technical Information of China (English)
蔡敏; 杨将新; 吴昭同
2004-01-01
Tolerance is essential for integration of CAD and CAM.Unfortunately,the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression,processing and data transferring with computers.How to interpret its semantics is becoming a focus of relevant studies.This work based on the mathematical definition of form tolerance in ANSI Y 14.5.1 M-1994,established the mathematical model of form tolerance for cylindrical feature.First,each tolerance in the national standard was established by vector equation.Then on the foundation of tolerance's mathematical definition theory,each tolerance zone's mathematical model was established by inequality based on degrees of feature.At last the variance area of each tolerance zone is derived.This model can interpret the semantics of form tolerance exactly and completely.
Wilson, John Martin, Jr.
The purpose of this study was to investigate the interrelationship of general mathematics skills, modern mathematics skills, modern mathematics achievement, prior mathematical attitudes, and postmathematical attitudes of prospective elementary teachers. A sample of 206 students was drawn from 286 students enrolled in a modern mathematics course.…
Mathematical analysis of epidemiological models with heterogeneity
Energy Technology Data Exchange (ETDEWEB)
Van Ark, J.W.
1992-01-01
For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.
Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.
2016-01-01
Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…
EVALUATION OF PLANING CRAFT MANEUVERABILITY USING MATHEMATICAL MODELING
Directory of Open Access Journals (Sweden)
Sajad Hajizadeh
2016-03-01
Full Text Available Ship transportation is increasing globally as is risk of collision especially in congested areas is a main concern. Numerical modeling method is major simulation method to predict ship maneuverability. Ship maneuvering in calm water is an important topic to avoid collisions and leads to safe navigation. Therefore reliable ship maneuvering simulations are required for incident analysis and prevention. In recent time within the research community orientated towards ship hydrodynamics an increasing attention has been paid to simultaneous solution of the maneuvering of planing ship problem. The maneuverability of planing crafts has been the subject of many research projects during the last few decades. To assess the maneuverability of planing crafts at the early design stage, reliable simulation models are required. Traditionally, these tools have used empiric descriptions of the forces and moments on the planing craft’s hull. Ship maneuvering calculations, horizontal plane motion control and development of maneuvering simulators need a mathematical description of ship maneuvering. In the recent years, different mathematical models are suggested for maneuvering of displacement vessels that are capable of estimation of vessel maneuvers with acceptable precision. But simulation of planing craft maneuverability through mathematical model is not common yet and is the subject of future research. Maneuvering of planing crafts is influenced greatly by action of rudder. But research efforts have been to include the rudder action in the mathematical models of planing ship maneuvering. In this paper a mathematical model is developed for planing craft maneuvering that includes the rudder forces and moments. Different maneuvers are executed through the mathematical model. Simulations are validated by model tests. Finally the influence of rudder angle on maneuverability of planing ship is studied. The mathematical model and hydrodynamic coefficients presented
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
Controllability, Observability, and Stability of Mathematical Models
Iggidr, Abderrahman
2004-01-01
International audience; This article presents an overview of three fundamental concepts in Mathematical System Theory: controllability, stability and observability. These properties play a prominent role in the study of mathematical models and in the understanding of their behavior. They constitute the main research subject in Control Theory. Historically the tools and techniques of Automatic Control have been developed for artificial engineering systems but nowadays they are more and more ap...
Mathematical Model of Hot Metal Desulfurization by Powder Injection
Directory of Open Access Journals (Sweden)
Yolanda Cepeda Rodríguez
2012-01-01
Full Text Available Although there have been a numerous number of studies on mathematical model of hot metal desulfurization by deep injection of calcium carbide, the research field as a whole is not well integrated. This paper presents a model that takes into account the kinetics, thermodynamics, and transport processes to predict the sulfur levels in the hot metal throughout a blow. The model could be utilized to assess the influence of the treatment temperature, rate of injection, gas flow rate, and initial concentration of sulfur on the desulfurization kinetics. In the second part of this paper an analysis of the industrial data for injection of calcium carbide using this model is described. From a mathematical model that describes the characteristics of a system, it is possible to predict the behavior of the variables involved in the process, resulting in savings of time and money. Discretization is realized through the finite difference method combined with interpolation in the border domain by Taylor series.
On the mathematical modeling of aeolian saltation
DEFF Research Database (Denmark)
Jensen, Jens Ledet; Sørensen, Michael
1983-01-01
The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...
A mathematical model of glutathione metabolism
Directory of Open Access Journals (Sweden)
James S Jill
2008-04-01
Full Text Available Abstract Background Glutathione (GSH plays an important role in anti-oxidant defense and detoxification reactions. It is primarily synthesized in the liver by the transsulfuration pathway and exported to provide precursors for in situ GSH synthesis by other tissues. Deficits in glutathione have been implicated in aging and a host of diseases including Alzheimer's disease, Parkinson's disease, cardiovascular disease, cancer, Down syndrome and autism. Approach We explore the properties of glutathione metabolism in the liver by experimenting with a mathematical model of one-carbon metabolism, the transsulfuration pathway, and glutathione synthesis, transport, and breakdown. The model is based on known properties of the enzymes and the regulation of those enzymes by oxidative stress. We explore the half-life of glutathione, the regulation of glutathione synthesis, and its sensitivity to fluctuations in amino acid input. We use the model to simulate the metabolic profiles previously observed in Down syndrome and autism and compare the model results to clinical data. Conclusion We show that the glutathione pools in hepatic cells and in the blood are quite insensitive to fluctuations in amino acid input and offer an explanation based on model predictions. In contrast, we show that hepatic glutathione pools are highly sensitive to the level of oxidative stress. The model shows that overexpression of genes on chromosome 21 and an increase in oxidative stress can explain the metabolic profile of Down syndrome. The model also correctly simulates the metabolic profile of autism when oxidative stress is substantially increased and the adenosine concentration is raised. Finally, we discuss how individual variation arises and its consequences for one-carbon and glutathione metabolism.
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers...... be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal situation......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers...... be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered...
Interfacial Fluid Mechanics A Mathematical Modeling Approach
Ajaev, Vladimir S
2012-01-01
Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail. Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also: Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...
Mathematical modeling and optimization of complex structures
Repin, Sergey; Tuovinen, Tero
2016-01-01
This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimiz...
Mathematical models and methods for planet Earth
Locatelli, Ugo; Ruggeri, Tommaso; Strickland, Elisabetta
2014-01-01
In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.
Mathematical model in economic environmental problems
Energy Technology Data Exchange (ETDEWEB)
Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)
1996-12-31
The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.
Mathematical modeling of complex noise barriers
Energy Technology Data Exchange (ETDEWEB)
Hayek, S.I.
1982-01-01
Mathematical modeling of the noise reduction efficiency of highway noise barriers depends on the shape and absorptivity of the barrier, the influence of the impedance of the ground under the receiver, the atmospheric conditions as well as traffic details. The mathematical model for a barrier's noise reduction requires the knowledge of point-to-point acoustic diffraction models. In many instances, the shape of the barrier is simple; such as thin wall (edge), sharp wedge, and cylindrically topped berms. However, new designs of more efficient barriers have been investigated recently.
Mathematical Modeling in Continuum Mechanics
Temam, Roger; Miranville, Alain
2005-06-01
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
MATHEMATICAL MODEL OF RIVER BED CHANGE DOWNSTREAM OF XIAOLANGDI RESERVOIR
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A mathematical model of river bed change downstream of the Xiaolangdi Reservoir was developed based on the most recent achievement of sediment theory in the Yellow River. The model was verified by the comparison of computed results and measured data from 1986 to 1996. Numerical prediction of the erosion and deposition downstream of the Xiaolangdi Reservoir in its first operation year was carried out, and a series of suggestions were given for reservoir operation mode in its early operation period.
About a mathematical model of market
Kulikov, D. A.
2017-01-01
In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.
Mathematical human modelling for impact loading
Happee, R.; Hoof, J.F.A.M. van; Lange, R. de
2001-01-01
Mathematical modeling of the human body is widely used for automotive crash-safety research and design. Simulations have contributed to a reduction of injury numbers by optimization of vehicle structures and restraint systems. Currently, such simulations are largely performed using occupant models b
Mathematical Modeling of Viral Zoonoses in Wildlife
2011-01-01
Zoonoses are a worldwide public health concern, accounting for approximately 75% of human infectious diseases. In addition, zoonoses adversely affect agricultural production and wildlife. We review some mathematical models developed for the study of viral zoonoses in wildlife and identify areas where further modeling efforts are needed.
Mathematical modelling of magnetically targeted drug delivery
Energy Technology Data Exchange (ETDEWEB)
Grief, Andrew D. [Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)]. E-mail: andrew.grief@nottingham.ac.uk; Richardson, Giles [Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)]. E-mail: giles.richardson@nottingham.ac.uk
2005-05-15
A mathematical model for targeted drug delivery using magnetic particles is developed. This includes a diffusive flux of particles arising from interactions between erythrocytes in the microcirculation. The model is used to track particles in a vessel network. Magnetic field design is discussed and we show that it is impossible to specifically target internal regions using an externally applied field.
Mathematical models of cell self-organization
Directory of Open Access Journals (Sweden)
Benoît Perthame
2011-04-01
More recently nonlinear hyperbolic and kinetic models also have been used to describe the phenomena at a smaller scale. We explain here some motivations for ‘microscopic’ descriptions, the mathematical difficulties arising in their analysis and how kinetic models can help in understanding the unity of these descriptions.
Mathematical human modelling for impact loading
Happee, R.; Hoof, J.F.A.M. van; Lange, R. de
2001-01-01
Mathematical modeling of the human body is widely used for automotive crash-safety research and design. Simulations have contributed to a reduction of injury numbers by optimization of vehicle structures and restraint systems. Currently, such simulations are largely performed using occupant models
Mathematical human body modelling for impact loading
Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.
1999-01-01
Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models
Mathematical model of electrotaxis in osteoblastic cells
Vanegas-Acosta, J.C.; Garzón-Alvarado, D.A.; Zwamborn, A.P.M.
2012-01-01
Electrotaxis is the cell migration in the presence of an electric field (EF). This migration is parallel to the EF vector and overrides chemical migration cues. In this paper we introduce a mathematical model for the electrotaxis in osteoblastic cells. The model is evaluated using different EF stren
A mathematical model of forgetting and amnesia
Murre, J.M.J.; Chessa, A.G.; Meeter, M.
2013-01-01
We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in strengt
Building Mathematical Models Of Solid Objects
Randall, Donald P.; Jones, Kennie H.; Von Ofenheim, William H.; Gates, Raymond L.; Matthews, Christine G.
1989-01-01
Solid Modeling Program (SMP) version 2.0 provides capability to model complex solid objects mathematically through aggregation of geometric primitives (parts). System provides designer with basic set of primitive parts and capability to define new primitives. Six primitives included in present version: boxes, cones, spheres, paraboloids, tori, and trusses. Written in VAX/VMS FORTRAN 77.
Mathematical human body modelling for impact loading
Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.
1999-01-01
Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models b
Mathematical modelling of clostridial acetone-butanol-ethanol fermentation.
Millat, Thomas; Winzer, Klaus
2017-03-01
Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the 'evolution' of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists.
Mathematical Model for Multicomponent Adsorption Equilibria Using Only Pure Component Data
DEFF Research Database (Denmark)
Marcussen, Lis
2000-01-01
A mathematical model for nonideal adsorption equilibria in multicomponent mixtures is developed. It is applied with good results for pure substances and for prediction of strongly nonideal multicomponent equilibria using only pure component data. The model accounts for adsorbent...
Berman, A. L.
1976-01-01
In the last two decades, increasingly sophisticated deep space missions have placed correspondingly stringent requirements on navigational accuracy. As part of the effort to increase navigational accuracy, and hence the quality of radiometric data, much effort has been expended in an attempt to understand and compute the tropospheric effect on range (and hence range rate) data. The general approach adopted has been that of computing a zenith range refraction, and then mapping this refraction to any arbitrary elevation angle via an empirically derived function of elevation. The prediction of zenith range refraction derived from surface measurements of meteorological parameters is presented. Refractivity is separated into wet (water vapor pressure) and dry (atmospheric pressure) components. The integration of dry refractivity is shown to be exact. Attempts to integrate wet refractivity directly prove ineffective; however, several empirical models developed by the author and other researchers at JPL are discussed. The best current wet refraction model is here considered to be a separate day/night model, which is proportional to surface water vapor pressure and inversely proportional to surface temperature. Methods are suggested that might improve the accuracy of the wet range refraction model.
Mathematical Modeling of Photochemical Air Pollution.
McRae, Gregory John
Air pollution is an environmental problem that is both pervasive and difficult to control. An important element of any rational control approach is a reliable means for evaluating the air quality impact of alternative abatement measures. This work presents such a capability, in the form of a mathematical description of the production and transport of photochemical oxidants within an urban airshed. The combined influences of advection, turbulent diffusion, chemical reaction, emissions and surface removal processes are all incorporated into a series of models that are based on the species continuity equations. A delineation of the essential assumptions underlying the formulation of a three-dimensional, a Lagrangian trajectory, a vertically integrated and single cell air quality model is presented. Since each model employs common components and input data the simpler forms can be used for rapid screening calculations and the more complex ones for detailed evaluations. The flow fields, needed for species transport, are constructed using inverse distance weighted polynomial interpolation techniques that map routine monitoring data onto a regular computational mesh. Variational analysis procedures are then employed to adjust the field so that mass is conserved. Initial concentration and mixing height distributions can be established with the same interpolation algorithms. Subgrid scale turbulent transport is characterized by a gradient diffusion hypothesis. Similarity solutions are used to model the surface layer fluxes. Above this layer different treatments of turbulent diffusivity are required to account for variations in atmospheric stability. Convective velocity scaling is utilized to develop eddy diffusivities for unstable conditions. The predicted mixing times are in accord with results obtained during sulfur hexafluoride (SF(,6)) tracer experiments. Conventional models are employed for neutral and stable conditions. A new formulation for gaseous deposition fluxes
Directory of Open Access Journals (Sweden)
Thu Thuy Nguyen
2014-09-01
Full Text Available Fecal excretion of antibiotics and resistant bacteria in the environment are major public health threats associated with extensive farming and modern medical care. Innovative strategies that can reduce the intestinal antibiotic concentrations during treatments are in development. However, the effect of lower exposure on the amount of resistant enterobacteria excreted has not been quantified, making it difficult to anticipate the impact of these strategies. Here, we introduce a bacterial kinetic model to capture the complex relationships between drug exposure, loss of susceptible enterobacteria and growth of resistant strains in the feces of piglets receiving placebo, 1.5 or 15 mg/kg/day ciprofloxacin, a fluoroquinolone, for 5 days. The model could well describe the kinetics of drug susceptible and resistant enterobacteria observed during treatment, and up to 22 days after treatment cessation. Next, the model was used to predict the expected amount of resistant enterobacteria excreted over an average piglet's lifetime (150 days when varying drug exposure and treatment duration. For the clinically relevant dose of 15 mg/kg/day for 5 days, the total amount of resistant enterobacteria excreted was predicted to be reduced by 75% and 98% when reducing treatment duration to 3 and 1 day treatment, respectively. Alternatively, for a fixed 5-days treatment, the level of resistance excreted could be reduced by 18%, 33%, 57.5% and 97% if 3, 5, 10 and 30 times lower levels of colonic drug concentrations were achieved, respectively. This characterization on in vivo data of the dynamics of resistance to antibiotics in the colonic flora could provide new insights into the mechanism of dissemination of resistance and can be used to design strategies aiming to reduce it.
A mathematical model for Neanderthal extinction
Flores, J C
1997-01-01
A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data we claim that the parameter of similarity, between both species, fluctuates between 0.992 and 0.997. An extension of the model including migration (diffusion) is also discussed nevertheless, extinction of Neanderthal seems unavoidable. Numerical analysis of travelling wave solution (fronts) comfirms the extinction. The wave-front-velocity is estimated from linear analysis and numerical simulations confirm this estimation. We conjecture a mathematical formulation for the principle of exclusion between competitive interacting species (Gause).
On the mathematical modeling of memristors
Radwan, Ahmed G.
2012-10-06
Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor\\'s resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.
Dynamics of mathematical models in biology bringing mathematics to life
Zazzu, Valeria; Guarracino, Mario
2016-01-01
This volume focuses on contributions from both the mathematics and life science community surrounding the concepts of time and dynamicity of nature, two significant elements which are often overlooked in modeling process to avoid exponential computations. The book is divided into three distinct parts: dynamics of genomes and genetic variation, dynamics of motifs, and dynamics of biological networks. Chapters included in dynamics of genomes and genetic variation analyze the molecular mechanisms and evolutionary processes that shape the structure and function of genomes and those that govern genome dynamics. The dynamics of motifs portion of the volume provides an overview of current methods for motif searching in DNA, RNA and proteins, a key process to discover emergent properties of cells, tissues, and organisms. The part devoted to the dynamics of biological networks covers networks aptly discusses networks in complex biological functions and activities that interpret processes in cells. Moreover, chapters i...
Mathematical Modelling of Unmanned Aerial Vehicles
Directory of Open Access Journals (Sweden)
Saeed Sarwar
2013-04-01
Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV
Predicting Mathematical Performance: The Effect of Cognitive Processes and Self-Regulation Factors
Directory of Open Access Journals (Sweden)
Mariel Musso
2012-01-01
Full Text Available A substantial number of research studies have investigated the separate influence of working memory, attention, motivation, and learning strategies on mathematical performance and self-regulation in general. There is still little understanding of their impact on performance when taken together, understanding their interactions, and how much each of them contributes to the prediction of mathematical performance. With the emergence of new methodologies and technologies, such as the modelling with predictive systems, it is now possible to study these effects with approaches which use a wide range of data, including student characteristics, to estimate future performance without the need of traditional testing (Boekaerts and Cascallar, 2006. This research examines the different cognitive patterns and complex relations between cognitive variables, motivation, and background variables associated with different levels of mathematical performance using artificial neural networks (ANNs. A sample of 800 entering university students was used to develop three ANN models to identify the expected future level of performance in a mathematics test. These ANN models achieved high degree of precision in the correct classification of future levels of performance, showing differences in the pattern of relative predictive weight amongst those variables. The impact on educational quality, improvement, and accountability is highlighted.
Shimotohno, Akie; Sotta, Naoyuki; Sato, Takafumi; De Ruvo, Micol; Marée, Athanasius F M; Grieneisen, Verônica A; Fujiwara, Toru
2015-04-01
Boron, an essential micronutrient, is transported in roots of Arabidopsis thaliana mainly by two different types of transporters, BORs and NIPs (nodulin26-like intrinsic proteins). Both are plasma membrane localized, but have distinct transport properties and patterns of cell type-specific accumulation with different polar localizations, which are likely to affect boron distribution. Here, we used mathematical modeling and an experimental determination to address boron distributions in the root. A computational model of the root is created at the cellular level, describing the boron transporters as observed experimentally. Boron is allowed to diffuse into roots, in cells and cell walls, and to be transported over plasma membranes, reflecting the properties of the different transporters. The model predicts that a region around the quiescent center has a higher concentration of soluble boron than other portions. To evaluate this prediction experimentally, we determined the boron distribution in roots using laser ablation-inductivity coupled plasma-mass spectrometry. The analysis indicated that the boron concentration is highest near the tip and is lower in the more proximal region of the meristem zone, similar to the pattern of soluble boron distribution predicted by the model. Our model also predicts that upward boron flux does not continuously increase from the root tip toward the mature region, indicating that boron taken up in the root tip is not efficiently transported to shoots. This suggests that root tip-absorbed boron is probably used for local root growth, and that instead it is the more mature root regions which have a greater role in transporting boron toward the shoots.
Applied Mathematics, Modelling and Computational Science
Kotsireas, Ilias; Makarov, Roman; Melnik, Roderick; Shodiev, Hasan
2015-01-01
The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26–30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics ...
Institute of Scientific and Technical Information of China (English)
姜爱民; 杨辉; 张明
2012-01-01
In this paper, the deterministic mathematical model for predicting the amount of water gushing in tunnel is introduced, and the common used methods are discussed. It is considered that the numerical simulation is the effective way to predict the amount of water gushing. Based on finite element numerical method, the water gushed yield is predicted in Nanliang tunnel of Shijiazhuang to Taiyuan special railway line. The results show that the predicted results are basically consistent with the actual situation.%本文介绍了确定性数学模型预测隧道涌水量的常用方法,认为数值模拟方法是隧道涌水量预测的有效方法。并基于有限单元数值法对石太客运专线南梁隧道可能集中涌水区段进行了预测,结果表明其预测结果与实际情况基本吻合。
Modeling eBook acceptance: A study on mathematics teachers
Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad
2014-12-01
The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.
Levy, R.; Mcginness, H.
1976-01-01
Investigations were performed to predict the power available from the wind at the Goldstone, California, antenna site complex. The background for power prediction was derived from a statistical evaluation of available wind speed data records at this location and at nearby locations similarly situated within the Mojave desert. In addition to a model for power prediction over relatively long periods of time, an interim simulation model that produces sample wind speeds is described. The interim model furnishes uncorrelated sample speeds at hourly intervals that reproduce the statistical wind distribution at Goldstone. A stochastic simulation model to provide speed samples representative of both the statistical speed distributions and correlations is also discussed.
The (mathematical modelling process in biosciences
Directory of Open Access Journals (Sweden)
Nestor V. Torres
2015-12-01
Full Text Available In this communication we introduce a general framework and discussion on the role of models and the modelling process within the scientific activity in the biosciences realm. The objective is sum up the common procedure during the formalization and analysis of a biological problem under the foundations of Systems Biology, which approach the study of biological systems as a whole.We begin by presenting the definitions of (biological system and model. Particular attention is given to the meaning of mathematical model within the context of the biology. Then, we present the modelization and analysis process of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model.All along this presentation the main features and shortcomings of the process are developed together with a set of rules that could help in the modelling endeavour of any biological system. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that the modelling are currently posing to the current biology.
Ohno, Yoshiharu; Koyama, Hisanobu; Fujisawa, Yasuko; Yoshikawa, Takeshi; Seki, Shinichiro; Sugihara, Naoki; Sugimura, Kazuro
2016-01-01
To determine the capability and influence of the mathematical method on dynamic contrast-enhanced (CE-) perfusion area detector CT (ADCT) for early prediction of treatment response as well as progression free and overall survival (PFS and OS) of non-small cell lung cancer (NSCLC) patients treated with chemoradiotherapy. Sixty-six consecutive stage III NSCLC patients underwent dynamic CE-perfusion ADCT examinations, chemoradiotherapy and follow-up examinations. Response Evaluation Criteria in Solid Tumors (RECIST) criteria were used to divide all patients into responders and non-responders. Differences in each of the indices for all targeted lesions between measurements obtained 2 weeks prior to the first and the third course of chemotherapy were determined for all patients. ROC analyses were employed to determine the capability of perfusion indices as markers for distinguishing RECIST responders from non-responders. To evaluate their capability for early prediction of therapeutic effect, OS of perfusion index-based responders and non-responders were compared by using the Kaplan-Meier method followed by log-rank test. Area under the curve (Az) for total perfusion by means of the dual-input maximum slope method was significantly larger than that of pulmonary arterial perfusion using the same method (p=0.007) and of perfusion with the single-input maximum slope method (p=0.007). Mean OS demonstrated significantly difference between responder- and non-responder groups for total perfusion (p=0.02). Mathematical models have significant influence on assessment for early prediction of treatment response, disease progression and overall survival using dynamic CE-perfusion ADCT for NSCLC patients treated with chemoradiotherapy. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.
Mathematical Viscosity Models for Ternary Metallic and Silicate Melts
Institute of Scientific and Technical Information of China (English)
FU Yuan-kun; MENG Xian-min; GUO Han-jie
2004-01-01
The mathematical viscosity models for metallic melts were discussed. The experimental data of Ag-Au-Cu systems were used to verify the models based on Chou's general geometric thermodynamic model and the calculated results are consistent with the reported experimental data. A new model predicting the viscosity of multi-component silicate melts was established. The CaO-MnO-SiO2, CaO-FeO-SiO2 and FeO-MnO-SiO2 silicate slag systems were used to verify the model.
Mathematical Modelling of Bridges with SAP2000
Maraž, Miha
2006-01-01
The present work describes a relatively new programme module, which is enhanced in the recently released versions of SAP2000 software. The new module, called Bridge Modeler, is intended for simple, parametric mathematical modelling of bridges. The modelling procedure is explained on a test case through the steps of a user-friendly Bridge Wizard. For each step, we described the basic principles and the application possibilities as well as some limitations. We also explained two types of analys...
Mathematical Modeling of Circadian and Homeostatic Interaction
2011-11-16
Williams and C. Diniz Behn. A Hodgkin- Huxley -type model orexin neuron. SLEEP 32, A25, 2009. 4) C. Diniz Behn, D. Pal, G. Vanini, R. Lydic, G. A. Mashour...Switzerland, September 2009. 11) K. Williams, “A Hodgkin- Huxley -type model orexin neuron”, Associated Professional Sleep Societies Annual Meeting...Seattle, WA, June 2009. 12) K. Williams, “Dynamics in a Hodgkin- Huxley -type model orexin neuron”, Society for Industrial and Applied Mathematics Annual
Mathematical System Theory and System Modeling
1980-01-01
Choosing models related effectively to the questions to be addressed is a central issue in the craft of systems analysis. Since the mathematical description the analyst chooses constrains the types of issues he candeal with, it is important for these models to be selected so as to yield limitations that are acceptable in view of the questions the systems analysis seeks to answer. In this paper, the author gives an overview of the central issues affecting the question of model choice. To ...
Mathematical modeling of a convective textile drying process
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G. Johann
2014-12-01
Full Text Available This study aims to develop a model that accurately represents the convective drying process of textile materials. The mathematical modeling was developed from energy and mass balances and, for the solution of the mathematical model, the technique of finite differences, in Cartesian coordinates, was used. It transforms the system of partial differential equations into a system of ordinary equations, with the unknowns, the temperature and humidity of both the air and the textile material. The simulation results were compared with experimental data obtained from the literature. In the statistical analysis the Shapiro-Wilk test was used to validate the model and, in all cases simulated, the results were p-values greater than 5 %, indicating normality of the data. The R-squared values were above 0.997 and the ratios Fcalculated/Fsimulated, at the 95 % confidence level, higher than five, indicating that the modeling was predictive in all simulations.
Pedagogical Content Knowledge in Mathematical Modelling Instruction
Tan, Liang Soon; Ang, Keng Cheng
2012-01-01
This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…
Ivorra, Benjamin; Ngom, Diène; Ramos, Ángel M
2015-09-01
Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the UK, the USA and Spain. Regarding the emergency of this situation, there is a need for the development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatial-temporal model, called Between-Countries Disease Spread (Be-CoDiS), to study the evolution of human diseases within and between countries. The main interesting characteristics of Be-CoDiS are the consideration of the movement of people between countries, the control measure effects and the use of time-dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model and explain how its parameters and inputs are obtained. Then, in order to validate our approach, we consider two numerical experiments regarding the 2014-2015 Ebola epidemic. The first one studies the ability of the model in predicting the EVD evolution between countries starting from the index cases in Guinea in December 2013. The second one consists of forecasting the evolution of the epidemic by using some recent data. The results obtained with Be-CoDiS are compared to real data and other model outputs found in the literature. Finally, a brief parameter sensitivity analysis is done. A free MATLAB version of Be-CoDiS is available at: http://www.mat.ucm.es/momat/software.htm.
Optimization and mathematical modeling in computer architecture
Sankaralingam, Karu; Nowatzki, Tony
2013-01-01
In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t
Mathematical models and numerical algorithms for option pricing and optimal trading
Song, Na; 宋娜.
2013-01-01
Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance. An option gives the holder ...
Mathematical Modeling of Column-Base Connections under Monotonic Loading
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Gholamreza Abdollahzadeh
2014-12-01
Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.
Bukova-Guzel, Esra
2011-01-01
This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…
Determining the Views of Mathematics Student Teachers Related to Mathematical Modelling
Tekin, Ayse; Kula, Semiha; Hidiroglu, Caglar Naci; Bukova-Guzel, Esra; Ugurel, Isikhan
2012-01-01
The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. For this reason, three open-ended questions…
Causal Bayes Model of Mathematical Competence in Kindergarten
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Božidar Tepeš
2016-06-01
Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.
Mathematical modeling models, analysis and applications
Banerjee, Sandip
2014-01-01
""…the reader may find quite a few interesting examples illustrating several important methods used in applied mathematics. … it may be well used as a valuable source of interesting examples as well as complementary reading in a number of courses.""-Svitlana P. Rogovchenko, Zentralblatt MATH 1298
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Mustafa İlhan
2015-12-01
Full Text Available In this study, it was aimed to determine the predictive power of students’ perceptions of classroom assessment environment for their mathematics anxiety. A correlational model was employed in this study, which was carried out with 410 high school students in the provinces of Diyarbakir in Turkey in the fall of 2014–2015. The Mathematics Anxiety Scale which was developed by Bindak (2005 was employed in the study to measure the students’ math anxiety. Then, in order to determine the students’ perceptions of the classroom assessment environment, the Classroom Assessment Environment Scale, which was developed by Ilhan and Cetin (2014a, was used. The relationships between students’ mathematics anxiety and their perceptions of the classroom assessment environment were investigated via correlation and multiple regression analysis. The results obtained from the correlation analysis demonstrated that learning oriented assessment environment was negatively related to mathematics anxiety. In contrary, performance oriented assessment environment was positively related to mathematics anxiety. As a result of regression analysis, it was determined that students’ perceptions of the classroom assessment environment explain 18% of the total variance on their mathematics anxiety.
Structured Mathematical Modeling of Industrial Boiler
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Abdullah Nur Aziz
2014-04-01
Full Text Available As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. The model describes the temperature dynamics of the boiler subsystems such as economizer, steam drum, desuperheater, and superheater. The mathematical model was examined using industrial boiler performance test data.It can be used to build a boiler simulator or help operators run a boiler effectively.
Constraint theory multidimensional mathematical model management
Friedman, George J
2017-01-01
Packed with new material and research, this second edition of George Friedman’s bestselling Constraint Theory remains an invaluable reference for all engineers, mathematicians, and managers concerned with modeling. As in the first edition, this text analyzes the way Constraint Theory employs bipartite graphs and presents the process of locating the “kernel of constraint” trillions of times faster than brute-force approaches, determining model consistency and computational allowability. Unique in its abundance of topological pictures of the material, this book balances left- and right-brain perceptions to provide a thorough explanation of multidimensional mathematical models. Much of the extended material in this new edition also comes from Phan Phan’s PhD dissertation in 2011, titled “Expanding Constraint Theory to Determine Well-Posedness of Large Mathematical Models.” Praise for the first edition: "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory...
Mathematical Modelling of Surfactant Self-assembly at Interfaces
Morgan, C. E.
2015-01-01
© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary differential equations that couple the rearrangement of surfactant within the multilayer to the surface adsorption kinetics is first derived. This model is then extended to the macroscopic scale by taking the continuum limit that exploits the typically large number of surfactant layers, which results in a novel third-order partial differential equation. The model is generalized to allow for the presence of two adsorbing boundaries, which results in an implicit free-boundary problem. The system predicts physically observed features in multilayer systems such as the initial formation of smaller lamellar structures and the typical number of layers that form in equilibrium.
Mathematical modeling of brain tumors: effects of radiotherapy and chemotherapy
Energy Technology Data Exchange (ETDEWEB)
Powathil, G [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Kohandel, M [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Sivaloganathan, S [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Oza, A [Center for Mathematical Medicine, Fields Institute for Research in Mathematical Sciences, Toronto, Ontario M5T 3J1 (Canada); Milosevic, M [Radiation Medicine Program, Princess Margaret Hospital, and Department of Radiation Oncology, University of Toronto, Toronto, Ontario M5G 2M9 (Canada)
2007-06-07
Gliomas, the most common primary brain tumors, are diffusive and highly invasive. The standard treatment for brain tumors consists of a combination of surgery, radiation therapy and chemotherapy. Over the past few years, mathematical models have been applied to study untreated and treated brain tumors. In an effort to improve treatment strategies, we consider a simple spatio-temporal mathematical model, based on proliferation and diffusion, that incorporates the effects of radiotherapeutic and chemotherapeutic treatments. We study the effects of different schedules of radiation therapy, including fractionated and hyperfractionated external beam radiotherapy, using a generalized linear quadratic (LQ) model. The results are compared with published clinical data. We also discuss the results for combination therapy (radiotherapy plus temozolomide, a new chemotherapy agent), as proposed in recent clinical trials. We use the model to predict optimal sequencing of the postoperative (combination of radiotherapy and adjuvant, neo-adjuvant or concurrent chemotherapy) treatments for brain tumors.
Hansson, Lena; Hansson, Örjan; Juter, Kristina; Redfors, Andreas
2015-01-01
This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the…
Mathematical models for Isoptera (Insecta mound growth
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MLT. Buschini
Full Text Available In this research we proposed two mathematical models for Isoptera mound growth derived from the Von Bertalanffy growth curve, one appropriated for Nasutitermes coxipoensis, and a more general formulation. The mean height and the mean diameter of ten small colonies were measured each month for twelve months, from April, 1995 to April, 1996. Through these data, the monthly volumes were calculated for each of them. Then the growth in height and in volume was estimated and the models proposed.
Structured Mathematical Modeling of Industrial Boiler
Abdullah Nur Aziz; Yul Yunazwin Nazaruddin; Parsaulian Siregar; Yazid Bindar
2014-01-01
As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. T...
Mathematical modeling of rewarming after cold therapy.
Avet, L M
1978-07-01
Statistical methods are presented for fitting mathematical models to skin temperature data. Three types of regression curves, namely, linear regression (Y = A + BX), second-degree regression (Y = A + BX + CX2), and asymptotic regression (Y = alpha + betapx), are discussed as possible models for the rewarming process following cold therapy. The data for fitting the curves consists of back surface temperature (degrees C) corresponding to various times after cold pack treatment (19 degrees C, administered for 20 minutes) was terminated.
Mathematical principles of predicting the probabilities of large earthquakes
Ghertzik, V M
2009-01-01
A multicomponent random process used as a model for the problem of space-time earthquake prediction; this allows us to develop consistent estimation for conditional probabilities of large earthquakes if the values of the predictor characterizing the seismicity prehistory are known. We introduce tools for assessing prediction efficiency, including a separate determination of efficiency for "time prediction" and "location prediction": a generalized correlation coefficient and the density of information gain. We suggest a technique for testing the predictor to decide whether the hypothesis of no prediction can be rejected.
Optimization of mathematical models for thematic maps
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The thematic map is a major class of maps designed to demonstrate particular features or concepts,functioning as an indispensable tool in geographical research.The process of thematic mapping is one into which geographical research goes deeply and broadly.The key activity and course of thematic map production is the use of mathematical models to create thematic data layers.Therefore,the selection and optimization of mathematical models is in the forefront of thematic map research.The theoretical foundations,mechanisms and methods of mathematical model optimization are expounded in this paper,including two approaches,the phase by phase mode and the multi-aim scheme balance mode.Case studies in eco-environment mapping and emergency mapping are described and analyzed,with a hierarchical analysis method being used in the model optimization for eco-environment fragility and sensitivity assessment mapping in Beibuwan (Guangxi) District,the dynamic system (DS) method being used in the model optimization for ecological security adjustment mapping in Xishuang Banna,Yunnan province,and the multi-phase mode being used in the models for forest fire and infectious diseases mapping.
Mathematical Modeling for Preservice Teachers: A Problem from Anesthesiology.
Lingefjard, Thomas
2002-01-01
Addresses the observed actions of prospective Swedish mathematics teachers as they worked with a modeling situation. Explores prospective teachers' preparation to teach in grades 4-12 during a course of mathematical modeling. Focuses on preservice teachers' understanding of modeling and how they relate mathematical models to the real world.…
Models and structures: mathematical physics
Energy Technology Data Exchange (ETDEWEB)
NONE
2003-07-01
This document gathers research activities along 5 main directions. 1) Quantum chaos and dynamical systems. Recent results concern the extension of the exact WKB method that has led to a host of new results on the spectrum and wave functions. Progress have also been made in the description of the wave functions of chaotic quantum systems. Renormalization has been applied to the analysis of dynamical systems. 2) Combinatorial statistical physics. We see the emergence of new techniques applied to various such combinatorial problems, from random walks to random lattices. 3) Integrability: from structures to applications. Techniques of conformal field theory and integrable model systems have been developed. Progress is still made in particular for open systems with boundary conditions, in connection to strings and branes physics. Noticeable links between integrability and exact WKB quantization to 2-dimensional disordered systems have been highlighted. New correlations of eigenvalues and better connections to integrability have been formulated for random matrices. 4) Gravities and string theories. We have developed aspects of 2-dimensional string theory with a particular emphasis on its connection to matrix models as well as non-perturbative properties of M-theory. We have also followed an alternative path known as loop quantum gravity. 5) Quantum field theory. The results obtained lately concern its foundations, in flat or curved spaces, but also applications to second-order phase transitions in statistical systems.
A mathematical prognosis model for pancreatic cancer patients receiving immunotherapy.
Li, Xuefang; Xu, Jian-Xin
2016-10-07
Pancreatic cancer is one of the most deadly types of cancer since it typically spreads rapidly and can seldom be detected in its early stage. Pancreatic cancer therapy is thus a challenging task, and appropriate prognosis or assessment for pancreatic cancer therapy is of critical importance. In this work, based on available clinical data in Niu et al. (2013) we develop a mathematical prognosis model that can predict the overall survival of pancreatic cancer patients who receive immunotherapy. The mathematical model incorporates pancreatic cancer cells, pancreatic stellate cells, three major classes of immune effector cells CD8+ T cells, natural killer cells, helper T cells, and two major classes of cytokines interleukin-2 (IL-2) and interferon-γ (IFN-γ). The proposed model describes the dynamic interaction between tumor and immune cells. In order for the model to be able to generate appropriate prognostic results for disease progression, the distribution and stability properties of equilibria in the mathematical model are computed and analysed in absence of treatments. In addition, numerical simulations for disease progression with or without treatments are performed. It turns out that the median overall survival associated with CIK immunotherapy is prolonged from 7 to 13months compared with the survival without treatment, this is consistent with the clinical data observed in Niu et al. (2013). The validity of the proposed mathematical prognosis model is thus verified. Our study confirms that immunotherapy offers a better prognosis for pancreatic cancer patients. As a direct extension of this work, various new therapy methods that are under exploration and clinical trials could be assessed or evaluated using the newly developed mathematical prognosis model.
Electrorheological fluids modeling and mathematical theory
Růžička, Michael
2000-01-01
This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.
Models of Non-Life Insurance Mathematics
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Constanta Nicoleta BODEA
2008-01-01
Full Text Available In this communication we will discuss two regression credibility models from Non Ã¢Â€Â“ Life Insurance Mathematics that can be solved by means of matrix theory. In the first regression credibility model, starting from a well-known representation formula of the inverse for a special class of matrices a risk premium will be calculated for a contract with risk parameter q. In the next regression credibility model, we will obtain a credibility solution in the form of a linear combination of the individual estimate (based on the data of a particular state and the collective estimate (based on aggregate USA data. Mathematics Subject Classification: 62P05.
Genetic models of homosexuality: generating testable predictions
Gavrilets, Sergey; Rice, William R.
2006-01-01
Homosexuality is a common occurrence in humans and other species, yet its genetic and evolutionary basis is poorly understood. Here, we formulate and study a series of simple mathematical models for the purpose of predicting empirical patterns that can be used to determine the form of selection that leads to polymorphism of genes influencing homosexuality. Specifically, we develop theory to make contrasting predictions about the genetic characteristics of genes influencing homosexuality inclu...
Building Mathematical Models of Simple Harmonic and Damped Motion.
Edwards, Thomas
1995-01-01
By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)
Mathematical modelling of the combustion of a single wood particle
Energy Technology Data Exchange (ETDEWEB)
Porteiro, J.; Miguez, J.L.; Granada, E.; Moran, J.C. [Departamento de Ingenieria Mecanica, Maquinas y Motores Termicos y Fluidos. Universidad de Vigo, Lagoas Marcosende 9 36200 Vigo (Spain)
2006-01-15
A mathematical model describing the thermal degradation of densified biomass particles is presented here. The model uses a novel discretisation scheme and combines intra-particle combustion processes with extra-particle transport processes, thereby including thermal and diffusional control mechanisms. The influence of structural changes on the physical-thermal properties of wood in its different stages is studied together with shrinkage of the particle during its degradation. The model is used to compare the predicted data with data on the mass loss dynamics and internal temperature of several particles from previous works and relevant literature, with good agreement. (author)
Mathematical Modeling of an Automobile Damper
Directory of Open Access Journals (Sweden)
N. B. Kate, T. A. Jadhav
2013-10-01
Full Text Available - In an automotive industry, to reduce product development time and increase quality of product, it is essential to reduce the number of physical prototypes and rely more on precise & reliable design for the final design of vehicles. This paper presents a mathematical model for the damping force of the hydraulic shock absorber which is implemented to analyse the shock absorbers mounting brackets attached to the vehicle structure. Physical testing results indicate that the considered shock absorber’s mathematical model is reliable and can be used to calculate the durability target life of mounting brackets. Thus this presented methodology can be utilized as an effective way to reduce time and cost in design and development of automotive components.
Mathematical modelling of the lower urinary tract.
Paya, Antonio Soriano; Fernandez, Daniel Ruiz; Gil, David; Garcia Chamizo, Juan Manuel; Perez, Francisco Macia
2013-03-01
The lower urinary tract is one of the most complex biological systems of the human body as it involved hydrodynamic properties of urine and muscle. Moreover, its complexity is increased to be managed by voluntary and involuntary neural systems. In this paper, a mathematical model of the lower urinary tract it is proposed as a preliminary study to better understand its functioning. Furthermore, another goal of that mathematical model proposal is to provide a basis for developing artificial control systems. Lower urinary tract is comprised of two interacting systems: the mechanical system and the neural regulator. The latter has the function of controlling the mechanical system to perform the voiding process. The results of the tests reproduce experimental data with high degree of accuracy. Also, these results indicate that simulations not only with healthy patients but also of patients with dysfunctions with neurological etiology present urodynamic curves very similar to those obtained in clinical studies.
Cestari, Andrea
2013-01-01
Predictive modeling is emerging as an important knowledge-based technology in healthcare. The interest in the use of predictive modeling reflects advances on different fronts such as the availability of health information from increasingly complex databases and electronic health records, a better understanding of causal or statistical predictors of health, disease processes and multifactorial models of ill-health and developments in nonlinear computer models using artificial intelligence or neural networks. These new computer-based forms of modeling are increasingly able to establish technical credibility in clinical contexts. The current state of knowledge is still quite young in understanding the likely future direction of how this so-called 'machine intelligence' will evolve and therefore how current relatively sophisticated predictive models will evolve in response to improvements in technology, which is advancing along a wide front. Predictive models in urology are gaining progressive popularity not only for academic and scientific purposes but also into the clinical practice with the introduction of several nomograms dealing with the main fields of onco-urology.
Learning to teach mathematical modelling in secondary and tertiary education
Ferri, Rita Borromeo
2017-07-01
Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.
A Mathematical Model for Suppression Subtractive Hybridization
2002-01-01
Suppression subtractive hybridization (SSH) is frequently used to unearth differentially expressed genes on a whole-genome scale. Its versatility is based on combining cDNA library subtraction and normalization, which allows the isolation of sequences of varying degrees of abundance and differential expression. SSH is a complex process with many adjustable parameters that affect the outcome of gene isolation.We present a mathematical model of SSH based on DNA hybridization kinetics for assess...
Mathematical modelling of wood and briquettes torrefaction
Energy Technology Data Exchange (ETDEWEB)
Felfli, Felix Fonseca; Luengo, Carlos Alberto [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Inst. de Fisica Gleb Wataghin. Grupo Combustiveis Alternativos; Soler, Pedro Beaton [Universidad de Oriente, Santiago de Cuba (Cuba). Fac. de Ingenieria Mecanica. Centro de Estudios de Eficiencia Energetica; Rocha, Jose Dilcio [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Nucleo Interdisciplinar de Planejamento Energetico (NIPE)
2004-07-01
A mathematical model valid for the torrefaction of wood logs and biomass briquettes is presented. The model described both chemical and physical processes, which take place in a moist piece of wood heated at temperatures between 503 and 573 K. Calibration measurements of the temperature profile and mass loss, were performed on dry cylinders of wood samples during torrefaction in an inert atmosphere at 503, 533, and 553 K. The calculated data shows a good agreement with experiments. The model can be a useful tool to estimate projecting and operating parameters for torrefaction furnaces such as minimum time of torrefaction, energy consumption and the mass yield. (author)
A novel mathematical model for controllable near-field electrospinning
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Changhai Ru
2014-01-01
Full Text Available Near-field electrospinning (NFES had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.
A novel mathematical model for controllable near-field electrospinning
Energy Technology Data Exchange (ETDEWEB)
Ru, Changhai, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [College of Automation, Harbin Engineering University, Harbin 150001 (China); Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Chen, Jie; Shao, Zhushuai [Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Pang, Ming [College of Automation, Harbin Engineering University, Harbin 150001 (China); Luo, Jun, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072 (China)
2014-01-15
Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.
Analysing the Competency of Mathematical Modelling in Physics
Redish, Edward F
2016-01-01
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of the maths we draw on grows as our students progress through a physics curriculum. Despite much research on the learning of both physics and math, the problem of how to successfully teach most of our students to use maths in physics effectively remains unsolved. A fundamental issue is that in physics, we don't just use maths, we think about the physical world with it. As a result, we make meaning with math-ematical symbology in a different way than mathematicians do. In this talk we analyze how developing the competency of mathematical modeling is more than just "learning to do math" but requires learning to blend physical meaning into mathematical representations and use that physical meaning in solving problems. Examples are drawn from across the curriculum.
Mathematical analysis of a muscle architecture model.
Navallas, Javier; Malanda, Armando; Gila, Luis; Rodríguez, Javier; Rodríguez, Ignacio
2009-01-01
Modeling of muscle architecture, which aims to recreate mathematically the physiological structure of the muscle fibers and motor units, is a powerful tool for understanding and modeling the mechanical and electrical behavior of the muscle. Most of the published models are presented in the form of algorithms, without mathematical analysis of mechanisms or outcomes of the model. Through the study of the muscle architecture model proposed by Stashuk, we present the analytical tools needed to better understand these models. We provide a statistical description for the spatial relations between motor units and muscle fibers. We are particularly concerned with two physiological quantities: the motor unit fiber number, which we expect to be proportional to the motor unit territory area; and the motor unit fiber density, which we expect to be constant for all motor units. Our results indicate that the Stashuk model is in good agreement with the physiological evidence in terms of the expectations outlined above. However, the resulting variance is very high. In addition, a considerable 'edge effect' is present in the outer zone of the muscle cross-section, making the properties of the motor units dependent on their location. This effect is relevant when motor unit territories and muscle cross-section are of similar size.
Laser filamentation mathematical methods and models
Lorin, Emmanuel; Moloney, Jerome
2016-01-01
This book is focused on the nonlinear theoretical and mathematical problems associated with ultrafast intense laser pulse propagation in gases and in particular, in air. With the aim of understanding the physics of filamentation in gases, solids, the atmosphere, and even biological tissue, specialists in nonlinear optics and filamentation from both physics and mathematics attempt to rigorously derive and analyze relevant non-perturbative models. Modern laser technology allows the generation of ultrafast (few cycle) laser pulses, with intensities exceeding the internal electric field in atoms and molecules (E=5x109 V/cm or intensity I = 3.5 x 1016 Watts/cm2 ). The interaction of such pulses with atoms and molecules leads to new, highly nonlinear nonperturbative regimes, where new physical phenomena, such as High Harmonic Generation (HHG), occur, and from which the shortest (attosecond - the natural time scale of the electron) pulses have been created. One of the major experimental discoveries in this nonlinear...
Using a Prediction Model to Manage Cyber Security Threats
National Research Council Canada - National Science Library
Jaganathan, Venkatesh; Cherurveettil, Priyesh; Muthu Sivashanmugam, Premapriya
2015-01-01
.... The cost impact due to worms, viruses, or other malicious software is significant. This paper proposes a mathematical model to predict the impact of an attack based on significant factors that influence cyber security...
The mathematical modeling revolution in extractive metallurgy
Szekely, Julian
1988-08-01
A brief review is presented of the current state of extractive metallurgy, and it is shown that it is still a significant part of the national economy. Then a definition is given of mathematical models, and the general philosophy of modeling is discussed, together with the cost of models, hardware, and software options. Several illustrative examples are given, drawn from aluminum electrolysis, flash smelting, tundish operations, and plasma systems. The paper is concluded with the future modeling tasks facing us; these include the more widespread applications of models to represent both existing and new processing operations. It is stressed that models can play a major role in developing a holistic approach to metals and materials processing, where the primary extraction and refining operations are combined with the final processing steps.
Mathematical Modelling of Immune Response in Tissues
Directory of Open Access Journals (Sweden)
B. Su
2009-01-01
Full Text Available We have developed a spatial–temporal mathematical model (PDE to capture fundamental aspects of the immune response to antigen. We have considered terms that broadly describe intercellular communication, cell movement, and effector function (activation or inhibition. The PDE model is robust to variation in antigen load and it can account for (1 antigen recognition, (2 an innate immune response, (3 an adaptive immune response, (4 the elimination of antigen and subsequent resolution of the immune response or (5 equilibrium of the immune response to the presence of persistent antigen (chronic infection and the formation of a granuloma.
Mathematical methods and models in composites
Mantic, Vladislav
2014-01-01
This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites. The topics cover
MATHEMATICAL MODEL OF THE MICROBIAL FLOODING
Institute of Scientific and Technical Information of China (English)
Lei Guang-lun; Zhang Zhong-zhi; Chen Yue-ming
2003-01-01
On the basis of growth kinetics of microorganism and the principle of material balance, equations were derived to describe microbial growth, nutrient consumption, metabolites production and their transport in formation. The changes in porosity, permeability, oil viscosity and capillary force were also described as the main facturs of microbial flooding. For reservoirs with black oil properties, three-dimensional three-phase mathematical models with the cosidaration of multi-microbial components were established to depict microbial flooding oil. With this model, calculated results are in good agreement with experimental data.
Mathematical Model of the Processoof Pearlite Austenitization
Directory of Open Access Journals (Sweden)
Olejarczyk-Wożeńska I.
2014-10-01
Full Text Available The paper presents a mathematical model of the pearlite - austenite transformation. The description of this process uses the diffusion mechanism which takes place between the plates of ferrite and cementite (pearlite as well as austenite. The process of austenite growth was described by means of a system of differential equations solved with the use of the finite difference method. The developed model was implemented in the environment of Delphi 4. The proprietary program allows for the calculation of the rate and time of the transformation at an assumed temperature as well as to determine the TTT diagram for the assigned temperature range.
A mathematical model of 'Pride and Prejudice'.
Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro
2014-04-01
A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.
Mathematical Modelling of Tyndall Star Initiation
Harvey, Peter; Katz, Richard F; Lacey, Andrew A
2015-01-01
The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid/liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes some of the experimental observations of Tyndall stars and a mathematical model for the early stages of their evolution. The modelling is complicated by the strong crystalline anisotropy, which results in an anisotropic kinetic undercooling at the interface, and it leads to an interesting class of codimension-2 free boundary problems.
The Erosion of Well-being: a Heuristic Mathematical Model
Thron, Chris
2015-01-01
This paper presents a heuristic mathematical model of the changes over time in the statistical distribution of well-being of individuals in a society. The model predicts that when individuals overvalue the more overtly conspicuous aspects of well-being in their lifestyle choices, then under certain conditions the average well-being of the overall population may experience continuous decline. We investigate the influence of various effects, including the incidence of personal misfortune, heterogeneity in the population, and economic and/or technological progress.
MODEL PREDICTIVE CONTROL FUNDAMENTALS
African Journals Online (AJOL)
2012-07-02
Jul 2, 2012 ... paper, we will present an introduction to the theory and application of MPC with Matlab codes written to ... model predictive control, linear systems, discrete-time systems, ... and then compute very rapidly for this open-loop con-.
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
influence of model regularization parameter choices on the model generalization, the reliability of the spatial brain patterns extracted from the analysis model, and the ability of the model to identify relevant brain networks defining the underlying neural encoding of the experiment. We show that known...... parts of brain networks can be overlooked in pursuing maximization of prediction accuracy. This supports the view that the quality of spatial patterns extracted from models cannot be assessed purely by focusing on prediction accuracy. Our results instead suggest that model regularization parameters must...
Exploring the Relationship between Mathematical Modelling and Classroom Discourse
Redmond, Trevor; Sheehy, Joanne; Brown, Raymond
2010-01-01
This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…
A mathematical model on Acquired Immunodeficiency Syndrome
Directory of Open Access Journals (Sweden)
Buddhadeo Mahato
2014-10-01
Full Text Available A mathematical model SEIA (susceptible-exposed-infectious-AIDS infected with vertical transmission of AIDS epidemic is formulated. AIDS is one of the largest health problems, the world is currently facing. Even with anti-retroviral therapies (ART, many resource-constrained countries are unable to meet the treatment needs of their infected populations. We consider a function of number of AIDS cases in a community with an inverse relation. A stated theorem with proof and an example to illustrate it, is given to find the equilibrium points of the model. The disease-free equilibrium of the model is investigated by finding next generation matrix and basic reproduction number R0 of the model. The disease-free equilibrium of the AIDS model system is locally asymptotically stable if R0⩽1 and unstable if R0>1. Finally, numerical simulations are presented to illustrate the results.
Mathematical Modelling of Involute Spur Gears Manufactured by Rack Cutter
Directory of Open Access Journals (Sweden)
Tufan Gürkan YILMAZ
2016-05-01
Full Text Available In this study, mathematical modelling of asymmetric involute spur gears was situated in by Litvin approach. In this context, firstly, mathematical expressions of rack cutter which manufacture asymmetric involute spur gear, then mathematical expression of asymmetric involute spur gear were obtained by using differential geometry, coordinate transformation and gear theory. Mathematical expressions were modelled in MATLAB and output files including points of involute spur gear’s teeth were designed automatically thanks to macros.
Preventing clonal evolutionary processes in cancer: Insights from mathematical models.
Rodriguez-Brenes, Ignacio A; Wodarz, Dominik
2015-07-21
Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.
Mathematical Modeling of Intestinal Iron Absorption Using Genetic Programming
Colins, Andrea; Gerdtzen, Ziomara P.; Nuñez, Marco T.; Salgado, J. Cristian
2017-01-01
Iron is a trace metal, key for the development of living organisms. Its absorption process is complex and highly regulated at the transcriptional, translational and systemic levels. Recently, the internalization of the DMT1 transporter has been proposed as an additional regulatory mechanism at the intestinal level, associated to the mucosal block phenomenon. The short-term effect of iron exposure in apical uptake and initial absorption rates was studied in Caco-2 cells at different apical iron concentrations, using both an experimental approach and a mathematical modeling framework. This is the first report of short-term studies for this system. A non-linear behavior in the apical uptake dynamics was observed, which does not follow the classic saturation dynamics of traditional biochemical models. We propose a method for developing mathematical models for complex systems, based on a genetic programming algorithm. The algorithm is aimed at obtaining models with a high predictive capacity, and considers an additional parameter fitting stage and an additional Jackknife stage for estimating the generalization error. We developed a model for the iron uptake system with a higher predictive capacity than classic biochemical models. This was observed both with the apical uptake dataset used for generating the model and with an independent initial rates dataset used to test the predictive capacity of the model. The model obtained is a function of time and the initial apical iron concentration, with a linear component that captures the global tendency of the system, and a non-linear component that can be associated to the movement of DMT1 transporters. The model presented in this paper allows the detailed analysis, interpretation of experimental data, and identification of key relevant components for this complex biological process. This general method holds great potential for application to the elucidation of biological mechanisms and their key components in other complex
Mathematical model of the Amazon Stirling engine
Energy Technology Data Exchange (ETDEWEB)
Vidal Medina, Juan Ricardo [Universidad Autonoma de Occidente (Colombia)], e-mail: jrvidal@uao.edu.co; Cobasa, Vladimir Melian; Silva, Electo [Universidade Federal de Itajuba, MG (Brazil)], e-mail: vlad@unifei.edu.br
2010-07-01
The Excellency Group in Thermoelectric and Distributed Generation (NEST, for its acronym in Portuguese) at the Federal University of Itajuba, has designed a Stirling engine prototype to provide electricity to isolated regions of Brazil. The engine was designed to operate with residual biomass from timber process. This paper presents mathematical models of heat exchangers (hot, cold and regenerator) integrated into second order adiabatic models. The general model takes into account the pressure drop losses, hysteresis and internal losses. The results of power output, engine efficiency, optimal velocity of the exhaust gases and the influence of dead volume in engine efficiency are presented in this paper. The objective of this modeling is to propose improvements to the manufactured engine design. (author)
Solar Panel Mathematical Modeling Using Simulink
Directory of Open Access Journals (Sweden)
Chandani Sharma
2014-05-01
Full Text Available For decades, electricity is a key driver of socio-economy development. Nowadays, in the context of competition there is a direct relationship between electricity generation and sustainable development of the country. This paper presents distinct use of a Photovoltaic array offering great potential as source of electricity. The simulation uses One-diode equivalent circuit in order to investigate I-V and P-V characteristics. The GUI model is designed with Simulink block libraries. The goals of proposed model are to perform a systematic analysis, modeling and evaluation of the key subsystems for obtaining Maximum Power Point of a solar cell. Effect of increasing number of cells is described at Standard Test Conditions by mathematical modeling of equations. It is desirable to achieve maximum power output at a minimum cost under various operating conditions. Index Terms—
Modified Mathematical Model For Neutralization System In Stirred Tank Reactor
Directory of Open Access Journals (Sweden)
Ahmmed Saadi Ibrehem
2011-05-01
Full Text Available A modified model for the neutralization process of Stirred Tank Reactors (CSTR reactor is presented in this study. The model accounts for the effect of strong acid [HCL] flowrate and strong base [NaOH] flowrate with the ionic concentrations of [Cl-] and [Na+] on the Ph of the system. In this work, the effect of important reactor parameters such as ionic concentrations and acid and base flowrates on the dynamic behavior of the CSTR is investigated and the behavior of mathematical model is compared with the reported models for the McAvoy model and Jutila model. Moreover, the results of the model are compared with the experimental data in terms of pH dynamic study. A good agreement is observed between our model prediction and the actual plant data. © 2011 BCREC UNDIP. All rights reserved(Received: 1st March 2011, Revised: 28th March 2011; Accepted: 7th April 2011[How to Cite: A.S. Ibrehem. (2011. Modified Mathematical Model For Neutralization System In Stirred Tank Reactor. Bulletin of Chemical Reaction Engineering & Catalysis, 6(1: 47-52. doi:10.9767/bcrec.6.1.825.47-52][How to Link / DOI: http://dx.doi.org/10.9767/bcrec.6.1.825.47-52 || or local: http://ejournal.undip.ac.id/index.php/bcrec/article/view/825 ] | View in
Casha, Aaron R; Camilleri, Liberato; Manché, Alexander; Gatt, Ruben; Attard, Daphne; Gauci, Marilyn; Camilleri-Podesta, Marie-Therese; Grima, Joseph N
2015-05-01
As ribs adapt to stress like all bones, and the chest behaves as a pressure vessel, the effect of stress on the ribs can be determined by measuring rib height and thickness. Rib height and thickness (depth) were measured using CT scans of seven rib cages from anonymized cadavers. A Finite Element Analysis (FEA) model of a rib cage was constructed using a validated approach and used to calculate intramuscular forces as the vectors of both circumferential and axial chest wall forces at right angles to the ribs. Nonlinear quadratic models were used to relate rib height and rib thickness to rib level, and intercostal muscle force to vector stress. Intercostal muscle force was also related to vector stress using Pearson correlation. For comparison, rib height and thickness were measured on CT scans of children. Rib height increased with rib level, increasing by 13% between the 3rd and 7th rib levels, where the 7th/8th rib was the widest part or "equator" of the rib cage, P Intercostal muscle force was significantly related to vector stress, Pearson correlation r = 0.944, P = 0.005. The three nonlinear quadratic models developed all had statistically significant parameter estimates with P intercostal muscle force, showing that environmental factors affect external rib morphology. © 2015 Wiley Periodicals, Inc.
Mathematical modelling of risk reduction in reinsurance
Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.
2017-01-01
The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.
Mathematical modeling of diesel fuel hydrotreating
Tataurshikov, A.; Ivanchina, E.; Krivtcova, N.; Krivtsov, E.; Syskina, A.
2015-11-01
Hydrotreating of the diesel fraction with the high initial sulfur content of 1,4 mass% is carried out in the flow-through laboratory setup with the industrial GKD-202 catalyst at various process temperature. On the basis of the experimental data the regularities of the hydrogenation reactions are revealed, and the formalized scheme of sulfur-containing components (sulfides, benzothiophenes, and dibenzothiophenes) transformations is made. The mathematical model of hydrotreating process is developed, the constant values for the reaction rate of hydrodesulfurization of the specified components are calculated.
Mathematical Modeling of Diaphragm Pneumatic Motors
Directory of Open Access Journals (Sweden)
Fojtášek Kamil
2014-03-01
Full Text Available Pneumatic diaphragm motors belong to the group of motors with elastic working parts. This part is usually made of rubber with a textile insert and it is deformed under the pressure of a compressed air or from the external mass load. This is resulting in a final working effect. In this type of motors are in contact two different elastic environments – the compressed air and the esaltic part. These motors are mainly the low-stroke and working with relatively large forces. This paper presents mathematical modeling static properties of diaphragm motors.
Mathematical modeling of tornadoes and squall storms
Directory of Open Access Journals (Sweden)
Sergey A. Arsen’yev
2011-04-01
Full Text Available Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running perturbation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave (soliton; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.
Mathematical Simulating Model of Phased-Array Antenna in Multifunction Array Radar
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
A mathematical simulating model of phased-array antenna in multifunction array radar has been approached in this paper, including the mathematical simulating model of plane phased-array pattern, the mathematical simulating model of directionality factor, the mathematical simulating model of array factor, the mathematical simulating model of array element factor and the mathematical simulating model of beam steering.
Nominal model predictive control
Grüne, Lars
2013-01-01
5 p., to appear in Encyclopedia of Systems and Control, Tariq Samad, John Baillieul (eds.); International audience; Model Predictive Control is a controller design method which synthesizes a sampled data feedback controller from the iterative solution of open loop optimal control problems.We describe the basic functionality of MPC controllers, their properties regarding feasibility, stability and performance and the assumptions needed in order to rigorously ensure these properties in a nomina...
Nominal Model Predictive Control
Grüne, Lars
2014-01-01
5 p., to appear in Encyclopedia of Systems and Control, Tariq Samad, John Baillieul (eds.); International audience; Model Predictive Control is a controller design method which synthesizes a sampled data feedback controller from the iterative solution of open loop optimal control problems.We describe the basic functionality of MPC controllers, their properties regarding feasibility, stability and performance and the assumptions needed in order to rigorously ensure these properties in a nomina...
Dalla Vecchia, Rodrigo
2015-01-01
This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…
Lee, Jeeyeon; Gwak, Eunji; Ha, Jimyeong; Kim, Sejeong; Lee, Soomin; Lee, Heeyoung; Oh, Mi-Hwa; Park, Beom-Young; Oh, Nam Su; Choi, Kyoung-Hee; Yoon, Yohan
2016-01-01
The objective of this study was to describe the growth patterns of Staphylococcus aureus in combinations of NaCl and NaNO2, using a probabilistic model. A mixture of S. aureus strains (NCCP10826, ATCC13565, ATCC14458, ATCC23235, and ATCC27664) was inoculated into nutrient broth plus NaCl (0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, and 1.75%) and NaNO2 (0, 15, 30, 45, 60, 75, 90, 105, and 120 ppm). The samples were then incubated at 4, 7, 10, 12 and 15℃ for up to 60 d under aerobic or vacuum conditions. Growth responses [growth (1) or no growth (0)] were then determined every 24 h by turbidity, and analyzed to select significant parameters (pvacuum packaging and even aerobic storage below 10℃. Furthermore, NaNO2 does not effectively inhibit S. aureus growth. PMID:28115886
Candidate Prediction Models and Methods
DEFF Research Database (Denmark)
Nielsen, Henrik Aalborg; Nielsen, Torben Skov; Madsen, Henrik
2005-01-01
This document lists candidate prediction models for Work Package 3 (WP3) of the PSO-project called ``Intelligent wind power prediction systems'' (FU4101). The main focus is on the models transforming numerical weather predictions into predictions of power production. The document also outlines...... the possibilities w.r.t. different numerical weather predictions actually available to the project....
Comparison of Different Mathematical Models of Cavitation
Directory of Open Access Journals (Sweden)
Dorota HOMA
2014-12-01
Full Text Available Cavitation occurs during the flow when local pressure drops to the saturation pressure according to the temperature of the flow. It includes both evaporation and condensation of the vapor bubbles, which occur alternately with high frequency. Cavitation can be very dangerous, especially for pumps, because it leads to break of flow continuity, noise, vibration, erosion of blades and change in pump’s characteristics. Therefore it is very important for pump designers and users to avoid working in cavitation conditions. Simulation of flow can be very useful in that and can indicate if there is risk of cavitating flow occurrence. As this is a multiphase flow and quite complicated phenomena, there are a few mathematical models describing it. The aim of this paper is to make a short review of them and describe their approach to model cavitation. It is desirable to know differences between them to model this phenomenon properly.
A MATHEMATICAL MODEL OF RESERVOIR SEDIMENTATION
Institute of Scientific and Technical Information of China (English)
HUANG Jinchi
2001-01-01
Reliable quantitative estimation of bed aggradation or degradation is important for river-training and water management projects. With the development of water resources, sediment problems associated with a dam are becoming more severe. This paper describes some special problems in mathematical model for calculation of degradation and aggradation in a reservoir. The main efforts of this study are on the treatment of some physical processes of fine sediment transport (＜0.05 mm). Problems in a reservoir are obviously different from a natural stream, such as the turbid current flow, orifice sediment flushing;and the initiation and consolidation of cohesive sediment deposition. The case of Liujiaxia Reservoir,which is located in the upper reaches of the Yellow River, is employed to verify the model. The results show that the model is applicable in the evaluation of an engineering planing with plenty of fine sediment movement.
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Building Mathematics Achievement Models in Four Countries Using TIMSS 2003
Wang, Ze; Osterlind, Steven J.; Bergin, David A.
2012-01-01
Using the Trends in International Mathematics and Science Study 2003 data, this study built mathematics achievement models of 8th graders in four countries: the USA, Russia, Singapore and South Africa. These 4 countries represent the full spectrum of mathematics achievement. In addition, they represent 4 continents, and they include 2 countries…
The Analysis of the New Road Traffic Prediction Mathematical Model%新建道路的交通量预测数学模型分析
Institute of Scientific and Technical Information of China (English)
吕高腾; 郑全成
2011-01-01
随着经济的发展,我国道路发展水平的提高,交通车辆的增加,交通拥堵问题已成为目前亟待解决的问题。采用交通阻抗分析和诱增经济增长模型法,对道路交通量进行预测,为新建交通道路的建立是否对其交通布局产生优化评价提供依据。%With the development of Economy, the country road development level improved, and the increased of vehicle, the problem of traffic congestion become our present life problems to be solved. This paper used the traffic impedance analysis and induced increase economic growth model method to forecast the road traffic volume, it provides the basis establishment of the traffic layout whether produce optimization evaluation to the new roads.
Building a Two Axes Process Model of Understanding Mathematics
Koyama, Masataka
1993-01-01
The purpose of this study is to make clear what kind of characteristics a model of understanding mathematics should have so as to be useful and effective in mathematics education. The models of understanding presented in preceding papers are classified into two large categories, i. e. "aspect model" and "process model". Focusing on the process of understanding mathematics, reflective thinking plays an important role to develop children's understanding, or to progress children's thinking from ...
Executive functioning predicts reading, mathematics, and theory of mind during the elementary years.
Cantin, Rachelle H; Gnaedinger, Emily K; Gallaway, Kristin C; Hesson-McInnis, Matthew S; Hund, Alycia M
2016-06-01
The goal of this study was to specify how executive functioning components predict reading, mathematics, and theory of mind performance during the elementary years. A sample of 93 7- to 10-year-old children completed measures of working memory, inhibition, flexibility, reading, mathematics, and theory of mind. Path analysis revealed that all three executive functioning components (working memory, inhibition, and flexibility) mediated age differences in reading comprehension, whereas age predicted mathematics and theory of mind directly. In addition, reading mediated the influence of executive functioning components on mathematics and theory of mind, except that flexibility also predicted mathematics directly. These findings provide important details about the development of executive functioning, reading, mathematics, and theory of mind during the elementary years. Copyright © 2016 Elsevier Inc. All rights reserved.
Mathematical Modeling of Hybrid Electrical Engineering Systems
Directory of Open Access Journals (Sweden)
A. A. Lobaty
2016-01-01
Full Text Available A large class of systems that have found application in various industries and households, electrified transportation facilities and energy sector has been classified as electrical engineering systems. Their characteristic feature is a combination of continuous and discontinuous modes of operation, which is reflected in the appearance of a relatively new term “hybrid systems”. A wide class of hybrid systems is pulsed DC converters operating in a pulse width modulation, which are non-linear systems with variable structure. Using various methods for linearization it is possible to obtain linear mathematical models that rather accurately simulate behavior of such systems. However, the presence in the mathematical models of exponential nonlinearities creates considerable difficulties in the implementation of digital hardware. The solution can be found while using an approximation of exponential functions by polynomials of the first order, that, however, violates the rigor accordance of the analytical model with characteristics of a real object. There are two practical approaches to synthesize algorithms for control of hybrid systems. The first approach is based on the representation of the whole system by a discrete model which is described by difference equations that makes it possible to synthesize discrete algorithms. The second approach is based on description of the system by differential equations. The equations describe synthesis of continuous algorithms and their further implementation in a digital computer included in the control loop system. The paper considers modeling of a hybrid electrical engineering system using differential equations. Neglecting the pulse duration, it has been proposed to describe behavior of vector components in phase coordinates of the hybrid system by stochastic differential equations containing generally non-linear differentiable random functions. A stochastic vector-matrix equation describing dynamics of the
Nakamura, Yasuyuki; Nishi, Shinnosuke; Muramatsu, Yuta; Yasutake, Koichi; Yamakawa, Osamu; Tagawa, Takahiro
2014-01-01
In this paper, we introduce a mathematical model for collaborative learning and the answering process for multiple-choice questions. The collaborative learning model is inspired by the Ising spin model and the model for answering multiple-choice questions is based on their difficulty level. An intensive simulation study predicts the possibility of…
Mathematical modeling of the neuron morphology using two dimensional images.
Rajković, Katarina; Marić, Dušica L; Milošević, Nebojša T; Jeremic, Sanja; Arsenijević, Valentina Arsić; Rajković, Nemanja
2016-02-01
In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images.
Advanced Mathematical Model to Describe the Production of Biodiesel Process
Directory of Open Access Journals (Sweden)
Hikmat S. Al-Salim
2009-12-01
Full Text Available Advanced mathematical model was used to capture the batch reactor characteristics of reacting compounds. The model was applied to batch reactor for the production of bio-diesel from palm and kapok oils. Results of the model were compared with experimental data in terms of conversion of transesterification reaction for the production of bio-diesel under unsteady state. A good agreement was obtained between our model predictions and the experimental data. Both experimental and modeling results showed that the conversion of triglycerides to methyl ester was affected by the process conditions. The transesterification process with temperature of about 70 oC, and methanol ratio to the triglyceride of about 5 times its stoichiometry, and the NAOH catalyst of wt 0.4%, appear to be acceptable process conditions for bio diesel process production from palm oil and kapok oil. The model can be applied for endothermic batch process. © 2009 BCREC UNDIP. All rights reserved[Received: 12 August 2009, Revised: 15 October 2009; Accepted: 18 October 2009][How to Cite: A.S. Ibrehem, H. S. Al-Salim. (2009. Advanced Mathematical Model to Describe the Production of Biodiesel Process. Bulletin of Chemical Reaction Engineering and Catalysis, 4(2: 37-42. doi:10.9767/bcrec.4.2.28.37-42][How to Link/DOI: http://dx.doi.org/10.9767/bcrec.4.2.28.37-42
Predictive Surface Complexation Modeling
Energy Technology Data Exchange (ETDEWEB)
Sverjensky, Dimitri A. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Earth and Planetary Sciences
2016-11-29
Surface complexation plays an important role in the equilibria and kinetics of processes controlling the compositions of soilwaters and groundwaters, the fate of contaminants in groundwaters, and the subsurface storage of CO_{2} and nuclear waste. Over the last several decades, many dozens of individual experimental studies have addressed aspects of surface complexation that have contributed to an increased understanding of its role in natural systems. However, there has been no previous attempt to develop a model of surface complexation that can be used to link all the experimental studies in order to place them on a predictive basis. Overall, my research has successfully integrated the results of the work of many experimentalists published over several decades. For the first time in studies of the geochemistry of the mineral-water interface, a practical predictive capability for modeling has become available. The predictive correlations developed in my research now enable extrapolations of experimental studies to provide estimates of surface chemistry for systems not yet studied experimentally and for natural and anthropogenically perturbed systems.
A Mathematical Model for Freeze-Drying
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Based on the experiments on freeze-drying carrot and potato slabs, the effects of some parameters, such as heating temperature and pressure on the freeze-drying process are examined. A simple model of freeze-drying is established to predict drying time and the mass variations of materials during the drying. The experimental results agree well with those calculated by the model.
A Mathematical model of copper corrosion
Clarelli, Fabrizio; Natalini, Roberto
2012-01-01
A new partial differential model for monitoring and detecting copper corrosion products (mainly brochantite and cuprite) is proposed to provide predictive tools suitable for describing the evolution of damage induced on bronze specimens by sulfur dioxide (SO_2) pollution. This model is characterized by the movement of a double free boundary. Numerical simulations show a nice agreement with experimental result.
Rudolph, Lee
2012-01-01
In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, in
Teaching Mathematical Modelling for Earth Sciences via Case Studies
Yang, Xin-She
2010-05-01
Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).
Mathematics Teacher Education: A Model from Crimea.
Ferrucci, Beverly J.; Evans, Richard C.
1993-01-01
Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)
Knowledge Map: Mathematical Model and Dynamic Behaviors
Institute of Scientific and Technical Information of China (English)
Hai Zhuge; Xiang-Feng Luo
2005-01-01
Knowledge representation and reasoning is a key issue of the Knowledge Grid. This paper proposes a Knowledge Map (KM) model for representing and reasoning causal knowledge as an overlay in the Knowledge Grid. It extends Fuzzy Cognitive Maps (FCMs) to represent and reason not only simple cause-effect relations, but also time-delay causal relations, conditional probabilistic causal relations and sequential relations. The mathematical model and dynamic behaviors of KM are presented. Experiments show that, under certain conditions, the dynamic behaviors of KM can translate between different states. Knowing this condition, experts can control or modify the constructed KM while its dynamic behaviors do not accord with their expectation. Simulations and applications show that KM is more powerful and natural than FCM in emulating real world.
Mathematical Models and Methods for Living Systems
Chaplain, Mark; Pugliese, Andrea
2016-01-01
The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods. Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.
Analysis of mathematical modelling on potentiometric biosensors.
Mehala, N; Rajendran, L
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.
Laser interaction with biological material mathematical modeling
Kulikov, Kirill
2014-01-01
This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.
Common Mathematical Model of Fatigue Characteristics
Directory of Open Access Journals (Sweden)
Z. Maléř
2004-01-01
Full Text Available This paper presents a new common mathematical model which is able to describe fatigue characteristics in the whole necessary range by one equation only:log N = A(R + B(R ∙ log Sawhere A(R = AR2 + BR + C and B(R = DR2 + AR + F.This model was verified by five sets of fatigue data taken from the literature and by our own three additional original fatigue sets. The fatigue data usually described the region of N 104 to 3 x 106 and stress ratio of R = -2 to 0.5. In all these cases the proposed model described fatigue results with small scatter. Studying this model, following knowledge was obtained:– the parameter ”stress ratio R” was a good physical characteristic– the proposed model provided a good description of the eight collections of fatigue test results by one equation only– the scatter of the results through the whole scope is only a little greater than that round the individual S/N curve– using this model while testing may reduce the number of test samples and shorten the test time– as the proposed model represents a common form of the S/N curve, it may be used for processing uniform objective fatigue life results, which may enable mutual comparison of fatigue characteristics.
HEMETβ: improvement of hepatocyte metabolism mathematical model.
Orsi, G; De Maria, C; Guzzardi, M; Vozzi, F; Vozzi, G
2011-10-01
This article describes hepatocyte metabolism mathematical model (HEMETβ), which is an improved version of HEMET, an effective and versatile virtual cell model based on hepatic cell metabolism. HEMET is based on a set of non-linear differential equations, implemented in Simulink®, which describes the biochemical reactions and energetic cell state, and completely mimics the principal metabolic pathways in hepatic cells. The cell energy function and modular structure are the core of this model. HEMETβ as HEMET model describes hepatic cellular metabolism in standard conditions (cell culture in a plastic multi-well placed in an incubator at 37° C with 5% of CO2) and with excess substrates concentration. The main improvements in HEMETβ are the introductions of Michaelis-Menten models for reversible reactions and enzymatic inhibition. In addition, we eliminated hard non-linearities and modelled cell proliferation and every single aminoacid degradation pathway. All these innovations, combined with a user-friendly aspect, allow researchers to create new cell types and validate new experimental protocols just varying 'peripheral' pathways or model inputs.
MATHEMATICAL MODELING OF OIL SPILL ON THE SEA AND APPLICATION OF THE MODELING IN DAYA BAY
Institute of Scientific and Technical Information of China (English)
CHEN Hai-zhou; LI Da-ming; LI Xiao
2007-01-01
Through the study of the theory of oil spill model, a mathematical modeling of oil spill on the sea is developed which with the consideration of spread, diffusion, drifting and attenuation of oil slick is influenced by evaporation and emulsification factors. A model that under the effect of ocean dynamic condition of tide, wind and wave, using Monte Carlo method to simulate the movement of oil slick is established. The modeling is applied to calculate and predict pollution range of oil spill at oil quay and oil ship in Daya Bay. The prediction results have basically shown the pollution situation by emergency of oil spill on the sea.
Evaluation of Mathematical Models for Tankers’ Maneuvering Motions
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Erhan AKSU
2017-03-01
Full Text Available In this study, the maneuvering performance of two tanker ships, KVLCC1 and KVLCC2 which have different stern forms are predicted using a system-based method. Two different 3 DOF (degrees of freedom mathematical models based on the MMG(Maneuvering Modeling Group concept areappliedwith the difference in representing lateral force and yawing moment by second and third order polynomials respectively. Hydrodynamic coefficients and related parameters used in the mathematical models of the same scale models of KVLCC1 and KVLCC2 ships are estimated by using experimental data of NMRI (National Maritime Research Institute. The simulations of turning circle with rudder angle ±35o , zigzag(±10o /±10o and zigzag (±20o /±20o maneuvers are carried out and compared with free running model test data of MARIN (Maritime Research Institute Netherlands in this study. As a result of the analysis, it can be summarised that MMG model based on the third order polynomial is superior to the one based on the second order polynomial in view of estimation accuracy of lateral hull force and yawing moment.
Linear models in the mathematics of uncertainty
Mordeson, John N; Clark, Terry D; Pham, Alex; Redmond, Michael A
2013-01-01
The purpose of this book is to present new mathematical techniques for modeling global issues. These mathematical techniques are used to determine linear equations between a dependent variable and one or more independent variables in cases where standard techniques such as linear regression are not suitable. In this book, we examine cases where the number of data points is small (effects of nuclear warfare), where the experiment is not repeatable (the breakup of the former Soviet Union), and where the data is derived from expert opinion (how conservative is a political party). In all these cases the data is difficult to measure and an assumption of randomness and/or statistical validity is questionable. We apply our methods to real world issues in international relations such as nuclear deterrence, smart power, and cooperative threat reduction. We next apply our methods to issues in comparative politics such as successful democratization, quality of life, economic freedom, political stability, and fail...
The use of mathematical models in teaching wastewater treatment engineering
DEFF Research Database (Denmark)
Morgenroth, Eberhard Friedrich; Arvin, Erik; Vanrolleghem, P.
2002-01-01
Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models...... efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available....
Mathematical problems in modeling artificial heart
Directory of Open Access Journals (Sweden)
Ahmed N. U.
1995-01-01
Full Text Available In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate. On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.
Candidate Prediction Models and Methods
DEFF Research Database (Denmark)
Nielsen, Henrik Aalborg; Nielsen, Torben Skov; Madsen, Henrik
2005-01-01
This document lists candidate prediction models for Work Package 3 (WP3) of the PSO-project called ``Intelligent wind power prediction systems'' (FU4101). The main focus is on the models transforming numerical weather predictions into predictions of power production. The document also outlines...
The Use of Models in Teaching Proof by Mathematical Induction
Ron, Gila; Dreyfus, Tommy
2004-01-01
Proof by mathematical induction is known to be conceptually difficult for high school students. This paper presents results from interviews with six experienced high school teachers, concerning the use of models in teaching mathematical induction. Along with creative and adequate use of models, we found explanations, models and examples that…
Mathematical models of the AIDS epidemic: An historical perspective
Energy Technology Data Exchange (ETDEWEB)
Stanley, E.A.
1988-01-01
Researchers developing mathematical models of the spreading of HIV, the Human Immunodeficiency Virus that causes AIDS, hope to achieve a number of goals. These goals may be classified rather broadly into three categories: understanding, prediction, and control. Understanding which are the key biological and sociological processes spreading this epidemic and leading to the deaths of those infected will allow AIDS researchers to collect better data and to identify ways of slowing the epidemic. Predicting the groups at risk and future numbers of ill people will allow an appropriate allocation of health-care resources. Analysis and comparison of proposed control methods will point out unexpected consequences and allow a better design of these programs. The processes which lead to the spread of HIV are biologically and sociologically complex. Mathematical models allow us to organize our knowledge into a coherent picture and examine the logical consequences, therefore they have the potential to be extremely useful in the search to control this disease. 24 refs., 3 figs.
Illustrations of mathematical modeling in biology: epigenetics, meiosis, and an outlook.
Richards, D; Berry, S; Howard, M
2012-01-01
In the past few years, mathematical modeling approaches in biology have begun to fulfill their promise by assisting in the dissection of complex biological systems. Here, we review two recent examples of predictive mathematical modeling in plant biology. The first involves the quantitative epigenetic silencing of the floral repressor gene FLC in Arabidopsis, mediated by a Polycomb-based system. The second involves the spatiotemporal dynamics of telomere bouquet formation in wheat-rye meiosis. Although both the biology and the modeling framework of the two systems are different, both exemplify how mathematical modeling can help to accelerate discovery of the underlying mechanisms in complex biological systems. In both cases, the models that developed were relatively minimal, including only essential features, but both nevertheless yielded fundamental insights. We also briefly review the current state of mathematical modeling in biology, difficulties inherent in its application, and its potential future development.
Mathematical Modelling of the Heald Shaft
Directory of Open Access Journals (Sweden)
Bílek Martin
2016-12-01
Full Text Available The manufacturers of weaving equipment recently endeavour to minimise the necessary designing plays in the weaving loom mechanisms. One of the mechanisms most exposed to stress is the shedding motion that defines the held-shaft stroke. Its end part is the heald shaft. The heald shaft constitutes a problematic assembly of the shedding motion. The design employed presently is characterised by dynamic impact loading caused by designing play in the suspension of healds into the heald shaft. During weaving cycle, the healds fly between the main beams of the heald shaft, producing a considerable force pulse. This paper is concerned with the description of dynamic behaviour of the existing design on the basis of mathematical modelling and verification of obtained results by means of experimental analysis.
Mathematical Modeling of Spiral Heat Exchanger
Directory of Open Access Journals (Sweden)
Probal Guha , Vaishnavi Unde
2014-04-01
Full Text Available Compact Heat Exchangers (CHEs are increasingly being used on small and medium scale industries. Due to their compact size and efficient design, they facilitate more efficient heat transfer. Better heat transfer would imply lesser fuel consumption for the operations of the plant, giving improvement to overall efficiency. This reduction in consumption of fuel is a step towards sustainable development. This report exclusively deals with the study the spiral heat exchanger.The design considerations for spiral heat exchanger is that the flow within the spiral has been assumed as flow through a duct and by using Shah London empirical equation for Nusselt number design parameters are further optimized.This is accompanied by a detailed energy balance to generate a concise mathematical model
Mathematical modelling on instability of shear fault
Institute of Scientific and Technical Information of China (English)
范天佑
1996-01-01
A study on mathematical modelling on instability of fault is reported.The fracture mechanics and fracture dynamics as a basis of the discussion,and the method of complex variable function (including the conformal mapping and approximate conformal mapping) are employed,and some analytic solutions of the problem in closed form are found.The fault body concept is emphasized and the characteristic size of fault body is introduced.The effect of finite size of the fault body and the effect of the fault propagating speed (especially the effect of the high speed) and their influence on the fault instability are discussed.These results further explain the low-stress drop phenomena observed in earthquake source.
Some Mathematical Models for ELM Signal
XIE, Hua-sheng
2012-01-01
There is no wide accepted theory for ELM (Edge Localized Mode) yet. Some fusion people feel that we may never get a final theory for ELM and H-mode, since which are too complicated (also related to the unsolved turbulence problem) and with at least three time scales. The only way out is using models. (This is analogous to that we believe quantum mechanics can explain chemistry and biology, but no one can calculate DNA structure from Schrodinger equation directly.) This manuscript gives some possible mathematical approaches to it. I should declare that these are just math toys for me yet. They may inspire to good understandings of ELM and H-mode, may not. Useful or useless, I don't know. One need not take too much care of it. Just for fun and enjoying different interesting ideas.
Mathematical Model for the Continuous Vacuum Drying
Institute of Scientific and Technical Information of China (English)
DAI Hui-liang
2002-01-01
An improved mathematical model for the continuous vacuum drying of highly viscous and heatsensitive foodstuffs was proposed, The process of continuous vacuum drying was presented as a moving boundary problem of moisture evaporation in cylindrical coordinates. Boundary condition of the first kind for the known functional dependence of the drying body surface temperature on time was considered. Finally, the appropriate system of differential equations was solved numerically and the values of drying rate, integral moisture content of the material, moving boundary position as well as temperature in any point of the material and at any moment time were obtained. This procedure was applied to continuous vacuum drying of foods such as natural cheese and fresh meat paste.
Mathematical Modeling of the Origins of Life
Pohorille, Andrew
2006-01-01
The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.
Mathematics in Nature Modeling Patterns in the Natural World
Adam, John A
2011-01-01
From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature.Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathem
An introduction to mathematical modeling a course in mechanics
Oden, Tinsley J
2011-01-01
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...
Mathematical modeling of endovenous laser treatment (ELT
Directory of Open Access Journals (Sweden)
Wassmer Benjamin
2006-04-01
Full Text Available Abstract Background and objectives Endovenous laser treatment (ELT has been recently proposed as an alternative in the treatment of reflux of the Great Saphenous Vein (GSV and Small Saphenous Vein (SSV. Successful ELT depends on the selection of optimal parameters required to achieve an optimal vein damage while avoiding side effects. Mathematical modeling of ELT could provide a better understanding of the ELT process and could determine the optimal dosage as a function of vein diameter. Study design/materials and methods The model is based on calculations describing the light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma Inc., Arlington, MA, USA. Damage to the vein wall for CW and single shot energy was calculated for 3 and 5 mm vein diameters. In pulsed mode, the pullback distance (3, 5 and 7 mm was considered. For CW mode simulation, the pullback speed (1, 2, 3 mm/s was the variable. The total dose was expressed as joules per centimeter in order to perform comparison to results already reported in clinical studies. Results In pulsed mode, for a 3 mm vein diameter, irrespective of the pullback distance (2, 5 or 7 mm, a minimum fluence of 15 J/cm is required to obtain a permanent damage of the intima. For a 5 mm vein diameter, 50 J/cm (15W-2s is required. In continuous mode, for a 3 mm and 5 mm vein diameter, respectively 65 J/cm and 100 J/cm are required to obtain a permanent damage of the vessel wall. Finally, the use of different wavelengths (810 nm or 980 nm played only a minor influence on these results. Discussion and conclusion The parameters
Physical and mathematical modelling of extrusion processes
DEFF Research Database (Denmark)
Arentoft, Mogens; Gronostajski, Z.; Niechajowics, A.
2000-01-01
The main objective of the work is to study the extrusion process using physical modelling and to compare the findings of the study with finite element predictions. The possibilities and advantages of the simultaneous application of both of these methods for the analysis of metal forming processes...
Physical and mathematical modelling of extrusion processes
DEFF Research Database (Denmark)
Arentoft, Mogens; Gronostajski, Z.; Niechajowics, A.
2000-01-01
The main objective of the work is to study the extrusion process using physical modelling and to compare the findings of the study with finite element predictions. The possibilities and advantages of the simultaneous application of both of these methods for the analysis of metal forming processes...
Mathematical Modeling Social Responsibility for Dynamic Organizations
Directory of Open Access Journals (Sweden)
Farzaneh Chavoshbashi
2012-03-01
Full Text Available Dynamic organizations as accountable organizations, for transparency and accountability to its stakeholders to stakeholders for their toward performance there should express their commitment to social responsibility are through their values and ensure that this commitment throughout the organization are now and thus will have a social responsibility for their mutual benefit, so there is more and more coherent in their ethical approach takes advantage and the community and stakeholders and the organization will have better performance and strengths. Because of interest in social responsibility, in this paper dynamic model is presented for Corporate Social Responsibility of Bionic organization. Model presented a new model is inspired by chaos theory and natural systems theory based on bifurcation in creation to be all natural systems, realizing the value of responsibility as one of the fundamental values of social and institutional development that the relationship between business and work environment in the global market economy and range will be specified. First Social Responsibility factors identified, then experts and scholars determine the weight of the components and technical coefficient for modeling and paired comparison has been done using MATLAB mathematical Software.
Cocaine addiction and personality: a mathematical model.
Caselles, Antonio; Micó, Joan C; Amigó, Salvador
2010-05-01
The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse.
Mathematical Model for the Mineralization of Bone
Martin, Bruce
1994-01-01
A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.
Mathematical Model of Oxygen Transport in Tuberculosis Granulomas
Datta, Meenal; Via, Laura E.; Chen, Wei; Baish, James W.; Xu, Lei; Barry, Clifton E.; Jain, Rakesh K.
2016-01-01
Pulmonary granulomas—the hallmark of Mycobacterium tuberculosis (MTB) infection—are dense cellular lesions that often feature regions of hypoxia and necrosis, partially due to limited transport of oxygen. Low oxygen in granulomas can impair the host immune response, while MTB are able to adapt and persist in hypoxic environments. Here, we used a physiologically based mathematical model of oxygen diffusion and consumption to calculate oxygen profiles within the granuloma, assuming Michaelis–Menten kinetics. An approximate analytical solution—using a priori and newly estimated parameters from experimental data in a rabbit model of tuberculosis—was able to predict the size of hypoxic and necrotic regions in agreement with experimental results from the animal model. Such quantitative understanding of transport limitations can inform future tuberculosis therapeutic strategies that may include adjunct host-directed therapies that facilitate oxygen and drug delivery for more effective treatment. PMID:26253038
A Mathematical Model for the Dynamics and Synchronization of Cows
Sun, Jie; Porter, Mason A; Dawkins, Marian S
2010-01-01
We formulate a mathematical model for daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds. We comment on the relevant biology and discuss extensions of our model. With this abstract approach, we not only investigate equations with interesting dynamics but also develop interesting biological predictions. In particular, our model illustrates that it is possible for cows to synchronize \\emph{less} when the coupling is increased.
Mathematical modeling of normal pharyngeal bolus transport: a preliminary study.
Chang, M W; Rosendall, B; Finlayson, B A
1998-07-01
Dysphagia (difficulty in swallowing) is a common clinical symptom associated with many diseases, such as stroke, multiple sclerosis, neuromuscular diseases, and cancer. Its complications include choking, aspiration, malnutrition, cachexia, and dehydration. The goal in dysphagia management is to provide adequate nutrition and hydration while minimizing the risk of choking and aspiration. It is important to advance the individual toward oral feeding in a timely manner to enhance the recovery of swallowing function and preserve the quality of life. Current clinical assessments of dysphagia are limited in providing adequate guidelines for oral feeding. Mathematical modeling of the fluid dynamics of pharyngeal bolus transport provides a unique opportunity for studying the physiology and pathophysiology of swallowing. Finite element analysis (FEA) is a special case of computational fluid dynamics (CFD). In CFD, the flow of a fluid in a space is modeled by covering the space with a grid and predicting how the fluid moves from grid point to grid point. FEA is capable of solving problems with complex geometries and free surfaces. A preliminary pharyngeal model has been constructed using FEA. This model incorporates literature-reported, normal, anatomical data with time-dependent pharyngeal/upper esophageal sphincter (UES) wall motion obtained from videofluorography (VFG). This time-dependent wall motion can be implemented as a moving boundary condition in the model. Clinical kinematic data can be digitized from VFG studies to construct and test the mathematical model. The preliminary model demonstrates the feasibility of modeling pharyngeal bolus transport, which, to our knowledge, has not been attempted before. This model also addresses the need and the potential for CFD in understanding the physiology and pathophysiology of the pharyngeal phase of swallowing. Improvements of the model are underway. Combining the model with individualized clinical data should potentially
Mathematical model for cyclodextrin alteration of bioavailability of organic pollutants.
Liu, Huihui; Cai, Xiyun; Chen, Jingwen
2013-06-04
While many cyclodextrin-based applications have been developed to assess or enhance bioavailability of organic pollutants, the choice of cyclodextrin (CD) is largely empirical, with little consideration of pollutant diversity and environmental matrix effects. This study aimed at developing a mathematical model for quantifying CD alteration of bioavailability of organic pollutants. Cyclodextrin appears to have multiple effects, together contributing to its bioavailability-enhancing property. Cyclodextrin is adsorbed onto the adsorbent matrix to different extents. The adsorbed CD is capable of sequestrating organic pollutants, highlighting the role of a pseudophase similar to solid environmental matrix. Aqueous CD can reduce adsorption of organic pollutants via inclusion complexation. The two effects cancel each other to a certain degree, which determines the levels of organic pollutants dissolved (comprising freely dissolved and CD-included forms). Additionally, the CD-included form is nearly identical in biological activity to the free form. A mathematical model of one variable (i.e., CD concentration) was derived to quantify effects of CD on the bioavailability of organic pollutants. Model analysis indicates that alteration of bioavailability of organic pollutants by CD depends on both CD (type and level) and environmental matrix. The selection of CD type and amendment level for a given application may be predicted by the model.
Optimisation of a large WWTP thanks to mathematical modelling.
Printemps, C; Baudin, A; Dormoy, T; Zug, M; Vanrolleghem, P A
2004-01-01
Better controlling and optimising the plant's processes has become a priority for WWTP (Wastewater Treatment Plant) managers. The main objective of this project is to develop a simplified mathematical tool able to reproduce and anticipate the behaviour of the Tougas WWTP (Nantes, France). This tool is aimed to be used directly by the managers of the site. The mathematical WWTP model was created using the software WEST. This paper describes the studied site and the modelling results obtained during the stage of the model calibration and validation. The good simulation results have allowed to show that despite a first very simple description of the WWTP, the model was able to correctly predict the nitrogen composition (ammonia and nitrate) of the effluent and the daily sludge extraction. Then, a second more detailed configuration of the WWTP was implemented. It has allowed to independently study the behaviour of each of four biological trains. Once this first stage will be completely achieved, the remainder of the study will focus on the operational use of a simplified simulator with the purpose of optimising the Tougas WWTP operation.
Melanoma risk prediction models
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Nikolić Jelena
2014-01-01
Full Text Available Background/Aim. The lack of effective therapy for advanced stages of melanoma emphasizes the importance of preventive measures and screenings of population at risk. Identifying individuals at high risk should allow targeted screenings and follow-up involving those who would benefit most. The aim of this study was to identify most significant factors for melanoma prediction in our population and to create prognostic models for identification and differentiation of individuals at risk. Methods. This case-control study included 697 participants (341 patients and 356 controls that underwent extensive interview and skin examination in order to check risk factors for melanoma. Pairwise univariate statistical comparison was used for the coarse selection of the most significant risk factors. These factors were fed into logistic regression (LR and alternating decision trees (ADT prognostic models that were assessed for their usefulness in identification of patients at risk to develop melanoma. Validation of the LR model was done by Hosmer and Lemeshow test, whereas the ADT was validated by 10-fold cross-validation. The achieved sensitivity, specificity, accuracy and AUC for both models were calculated. The melanoma risk score (MRS based on the outcome of the LR model was presented. Results. The LR model showed that the following risk factors were associated with melanoma: sunbeds (OR = 4.018; 95% CI 1.724- 9.366 for those that sometimes used sunbeds, solar damage of the skin (OR = 8.274; 95% CI 2.661-25.730 for those with severe solar damage, hair color (OR = 3.222; 95% CI 1.984-5.231 for light brown/blond hair, the number of common naevi (over 100 naevi had OR = 3.57; 95% CI 1.427-8.931, the number of dysplastic naevi (from 1 to 10 dysplastic naevi OR was 2.672; 95% CI 1.572-4.540; for more than 10 naevi OR was 6.487; 95%; CI 1.993-21.119, Fitzpatricks phototype and the presence of congenital naevi. Red hair, phototype I and large congenital naevi were
Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe
2016-01-01
Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…
A mathematical model of aerosol holding chambers
DEFF Research Database (Denmark)
Zak, M; Madsen, J; Berg, E
1999-01-01
in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London......, Ontario, Canada), NebuChamber (Astra, Södirtälje, Sweden) and Nebuhaler (Astra) adapted for babies. The dose of fluticasone proportionate delivered by the Babyhaler (Glaxco Wellcome, Oxbridge, Middlesex, UK) was 80% of that predicted, probably because of incomplete priming of this spacer. Of the above...
Mathematical model of the Savannah River Site waste tank farm
Energy Technology Data Exchange (ETDEWEB)
Smith, F.G. III.
1991-07-15
A mathematical model has been developed to simulate operation of the waste tank farm and the associated evaporator systems at the Savannah River Site. The model solves material balance equations to predict the volumes of liquid waste, salt, and sludge for all of the tanks within each of the evaporator systems. Additional logic is included to model the behavior of waste tanks not directly associated with the evaporators. Input parameters include the Material Management Plan forecast of canyon operations, specification of other waste sources for the evaporator systems, evaporator operating characteristics, and salt and sludge removal schedules. The model determines how the evaporators will operate, when waste transfers can be made, and waste accumulation rates. Output from the model includes waste tank contents, summaries of systems operations, and reports of space gain and the remaining capacity to store waste materials within the tank farm. Model simulations can be made to predict waste tank capacities on a daily basis for up to 20 years. The model is coded as a set of three computer programs designed to run on either IBM compatible or Apple Macintosh II personal computers.
Mathematical model of electrotaxis in osteoblastic cells.
Vanegas-Acosta, J C; Garzón-Alvarado, D A; Zwamborn, A P M
2012-12-01
Electrotaxis is the cell migration in the presence of an electric field (EF). This migration is parallel to the EF vector and overrides chemical migration cues. In this paper we introduce a mathematical model for the electrotaxis in osteoblastic cells. The model is evaluated using different EF strengths and different configurations of both electrical and chemical stimuli. Accordingly, we found that the cell migration speed is described as the combination of an electrical and a chemical term. Cell migration is faster when both stimuli orient cell migration towards the same direction. In contrast, a reduced speed is obtained when the EF vector is opposed to the direction of the chemical stimulus. Numerical relations were obtained to quantify the cell migration speed at each configuration. Additional calculations for the cell colonization of a substrate also show mediation of the EF strength. Therefore, the term electro-osteoconduction is introduced to account the electrically induced cell colonization. Since numerical results compare favorably with experimental evidence, the model is suitable to be extended to other types of cells, and to numerically explore the influence of EF during wound healing. Copyright © 2012 Elsevier B.V. All rights reserved.
Mathematical Modelling of Silica Scaling Deposition in Geothermal Wells
Nizami, M.; Sutopo
2016-09-01
Silica scaling is widely encountered in geothermal wells in which produce two-phase geothermal fluid. Silica scaling could be formed due to chemical reacting by mixing a geothermal fluid with other geothermal fluid in different compositions, or also can be caused by changes in fluid properties due to changes pressure and temperature. One of method to overcome silica scaling which is occurred around geothermal well is by workover operation. Modelling of silica deposition in porous medium has been modeled in previously. However, the growth of silica scaling deposition in geothermal wells has never been modeled. Modelling of silica deposition through geothermal is important aspects to determine depth of silica scaling growth and best placing for workover device to clean silica scaling. This study is attempted to develop mathematical models for predicting silica scaling through geothermal wells. The mathematical model is developed by integrating the solubility-temperature correlation and two-phase pressure drop coupled wellbore fluid temperature correlation in a production well. The coupled model of two-phase pressure drop and wellbore fluid temperature correlation which is used in this paper is Hasan-Kabir correlation. This modelling is divided into two categories: single and two phase fluid model. Modelling of silica deposition is constrained in temperature distribution effect through geothermal wells by solubility correlation for silica. The results of this study are visualizing the growth of silica scaling thickness through geothermal wells in each segment of depth. Sensitivity analysis is applied in several parameters, such as: bottom-hole pressure, temperature, and silica concentrations. Temperature is most impact factor for silica scaling through geothermal wellbore and depth of flash point. In flash point, silica scaling thickness has reached maximum because reducing of mole in liquid portion.
A mathematical model of traffic noise at a signalized intersection
Directory of Open Access Journals (Sweden)
Sorawit Narupiti
2005-05-01
Full Text Available This research aims at modeling interrupted flow traffic noise at a signalized intersection. The models are mathematically derived by applying the inverse square law of sound pressure incorporating with theories of traffic flow at an intersection. The traffic flow theories utilized for developing the model consist of characteristics of individual vehicle motion at intersection, shock wave model, and queuing analysis. The modelformulation is divided into two different approaches and takes into account of all regimes of vehicle movement while traversing an intersection (i.e. idling, decelerating, accelerating, and cruising conditions. The first approach assumes a constant acceleration/deceleration rate for each type of vehicle. Another appliesinconstant acceleration/deceleration which comes from speed-distance relationship. The final models are expressed in LAeq (1 hr.Eventually, the developed models are validated by collecting equivalent continuous noise level in 1 min as well as traffic parameters (i.e. red time, number of vehicle in the queue, queue length, time of queue dissipation, and final cruise speed from fifteen vehicle platoons. The noise levels predicted from the developed models are compared with the measured ones. The results show that the inconstant acceleration model gives the predicted levels closer to the measured ones than constant acceleration model. The error of inconstant acceleration model ranges from 0.1-3.9 dB(A with the average value of 2 dB(A overestimated and that of constant acceleration model ranges from 1.8-6.5 dB(A with the average value of 3 dB(A underestimated. It might be concluded that movement characteristic of vehicle is an important factor that apparently affects the accuracy of traffic noise prediction at an intersection.
MATHEMATICAL MODELING OF ORANGE SEED DRYING KINETICS
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Daniele Penteado Rosa
2015-06-01
Full Text Available Drying of orange seeds representing waste products from juice processing was studied in the temperatures of 40, 50, 60 and 70 °C and drying velocities of 0.6, 1.0 and 1.4 m/s. Experimental drying kinetics of orange seeds were obtained using a convective air forced dryer. Three thin-layer models: Page model, Lewis model, and the Henderson-Pabis model and the diffusive model were used to predict the drying curves. The Henderson-Pabis and the diffusive models show the best fitting performance and statistical evaluations. Moreover, the temperature dependence on the effective diffusivity followed an Arrhenius relationship, and the activation energies ranging from 16.174 to 16.842 kJ/mol
A spatially-averaged mathematical model of kidney branching morphogenesis
Zubkov, V.S.
2015-08-01
© 2015 Published by Elsevier Ltd. Kidney development is initiated by the outgrowth of an epithelial ureteric bud into a population of mesenchymal cells. Reciprocal morphogenetic responses between these two populations generate a highly branched epithelial ureteric tree with the mesenchyme differentiating into nephrons, the functional units of the kidney. While we understand some of the mechanisms involved, current knowledge fails to explain the variability of organ sizes and nephron endowment in mice and humans. Here we present a spatially-averaged mathematical model of kidney morphogenesis in which the growth of the two key populations is described by a system of time-dependant ordinary differential equations. We assume that branching is symmetric and is invoked when the number of epithelial cells per tip reaches a threshold value. This process continues until the number of mesenchymal cells falls below a critical value that triggers cessation of branching. The mathematical model and its predictions are validated against experimentally quantified C57Bl6 mouse embryonic kidneys. Numerical simulations are performed to determine how the final number of branches changes as key system parameters are varied (such as the growth rate of tip cells, mesenchyme cells, or component cell population exit rate). Our results predict that the developing kidney responds differently to loss of cap and tip cells. They also indicate that the final number of kidney branches is less sensitive to changes in the growth rate of the ureteric tip cells than to changes in the growth rate of the mesenchymal cells. By inference, increasing the growth rate of mesenchymal cells should maximise branch number. Our model also provides a framework for predicting the branching outcome when ureteric tip or mesenchyme cells change behaviour in response to different genetic or environmental developmental stresses.
A mathematical model to detect inspiratory flow limitation during sleep.
Mansour, Khaled F; Rowley, James A; Meshenish, A A; Shkoukani, Mahdi A; Badr, M Safwan
2002-09-01
The physiological significance of inspiratory flow limitation (IFL) has recently been recognized, but methods of detecting IFL can be subjective. We sought to develop a mathematical model of the upper airway pressure-flow relationship that would objectively detect flow limitation. We present a theoretical discussion that predicts that a polynomial function [F(P) = AP(3) + BP(2) + CP + D, where F(P) is flow and P is supraglottic pressure] best characterizes the pressure-flow relationship and allows for the objective detection of IFL. In protocol 1, step 1, we performed curve-fitting of the pressure-flow relationship of 20 breaths to 5 mathematical functions and found that highest correlation coefficients (R(2)) for quadratic (0.88 +/- 0.10) and polynomial (0.91 +/- 0.05; P polynomial functions and found that the error fit was lowest for the polynomial function (3.3 +/- 0.06 vs. 21.1 +/- 19.0%; P 99% for each). We conclude that a polynomial function can be used to predict the relationship between pressure and flow in the upper airway and objectively determine the presence of IFL.
Mathematical Modelling Research in Turkey: A Content Analysis Study
Çelik, H. Coskun
2017-01-01
The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…
Modelling Mathematical Reasoning in Physics Education
Uhden, Olaf; Karam, Ricardo; Pietrocola, Mauricio; Pospiech, Gesche
2012-01-01
Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a…
Mathematics Teacher TPACK Standards and Development Model
Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis
2009-01-01
What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…
Geary, David C; vanMarle, Kristy
2016-12-01
At the beginning of preschool (M = 46 months of age), 197 (94 boys) children were administered tasks that assessed a suite of nonsymbolic and symbolic quantitative competencies as well as their executive functions, verbal and nonverbal intelligence, preliteracy skills, and their parents' education level. The children's mathematics achievement was assessed at the end of preschool (M = 64 months). We used a series of Bayesian and standard regression analyses to winnow this broad set of competencies down to the core subset of quantitative skills that predict later mathematics achievement, controlling other factors. This knowledge included children's fluency in reciting the counting string, their understanding of the cardinal value of number words, and recognition of Arabic numerals, as well as their sensitivity to the relative quantity of 2 collections of objects. The results inform theoretical models of the foundations of children's early quantitative development and have practical implications for the design of early interventions for children at risk for poor long-term mathematics achievement. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Predicting a DNA-binding protein using random forest with multiple mathematical features.
Guan, Changge; Niu, Xiaohui; Shi, Feng; Yang, Kun; Li, Nana
2015-01-01
DNA-binding proteins are involved and play a crucial role in a lot of important biological processes. Hence, the identification of the DNA-binding proteins is a challenging and significant problem. In order to reveal the intrinsic information correlated to DNA-binding, nine classes of candidate features based on different mathematical fields are applied to construct the prediction model with random forest. They are fractal dimension, conjoint triad feature, Hilbert-Huang Transformation, amino acid composition, dipeptide composition, chaos game representation, and the corresponding information entropies. These mathematical expressions are evaluated with 5-fold cross validation test. The results of numerical simulations show that the mathematical features consisted of amino acid composition, fractal dimension and information entropies of amino acid and chaos game representation achieve the best performance. Its accuracy is 0.8157, and Matthew's correlation coefficient (MCC) achieves 0.5968 on the benchmark dataset from DNA-Prot. By analyzing the components of top combination of the nine candidate features, the concepts of fractal dimension and information entropy are the effective and vital features, which can provide complementary sequence-order information on the basis of amino acid composition.
Mathematical Modeling of Bacteria Communication in Continuous Cultures
Directory of Open Access Journals (Sweden)
Maria Vittoria Barbarossa
2016-05-01
Full Text Available Quorum sensing is a bacterial cell-to-cell communication mechanism and is based on gene regulatory networks, which control and regulate the production of signaling molecules in the environment. In the past years, mathematical modeling of quorum sensing has provided an understanding of key components of such networks, including several feedback loops involved. This paper presents a simple system of delay differential equations (DDEs for quorum sensing of Pseudomonas putida with one positive feedback plus one (delayed negative feedback mechanism. Results are shown concerning fundamental properties of solutions, such as existence, uniqueness, and non-negativity; the last feature is crucial for mathematical models in biology and is often violated when working with DDEs. The qualitative behavior of solutions is investigated, especially the stationary states and their stability. It is shown that for a certain choice of parameter values, the system presents stability switches with respect to the delay. On the other hand, when the delay is set to zero, a Hopf bifurcation might occur with respect to one of the negative feedback parameters. Model parameters are fitted to experimental data, indicating that the delay system is sufficient to explain and predict the biological observations.
Neuro-fuzzy modeling in bankruptcy prediction
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Vlachos D.
2003-01-01
Full Text Available For the past 30 years the problem of bankruptcy prediction had been thoroughly studied. From the paper of Altman in 1968 to the recent papers in the '90s, the progress of prediction accuracy was not satisfactory. This paper investigates an alternative modeling of the system (firm, combining neural networks and fuzzy controllers, i.e. using neuro-fuzzy models. Classical modeling is based on mathematical models that describe the behavior of the firm under consideration. The main idea of fuzzy control, on the other hand, is to build a model of a human control expert who is capable of controlling the process without thinking in a mathematical model. This control expert specifies his control action in the form of linguistic rules. These control rules are translated into the framework of fuzzy set theory providing a calculus, which can stimulate the behavior of the control expert and enhance its performance. The accuracy of the model is studied using datasets from previous research papers.
A mathematical model of embodied consciousness.
Rudrauf, David; Bennequin, Daniel; Granic, Isabela; Landini, Gregory; Friston, Karl; Williford, Kenneth
2017-09-07
We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM combines multisensory evidence with prior beliefs in memory and frames them by selecting points of view and perspectives according to preferences. The choice of projective frames governs how expectations are transformed by consciousness. Violations of expectation are encoded as free energy. Free energy minimization drives perspective taking, and controls the switch between perception, imagination and action. In the PCM, consciousness functions as an algorithm for the maximization of resilience, using projective perspective taking and imagination in order to escape local minima of free energy. The PCM can account for a variety of psychological phenomena: the characteristic spatial phenomenology of subjective experience, the distinctions and integral relationships between perception, imagination and action, the role of affective processes in intentionality, but also perceptual phenomena such as the dynamics of bistable figures and body swap illusions in virtual reality. It relates phenomenology to function, showing the computational advantages of consciousness. It suggests that changes of brain states from unconscious to conscious reflect the action of projective transformations and suggests specific neurophenomenological hypotheses about the brain, guidelines for designing artificial systems, and formal principles for psychology. Copyright © 2017 Elsevier Ltd. All rights reserved.
Simple mathematical models of gene regulatory dynamics
Mackey, Michael C; Tyran-Kamińska, Marta; Zeron, Eduardo S
2016-01-01
This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch. The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduat...
A mathematical model of forgetting and amnesia
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Jaap M. J. Murre
2013-02-01
Full Text Available We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time-scales share two fundamental properties: (1 representations in a store decline in strength (2 while trying to induce new representations in higher-level more permanent stores. This paper addresses several types of experimental and clinical phenomena: (i the temporal gradient of retrograde amnesia (Ribot's Law, (ii forgetting curves with and without anterograde amnesia, and (iii learning and forgetting curves with impaired cortical plasticity. Results are in the form of closed-form expressions that are applied to studies with mice, rats, and monkeys. In order to analyze human data in a quantitative manner, we also derive a relative measure of retrograde amnesia that removes the effects of non-equal item difficulty for different time periods commonly found with clinical retrograde amnesia tests. Using these analytical tools, we review studies of temporal gradients in the memory of patients with Korsakoff's Disease, Alzheimer's Dementia, Huntington's Disease, and other disorders.
Mathematical model I. Electron and quantum mechanics
Gadre, Nitin Ramchandra
2011-03-01
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Mathematical model I. Electron and quantum mechanics
Directory of Open Access Journals (Sweden)
Nitin Ramchandra Gadre
2011-03-01
Full Text Available The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is ‘difficult’ to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Mathematical modeling of Chikungunya fever control
Hincapié-Palacio, Doracelly; Ospina, Juan
2015-05-01
Chikungunya fever is a global concern due to the occurrence of large outbreaks, the presence of persistent arthropathy and its rapid expansion throughout various continents. Globalization and climate change have contributed to the expansion of the geographical areas where mosquitoes Aedes aegypti and Aedes albopictus (Stegomyia) remain. It is necessary to improve the techniques of vector control in the presence of large outbreaks in The American Region. We derive measures of disease control, using a mathematical model of mosquito-human interaction, by means of three scenarios: a) a single vector b) two vectors, c) two vectors and human and non-human reservoirs. The basic reproductive number and critical control measures were deduced by using computer algebra with Maple (Maplesoft Inc, Ontario Canada). Control measures were simulated with parameter values obtained from published data. According to the number of households in high risk areas, the goals of effective vector control to reduce the likelihood of mosquito-human transmission would be established. Besides the two vectors, if presence of other non-human reservoirs were reported, the monthly target of effective elimination of the vector would be approximately double compared to the presence of a single vector. The model shows the need to periodically evaluate the effectiveness of vector control measures.
Mathematical and Computational Modeling of Polymer Exchange Membrane Fuel Cells
Ulusoy, Sehribani
In this thesis a comprehensive review of fuel cell modeling has been given and based on the review, a general mathematical fuel cell model has been developed in order to understand the physical phenomena governing the fuel cell behavior and in order to contribute to the efforts investigating the optimum performance at different operating conditions as well as with different physical parameters. The steady state, isothermal model presented here accounts for the combined effects of mass and species transfer, momentum conservation, electrical current distribution through the gas channels, the electrodes and the membrane, and the electrochemical kinetics of the reactions in the anode and cathode catalyst layers. One of the important features of the model is that it proposes a simpler modified pseudo-homogeneous/agglomerate catalyst layer model which takes the advantage of the simplicity of pseudo-homogenous modeling while taking into account the effects of the agglomerates in the catalyst layer by using experimental geometric parameters published. The computation of the general mathematical model can be accomplished in 3D, 2D and 1D with the proper assumptions. Mainly, there are two computational domains considered in this thesis. The first modeling domain is a 2D Membrane Electrode Assembly (MEA) model including the modified agglomerate/pseudo-homogeneous catalyst layer modeling with consistent treatment of water transport in the MEA while the second domain presents a 3D model with different flow filed designs: straight, stepped and tapered. COMSOL Multiphysics along with Batteries and Fuel Cell Module have been used for 2D & 3D model computations while ANSYS FLUENT PEMFC Module has been used for only 3D two-phase computation. Both models have been validated with experimental data. With 2D MEA model, the effects of temperature and water content of the membrane as well as the equivalent weight of the membrane on the performance have been addressed. 3D COMSOL simulation
Mathematical Modelling and Parameter Optimization of Pulsating Heat Pipes
Yang, Xin-She; Luan, Tao; Koziel, Slawomir
2014-01-01
Proper heat transfer management is important to key electronic components in microelectronic applications. Pulsating heat pipes (PHP) can be an efficient solution to such heat transfer problems. However, mathematical modelling of a PHP system is still very challenging, due to the complexity and multiphysics nature of the system. In this work, we present a simplified, two-phase heat transfer model, and our analysis shows that it can make good predictions about startup characteristics. Furthermore, by considering parameter estimation as a nonlinear constrained optimization problem, we have used the firefly algorithm to find parameter estimates efficiently. We have also demonstrated that it is possible to obtain good estimates of key parameters using very limited experimental data.
Mathematical modeling of a primary zinc/air battery
Mao, Z.; White, R. E.
1992-01-01
The mathematical model developed by Sunu and Bennion has been extended to include the separator, precipitation of both solid ZnO and K2Zn(OH)4, and the air electrode, and has been used to investigate the behavior of a primary Zn-Air battery with respect to battery design features. Predictions obtained from the model indicate that anode material utilization is predominantly limited by depletion of the concentration of hydroxide ions. The effect of electrode thickness on anode material utilization is insignificant, whereas material loading per unit volume has a great effect on anode material utilization; a higher loading lowers both the anode material utilization and delivered capacity. Use of a thick separator will increase the anode material utilization, but may reduce the cell voltage.
Synthesising 30 years of mathematical modelling of Echinococcus transmission.
Directory of Open Access Journals (Sweden)
Jo-An M Atkinson
Full Text Available BACKGROUND: Echinococcosis is a complex zoonosis that has domestic and sylvatic lifecycles, and a range of different intermediate and definitive host species. The complexities of its transmission and the sparse evidence on the effectiveness of control strategies in diverse settings provide significant challenges for the design of effective public health policy against this disease. Mathematical modelling is a useful tool for simulating control packages under locally specific transmission conditions to inform optimal timing and frequency of phased interventions for cost-effective control of echinococcosis. The aims of this review of 30 years of Echinococcus modelling were to discern the epidemiological mechanisms underpinning models of Echinococcus granulosus and E. multilocularis transmission and to establish the need to include a human transmission component in such models. METHODOLOGY/PRINCIPAL FINDINGS: A search was conducted of all relevant articles published up until July 2012, identified from the PubMED, Web of Knowledge and Medline databases and review of bibliographies of selected papers. Papers eligible for inclusion were those describing the design of a new model, or modification of an existing mathematical model of E. granulosus or E. multilocularis transmission. A total of 13 eligible papers were identified, five of which described mathematical models of E. granulosus and eight that described E. multilocularis transmission. These models varied primarily on the basis of six key mechanisms that all have the capacity to modulate model dynamics, qualitatively affecting projections. These are: 1 the inclusion of a 'latent' class and/or time delay from host exposure to infectiousness; 2 an age structure for animal hosts; 3 the presence of density-dependent constraints; 4 accounting for seasonality; 5 stochastic parameters; and 6 inclusion of spatial and risk structures. CONCLUSIONS/SIGNIFICANCE: This review discusses the conditions under
Mathematical modeling of biomass fuels formation process.
Gaska, Krzysztof; Wandrasz, Andrzej J
2008-01-01
The increasing demand for thermal and electric energy in many branches of industry and municipal management accounts for a drastic diminishing of natural resources (fossil fuels). Meanwhile, in numerous technical processes, a huge mass of wastes is produced. A segregated and converted combustible fraction of the wastes, with relatively high calorific value, may be used as a component of formed fuels. The utilization of the formed fuel components from segregated groups of waste in associated processes of co-combustion with conventional fuels causes significant savings resulting from partial replacement of fossil fuels, and reduction of environmental pollution resulting directly from the limitation of waste migration to the environment (soil, atmospheric air, surface and underground water). The realization of technological processes with the utilization of formed fuel in associated thermal systems should be qualified by technical criteria, which means that elementary processes as well as factors of sustainable development, from a global viewpoint, must not be disturbed. The utilization of post-process waste should be preceded by detailed technical, ecological and economic analyses. In order to optimize the mixing process of fuel components, a mathematical model of the forming process was created. The model is defined as a group of data structures which uniquely identify a real process and conversion of this data in algorithms based on a problem of linear programming. The paper also presents the optimization of parameters in the process of forming fuels using a modified simplex algorithm with a polynomial worktime. This model is a datum-point in the numerical modeling of real processes, allowing a precise determination of the optimal elementary composition of formed fuels components, with assumed constraints and decision variables of the task.
MATHEMATICAL MODELING OF AC ELECTRIC POINT MOTOR
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S. YU. Buryak
2014-03-01
Full Text Available Purpose. In order to ensure reliability, security, and the most important the continuity of the transportation process, it is necessary to develop, implement, and then improve the automated methods of diagnostic mechanisms, devices and rail transport systems. Only systems that operate in real time mode and transmit data on the instantaneous state of the control objects can timely detect any faults and thus provide additional time for their correction by railway employees. Turnouts are one of the most important and responsible components, and therefore require the development and implementation of such diagnostics system.Methodology. Achieving the goal of monitoring and control of railway automation objects in real time is possible only with the use of an automated process of the objects state diagnosing. For this we need to know the diagnostic features of a control object, which determine its state at any given time. The most rational way of remote diagnostics is the shape and current spectrum analysis that flows in the power circuits of railway automatics. Turnouts include electric motors, which are powered by electric circuits, and the shape of the current curve depends on both the condition of the electric motor, and the conditions of the turnout maintenance. Findings. For the research and analysis of AC electric point motor it was developed its mathematical model. The calculation of parameters and interdependencies between the main factors affecting the operation of the asynchronous machine was conducted. The results of the model operation in the form of time dependences of the waveform curves of current on the load on engine shaft were obtained. Originality. During simulation the model of AC electric point motor, which satisfies the conditions of adequacy was built. Practical value. On the basis of the constructed model we can study the AC motor in various mode of operation, record and analyze current curve, as a response to various changes
Verification of temporal-causal network models by mathematical analysis
Directory of Open Access Journals (Sweden)
Jan Treur
2016-04-01
Full Text Available Abstract Usually dynamic properties of models can be analysed by conducting simulation experiments. But sometimes, as a kind of prediction properties can also be found by calculations in a mathematical manner, without performing simulations. Examples of properties that can be explored in such a manner are: whether some values for the variables exist for which no change occurs (stationary points or equilibria, and how such values may depend on the values of the parameters of the model and/or the initial values for the variables whether certain variables in the model converge to some limit value (equilibria and how this may depend on the values of the parameters of the model and/or the initial values for the variables whether or not certain variables will show monotonically increasing or decreasing values over time (monotonicity how fast a convergence to a limit value takes place (convergence speed whether situations occur in which no convergence takes place but in the end a specific sequence of values is repeated all the time (limit cycle Such properties found in an analytic mathematical manner can be used for verification of the model by checking them for the values observed in simulation experiments. If one of these properties is not fulfilled, then there will be some error in the implementation of the model. In this paper some methods to analyse such properties of dynamical models will be described and illustrated for the Hebbian learning model, and for dynamic connection strengths in social networks. The properties analysed by the methods discussed cover equilibria, increasing or decreasing trends, recurring patterns (limit cycles, and speed of convergence to equilibria.
Mathematics of epidemics on networks from exact to approximate models
Kiss, István Z; Simon, Péter L
2017-01-01
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...
Garcia-Santillan, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe
2016-01-01
Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of technology modified the educational process, thus generating a meaningful impact as presented by studies carried out by Galbraith and Haines (2000). They d...
Mathematical modeling suggests that periodontitis behaves as a non-linear chaotic dynamical process
Papantonopoulos, G.H.; Takahashi, K.; Bountis, T.; Loos, B.G.
2013-01-01
Background: This study aims to expand on a previously presented cellular automata model and further explore the non-linear dynamics of periodontitis. Additionally the authors investigated whether their mathematical model could predict the two known types of periodontitis, aggressive (AgP) and
Mathematical modeling suggests that periodontitis behaves as a non-linear chaotic dynamical process
Papantonopoulos, G.H.; Takahashi, K.; Bountis, T.; Loos, B.G.
2013-01-01
Background: This study aims to expand on a previously presented cellular automata model and further explore the non-linear dynamics of periodontitis. Additionally the authors investigated whether their mathematical model could predict the two known types of periodontitis, aggressive (AgP) and chroni
Selection of fire spread model for Russian fire behavior prediction system
Alexandra V. Volokitina; Kevin C. Ryan; Tatiana M. Sofronova; Mark A. Sofronov
2010-01-01
Mathematical modeling of fire behavior prediction is only possible if the models are supplied with an information database that provides spatially explicit input parameters for modeled area. Mathematical models can be of three kinds: 1) physical; 2) empirical; and 3) quasi-empirical (Sullivan, 2009). Physical models (Grishin, 1992) are of academic interest only because...
System and mathematical modeling of quadrotor dynamics
Goodman, Jacob M.; Kim, Jinho; Gadsden, S. Andrew; Wilkerson, Stephen A.
2015-05-01
Unmanned aerial systems (UAS) are becoming increasingly visible in our daily lives; and range in operation from search and rescue, monitoring hazardous environments, and to the delivery of goods. One of the most popular UAS are based on a quad-rotor design. These are typically small devices that rely on four propellers for lift and movement. Quad-rotors are inherently unstable, and rely on advanced control methodologies to keep them operating safely and behaving in a predictable and desirable manner. The control of these devices can be enhanced and improved by making use of an accurate dynamic model. In this paper, we examine a simple quadrotor model, and note some of the additional dynamic considerations that were left out. We then compare simulation results of the simple model with that of another comprehensive model.
Mathematical modeling of laser based potato cutting and peeling.
Ferraz, A Carlos O; Mittal, Gauri S; Bilanski, Walter K; Abdullah, Hussein A
2007-01-01
A mathematical model is developed and validated to predict the depth of cut in potato tuber slabs as a function of laser power and travel speed. The model considers laser processing parameters such as input power, spot size and exposure time as well as the properties of the material being cut such as specific heat, thermal conductivity, surface reflectance, etc. The model also considers the phase change of water in potato and the ignition temperature of the solid portion. The composition of the potato tuber is assumed to be of water and solid. The model also assumes that the ablation process is accomplished through ejection of liquid water, debris and water vapour, and combustion of solid. A CO(2) laser operating in c.w. mode was chosen for the experimental work because water absorbs laser energy highly at 10.6 microm, and CO(2) laser units with relatively high output power are available. Slabs of potato tuber were chosen to be laser processed since potato contains high moisture and large amounts of relatively homogeneous tissue. The results of the preliminary calculations and experiments concluded that the model is able to predict the depth of cut in potato tuber parenchyma when subjected to a CO(2) laser beam.
Modelling Of Flotation Processes By Classical Mathematical Methods - A Review
Jovanović, Ivana; Miljanović, Igor
2015-12-01
Flotation process modelling is not a simple task, mostly because of the process complexity, i.e. the presence of a large number of variables that (to a lesser or a greater extent) affect the final outcome of the mineral particles separation based on the differences in their surface properties. The attempts toward the development of the quantitative predictive model that would fully describe the operation of an industrial flotation plant started in the middle of past century and it lasts to this day. This paper gives a review of published research activities directed toward the development of flotation models based on the classical mathematical rules. The description and systematization of classical flotation models were performed according to the available references, with emphasize exclusively given to the flotation process modelling, regardless of the model application in a certain control system. In accordance with the contemporary considerations, models were classified as the empirical, probabilistic, kinetic and population balance types. Each model type is presented through the aspects of flotation modelling at the macro and micro process levels.
Mathematical model of radon activity measurements
Energy Technology Data Exchange (ETDEWEB)
Paschuk, Sergei A.; Correa, Janine N.; Kappke, Jaqueline; Zambianchi, Pedro, E-mail: sergei@utfpr.edu.br, E-mail: janine_nicolosi@hotmail.com [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil); Denyak, Valeriy, E-mail: denyak@gmail.com [Instituto de Pesquisa Pele Pequeno Principe, Curitiba, PR (Brazil)
2015-07-01
Present work describes a mathematical model that quantifies the time dependent amount of {sup 222}Rn and {sup 220}Rn altogether and their activities within an ionization chamber as, for example, AlphaGUARD, which is used to measure activity concentration of Rn in soil gas. The differential equations take into account tree main processes, namely: the injection of Rn into the cavity of detector by the air pump including the effect of the traveling time Rn takes to reach the chamber; Rn release by the air exiting the chamber; and radioactive decay of Rn within the chamber. Developed code quantifies the activity of {sup 222}Rn and {sup 220}Rn isotopes separately. Following the standard methodology to measure Rn activity in soil gas, the air pump usually is turned off over a period of time in order to avoid the influx of Rn into the chamber. Since {sup 220}Rn has a short half-life time, approximately 56s, the model shows that after 7 minutes the activity concentration of this isotope is null. Consequently, the measured activity refers to {sup 222}Rn, only. Furthermore, the model also addresses the activity of {sup 220}Rn and {sup 222}Rn progeny, which being metals represent potential risk of ionization chamber contamination that could increase the background of further measurements. Some preliminary comparison of experimental data and theoretical calculations is presented. Obtained transient and steady-state solutions could be used for planning of Rn in soil gas measurements as well as for accuracy assessment of obtained results together with efficiency evaluation of chosen measurements procedure. (author)
Advanced Mathematical Model to Describe the Production of Biodiesel Process
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Ahmmed S. Ibrehem
2009-12-01
Full Text Available Advanced mathematical model was used to capture the batch reactor characteristics of reacting compounds. The model was applied to batch reactor for the production of bio-diesel from palm and kapok oils. Results of the model were compared with experimental data in terms of conversion of transesterification reaction for the production of bio-diesel under unsteady state. A good agreement was obtained between our model predictions and the experimental data. Both experimental and modeling results showed that the conversion of triglycerides to methyl ester was affected by the process conditions. The transesterification process with temperature of about 70 oC, and methanol ratio to the triglyceride of about 5 times its stoichiometry, and the NAOH catalyst of wt 0.4%, appear to be acceptable process conditions for bio diesel process production from palm oil and kapok oil. The model can be applied for endothermic batch process. © 2009 BCREC UNDIP. All rights reserved[Received: 12 August 2009, Revised: 15 October 2009; Accepted: 18 October 2009][How to Cite: A.S. Ibrehem, H. S. Al-Salim. (2009. Advanced Mathematical Model to Describe the Production of Biodiesel Process. Bulletin of Chemical Reaction Engineering and Catalysis, 4(2: 37-42. doi:10.9767/bcrec.4.2.7109.37-42][How to Link/DOI: http://dx.doi.org/10.9767/bcrec.4.2.7109.37-42 || or local: http://ejournal.undip.ac.id/index.php/bcrec/article/view/7109 ]
Symmetrization of mathematical model of charge transport in semiconductors
Directory of Open Access Journals (Sweden)
Alexander M. Blokhin
2002-11-01
Full Text Available A mathematical model of charge transport in semiconductors is considered. The model is a quasilinear system of differential equations. A problem of finding an additional entropy conservation law and system symmetrization are solved.
A basic mathematical and numerical model for gas injection
Molenaar, J.
1996-01-01
In this paper we discuss a mathematical model for gas storage processes. In addition we outline an approach for numerical simulations. The focus is on model assumptions and limitations with respect to the software to be developed.
A basic mathematical and numerical model for gas injection
J. Molenaar (Gijs)
1996-01-01
textabstractIn this paper we discuss a mathematical model for gas storage processes. In addition we outline an approach for numerical simulations. The focus is on model assumptions and limitations with respect to the software to be developed.
A mathematical model of bipolar radiofrequency-induced thermofusion.
Wagenpfeil, J; Nold, B; Fischer, K; Neugebauer, A; Rothmund, R; Krämer, B; Brucker, S; Mischinger, J; Schwentner, C; Schenk, M; Wallwiener, D; Stenzl, A; Enderle, M; Sawodny, O; Ederer, M
2014-01-01
Bipolar radiofrequency-induced thermofusion has become a widely accepted method successfully used in open and particularly in minimally-invasive surgery for the sealing of blood vessels and tissue of up to several millimeters diameter. Despite its wide-spread application, the thermofusion process itself is not well understood on a quantitative and dynamic level, and manufacturers largely rely on trial-and-error methods to improve existing instruments. To predict the effect of alternative generator control strategies and to allow for a more systematic approach to improve thermofusion instruments, a mathematical model of the thermofusion process is developed. The system equations describe the spatial and temporal evolution of the tissue temperature due to Joule heating and heat transfer, and the loss of tissue water due to vaporization. The resulting effects on the tissue properties, most importantly the electrical resistivity, heat capacity and thermal conductivity, are considered as well. Experimental results indicate that the extent of the lateral thermal damage is directly affected by Joule heating of the lateral tissue. The experimental findings are supported by simulation results using the proposed mathematical model of thermofusion.
MATHEMATICAL MODEL SUGGESTED FOR THE STUDY OF THE KNEE MECHANICS
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Marius GRĂMADĂ
2012-07-01
Full Text Available Knowing the operated the knee biomechanical behavior is important during the life of the endoprosthesis,lifestyle changes and medical rehabilitation. One of the main causes of failure of a primary total prosthetic knee joint isthe instability. From the moment of its implantation, the endoprosthesis is subjected to external forces, which tend todestabilize it, while the muscles and pericapsulare ligaments oppose it. Theoretically there is a relationship between theexternal disturbing force, respectively ligament tension and the knee frontal plane deviation. The purpose of this paperis to test several mathematical models describing the biomechanical behavior of knee ligaments in relation todeviation. On a group of 39 patients we measured the torque of the joint capsule in relation to the deviation using apressure sensor tensor and a torque screwdriver, and we analyzed these data using a statistical program. We havedemonstrated the existence of this relationship as a function of degree 2 and we made predictions based on itcalculating ligament torque and ligament stiffness at 0 and 5 degrees of deviation. The conclusion of this study showsthat there is a strong relationship between ligament torque and deviation knee, which can be described mathematically.This model can be used to study the knee operated and improve the prosthetic devices.
A mathematical model of the Mafia game
Migdal, Piotr
2010-01-01
Mafia (also called Werewolf) is a party game. The participants are divided into two competing groups: citizens and a mafia. The objective is to eliminate the opponent group. The game consists of two consecutive phases (day and night) and a certain set of actions (e.g. lynching during day). The mafia members have additional powers (knowing each other, killing during night) whereas the citizens are more numerous. We propose a simple mathematical model of the game, which is essentially a pure death process with discrete time. We find closed-form formulas for mafia winning chances $w(n,m)$ as well as for evolution of the game. Moreover, we investigate discrete properties of results, as well as its continuous-time approximation. I turns out that a relatively small number of the mafia members $m$ (among $n$ players) give $50:50$ winning chances, i.e. $m\\approx\\sqrt{n}$. Furthermore, the game strongly depends on the parity of the total number of players.
A MATHEMATICAL MODELING OF CAMPUS INFORMATION SYSTEM
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S. STALIN KUMAR
2016-07-01
Full Text Available An H-magic labeling in a H-decomposable graph G is a bijection f : V (G ∪ E(G → {1, 2, ..., p + q} such that for every copy H in the decomposition, \\sum\\limits_{v∈V (H}{f(v}+\\sum\\limits_{e∈E(H}{ f(e} is constant. f is said to be H-V -super magic if f(V (G = {1, 2, ..., p}. Suppose that V (G = U(G ∪ W(G with |U(G| = m and |W(G| = n. Then f is said to be H-V -super-strong magic labeling if f(U(G = {1, 2, ..., m} and f(W(G = {m + 1, m + 2, ...,(m + n = p}. A graph that admits a H-V -super-strong magic labeling is called a H-V -super-strong magic decomposable graph. In this paper, we pay our attention to provide a mathematical modeling of campus information system.
Mathematical modelling for nanotube bundle oscillators
Thamwattana, Ngamta; Cox, Barry J.; Hill, James M.
2009-07-01
This paper investigates the mechanics of a gigahertz oscillator comprising a nanotube oscillating within the centre of a uniform concentric ring or bundle of nanotubes. The study is also extended to the oscillation of a fullerene inside a nanotube bundle. In particular, certain fullerene-nanotube bundle oscillators are studied, namely C60-carbon nanotube bundle, C60-boron nitride nanotube bundle, B36N36-carbon nanotube bundle and B36N36-boron nitride nanotube bundle. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the fullerene and the nanotube bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques which provides considerable insight into the underlying mechanisms. The paper presents a synopsis of the major results derived in detail by the present authors in [1, 2].
Directory of Open Access Journals (Sweden)
Universidade Estadual do Oeste do Paraná
2012-12-01
Full Text Available This paper presents an analysis of scientific communications published in the IV Mathematical Modeling National Conference (CNMEM in the Brazilian abbreviation, which took place in 2005. The analysis consists of a meta-analytical and content qualitative approach, aided by the software Atlas T.i. The data collected was originated in the above mentioned conference which is the first of the three which will be analyzed in the study that aims to unveil the research on Mathematical Modeling in Brazil. The categories established in this paper and which will be interpreted are: a Meta-study on Mathematics Modeling; b Modeling application; c Articulation between Modeling and other theories, and d Modeling and teachers education.
Economic mathematical methods and forecasting models
K. Karpovska-Skoryk
2000-01-01
In the article the questions of the expert system, based on the fuzzy mathematics, are discussed. It is pointed out that usage of such a system for medical insurance in the conditions of the Ukrainian economy is very convenient.
Quantum Gravity Mathematical Models and Experimental Bounds
Fauser, Bertfried; Zeidler, Eberhard
2007-01-01
The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on ...
Methods and models in mathematical biology deterministic and stochastic approaches
Müller, Johannes
2015-01-01
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
Retrospective Study on Mathematical Modeling Based on Computer Graphic Processing
Zhang, Kai Li
Graphics & image making is an important field in computer application, in which visualization software has been widely used with the characteristics of convenience and quick. However, it was thought by modeling designers that the software had been limited in it's function and flexibility because mathematics modeling platform was not built. A non-visualization graphics software appearing at this moment enabled the graphics & image design has a very good mathematics modeling platform. In the paper, a polished pyramid is established by multivariate spline function algorithm, and validate the non-visualization software is good in mathematical modeling.
Development of mathematic model for coffee decaffeination with leaching method
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Sukrisno Widyotomo
2011-08-01
Full Text Available A simple mathematic model for caffeine kinetic description during the extraction process (leaching of coffee bean was developed. A nonsteady diffusion equation coupled with a macroscopic mass transfer equation for solvent was developed and them solved analytically. The kinetic of caffeine extraction from coffee bean is depend on initial caffeine content, final caffeine content, caffeine content at certain time, masstransfer coefficient, solvent volume, surface area of coffee beans, process time, radius of coffee bean, leaching rate of caffeine, caffeine diffusivity and a are constan, solvent concentration, activation energy, temperature absolute and gas constant. Caffeine internal mass diffusivity was estimated by fitting the model to an experiment using acetic acid and liquid waste of cocoa beans fermentation. The prediction equation for leaching rate of caffeine in coffee beans has been found. It was found that Dk (m2/sec=1.345x107—4.1638x107, and kL (m/sec=2.445x105—5.551x105 by acetic acid as solvent depended on temperature and solvent concentration. The prediction equation for length of time to reduce initial caffeine content to certain concentration in coffee beans has been developed, Caffeine diffusivity (Dk and masstransfer coefficient (kL was found respectively 1.591x 107—2.122x107 m2/sec and 4.897x105—6.529x105 m/sec using liquid waste of cocoa bean fermentation as solvent which depend on temperature and solvent concentration. Key words: Coffee, caffeine, decaffeination, leaching, mathematic model.
Mathematical Modeling of the Vacuum Circulation Refining Processof Molten Steel
Institute of Scientific and Technical Information of China (English)
魏季和
2003-01-01
The available studies in the literature on mathematical modeling of the vacuum circulation (RH) refining process of molten steel have briefly been reviewed. The latest advances obtained by the author with his research group have been Summarized. On the basis of the mass and momentum balances in the system, a new mathematical model for decarburization and degassing during the RH and RH-KTB refining processes of molten steel was proposed and developed. The refining roles of the three reaction sites, i.e. the up-snorkel zone, the droplet group and steel bath in the vacuum vessel, were considered in the model. It was assumed that the mass transfer of reactive components in the molten steel is the rate control step of the refining reactions. And the friction losses and drags of flows in the snorkels and vacuum vessel were all counted. The model was applied to the refining of molten steel in a multifunction RH degasser of 90 t capacity. The decarburization and degassing processes in the degasser under the RH and RH-KTB operating condi-tions were modeled and analyzed using this model. Besides, proceeded from the two-resistance mass transfer theory and the mass bal-ance of sulphur in the system, a kinetic model for the desulphurization by powder injection and blowing in the RH refining of molten steel was developed. Modeling and predictions of the process of injecting and blowing the lime based powder flux under assumed oper-ating modes with the different initial contents of sulphur and amounts of powder injected and blown in a RH degasser of 300 t capacity were carried out using the model. It was demonstrated that for the RH and RH-KTB refining processes, and the desulphurization by powder injection and blowing in the RH refining, the results predicted by the models were all in good agreement respectively with data from industrial experiments and practice. These models may be expected to offer some useful information and a reliable basis for de-termining and optimizing
Wada, B. K.; Kuo, C-P.; Glaser, R. J.
1986-01-01
For the structural dynamic analysis of large space structures, the technology in structural synthesis and the development of structural analysis software have increased the capability to predict the dynamic characteristics of the structural system. The various subsystems which comprise the system are represented by various displacement functions; the displacement functions are then combined to represent the total structure. Experience has indicated that even when subsystem mathematical models are verified by test, the mathematical representations of the total system are often in error because the mathematical model of the structural elements which are significant when loads are applied at the interconnection points are not adequately verified by test. A multiple test concept, based upon the Multiple Boundary Condition Test (MBCT), is presented which will increase the accuracy of the system mathematical model by improving the subsystem test and test/analysis correlation procedure.
Typhoid transmission: a historical perspective on mathematical model development.
Bakach, Iurii; Just, Matthew R; Gambhir, Manoj; Fung, Isaac Chun-Hai
2015-11-01
Mathematical models of typhoid transmission were first developed nearly half a century ago. To facilitate a better understanding of the historical development of this field, we reviewed mathematical models of typhoid and summarized their structures and limitations. Eleven models, published in 1971 to 2014, were reviewed. While models of typhoid vaccination are well developed, we highlight the need to better incorporate water, sanitation and hygiene interventions into models of typhoid and other foodborne and waterborne diseases. Mathematical modeling is a powerful tool to test and compare different intervention strategies which is important in the world of limited resources. By working collaboratively, epidemiologists and mathematicians should build better mathematical models of typhoid transmission, including pharmaceutical and non-pharmaceutical interventions, which will be useful in epidemiological and public health practice.
Genetic models of homosexuality: generating testable predictions.
Gavrilets, Sergey; Rice, William R
2006-12-22
Homosexuality is a common occurrence in humans and other species, yet its genetic and evolutionary basis is poorly understood. Here, we formulate and study a series of simple mathematical models for the purpose of predicting empirical patterns that can be used to determine the form of selection that leads to polymorphism of genes influencing homosexuality. Specifically, we develop theory to make contrasting predictions about the genetic characteristics of genes influencing homosexuality including: (i) chromosomal location, (ii) dominance among segregating alleles and (iii) effect sizes that distinguish between the two major models for their polymorphism: the overdominance and sexual antagonism models. We conclude that the measurement of the genetic characteristics of quantitative trait loci (QTLs) found in genomic screens for genes influencing homosexuality can be highly informative in resolving the form of natural selection maintaining their polymorphism.
A mathematical model for apoptotic switch in Drosophila
Ziraldo, Riccardo; Ma, Lan
2015-10-01
Apoptosis is an evolutionarily-conserved process of autonomous cell death. The molecular switch mechanism underlying the fate decision of apoptosis in mammalian cells has been intensively studied by mathematical modeling. In contrast, the apoptotic switch in invertebrates, with highly conserved signaling proteins and pathway, remains poorly understood mechanistically and calls for theoretical elucidation. In this study, we develop a mathematical model of the apoptosis pathway in Drosophila and compare the switch mechanism to that in mammals. Enumeration of the elementary reactions for the model demonstrates that the molecular interactions among the signaling components are considerably different from their mammalian counterparts. A notable distinction in network organization is that the direct positive feedback from the effector caspase (EC) to the initiator caspase in mammalian pathway is replaced by a double-negative regulation in Drosophila. The model is calibrated by experimental input-output relationship and the simulated trajectories exhibit all-or-none bimodal behavior. Bifurcation diagrams confirm that the model of Drosophila apoptotic switch possesses bistability, a well-recognized feature for an apoptosis system. Since the apoptotic protease activating factor-1 (APAF1) induced irreversible activation of caspase is an essential and beneficial property for the mammalian apoptotic switch, we perform analysis of the bistable caspase activation with respect to the input of DARK protein, the Drosophila homolog of APAF1. Interestingly, this bistable behavior in Drosophila is predicted to be reversible. Further analysis suggests that the mechanism underlying the systems property of reversibility is the double-negative feedback from the EC to the initiator caspase. Using theoretical modeling, our study proposes plausible evolution of the switch mechanism for apoptosis between organisms.
Mathematical modeling and computational intelligence in engineering applications
Silva Neto, Antônio José da; Silva, Geraldo Nunes
2016-01-01
This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.
A mathematical model of the spread of the AIDS virus
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Hyman, J.M.; Stanley, E.A.
1987-01-01
A mathematical computer model of the spread of the AIDS epidemic in the US is being developed at Los Alamos National Laboratory. This model predicts the spreading of the HIV infection, and subsequent development of clinical AIDS in various population groups. These groups are chosen according to age, frequency and type of sexual contact, population density, and region of the country. Type of sexual contact includes not only the heterosexual, homosexual differentiation but also repeated contacts with such primary partners as spouses. In conjunction with the computer model, we are developing a database containing relevant information on the natural history of the viral infection, the prevalence of the infection and of clinical AIDS in the population, the distribution of people into sexual behavior groups as a function of age and information on interregional contacts. The effects of variable infectiousness and sexual activity during the long period from infection to disease are found to have a major impact on the predictions of the model. 24 refs., 5 figs.
Teaching Writing and Communication in a Mathematical Modeling Course
Linhart, Jean Marie
2014-01-01
Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…
An Assessment Model for Proof Comprehension in Undergraduate Mathematics
Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron
2012-01-01
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…
Wright, Vince
2014-01-01
Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…
Wright, Vince
2014-01-01
Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…
Chu, Felicia W; vanMarle, Kristy; Geary, David C
2016-01-01
One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted
Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani
2017-05-01
The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.
Priess-Groben, Heather A; Hyde, Janet Shibley
2017-06-01
Mathematics motivation declines for many adolescents, which limits future educational and career options. The present study sought to identify predictors of this decline by examining whether implicit theories assessed in ninth grade (incremental/entity) predicted course-taking behaviors and utility value in college. The study integrated implicit theory with variables from expectancy-value theory to examine potential moderators and mediators of the association of implicit theories with college mathematics outcomes. Implicit theories and expectancy-value variables were assessed in 165 American high school students (47 % female; 92 % White), who were then followed into their college years, at which time mathematics courses taken, course-taking intentions, and utility value were assessed. Implicit theories predicted course-taking intentions and utility value, but only self-concept of ability predicted courses taken, course-taking intentions, and utility value after controlling for prior mathematics achievement and baseline values. Expectancy for success in mathematics mediated associations between self-concept of ability and college outcomes. This research identifies self-concept of ability as a stronger predictor than implicit theories of mathematics motivation and behavior across several years: math self-concept is critical to sustained engagement in mathematics.
Mathematical model for radon diffusion in earthen materials
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Nielson, K.K.; Rogers, V.C.
1982-10-01
Radon migration in porous, earthen materials is characterized by diffusion in both the air and water components of the system as well as by the interaction of the radon between the air and water. The size distribution and configuration of the pore spaces and their moisture distributions are key parameters in determining the radon diffusion coefficient for the bulk material. A mathematical model is developed and presented for calculating radon diffusion coefficients solely from the moisture content and pore size distribution of a soil, reducing the need for resorting to radon diffusion measurements. The resulting diffusion coefficients increase with the median pore diameter of the soil and decrease with increasing widths of the pore size distribution. The calculated diffusion coefficients are suitable for use in simple homogeneous-medium diffusion expressions for predicting radon transport and compare well with measured diffusion coefficients and with empirical diffusion coefficient correlations.
Deductive Nomological Model and Mathematics: Making Dissatisfaction more Satisfactory
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Daniele Molinini
2014-06-01
Full Text Available The discussion on mathematical explanation has inherited the same sense of dissatisfaction that philosophers of science expressed, in the context of scientific explanation, towards the deductive-nomological model. This model is regarded as unable to cover cases of bona fide mathematical explanations and, furthermore, it is largely ignored in the relevant literature. Surprisingly, the reasons for this ostracism are not sufficiently manifest. In this paper I explore a possible extension of the model to the case of mathematical explanations and I claim that there are at least two reasons to judge the deductive-nomological picture of explanation as inadequate in that context.
A New Activity-Based Cost (ABC) Mathematical Model
Institute of Scientific and Technical Information of China (English)
JIANG Shuo; SONG Lei
2003-01-01
Along with the product price competition growing intensely, it is apparently important for reasonably distributing and counting cost. But, in sharing indirect cost, traditional cost accounting unveils the limitations increasingly, especially in authenticity of cost information. And the accounting theory circles and industry circles begin seeking one kind of new accurate cost calculation method, and the activity-based cost (ABC) method emerges as the times require. In this paper, we will build its mathematical model by the basic principle of ABC, and will improve its mathematical model further. We will establish its comparison mathematical model and make the ABC method go a step further to its practical application.
Mathematical Model of Asynchronous Motor with Embedded Combined Braking Device
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V. Solencov
2013-01-01
Full Text Available The paper presents a conclusion of a mathematical model pertaining to asynchronous motor with embedded combined braking device on the basis of electromechanical brake and electromagnetic slip coupling. The mathematical model has been obtained in an orthogonal coordinate system a, b, which is fixed with respect to the asymmetric part of the asynchronous motor with embedded combined braking device. The model makes it possible to investigate transient processes in various asynchronous motors with embedded braking devices.
Mathematical Model of Extrinsic Blood Coagulation Cascade Dynamic System
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The blood coagulation system is very important to life. This paper presents a mathematical blood coagulation model for the extrinsic pathway. This model simulates clotting factor VIII, which plays an important role in the coagulation mechanism. The mathematical model is used to study the equilibrium stability, orbit structure, attractors and global stability behavior, with conclusions in accordance with the physiological phenomena. Moreover, the results provide information about blood related illnesses, which can be used for further study of the coagulation mechanism.
[Mathematical models of decision making and learning].
Ito, Makoto; Doya, Kenji
2008-07-01
Computational models of reinforcement learning have recently been applied to analysis of brain imaging and neural recording data to identity neural correlates of specific processes of decision making, such as valuation of action candidates and parameters of value learning. However, for such model-based analysis paradigms, selecting an appropriate model is crucial. In this study we analyze the process of choice learning in rats using stochastic rewards. We show that "Q-learning," which is a standard reinforcement learning algorithm, does not adequately reflect the features of choice behaviors. Thus, we propose a generalized reinforcement learning (GRL) algorithm that incorporates the negative reward effect of reward loss and forgetting of values of actions not chosen. Using the Bayesian estimation method for time-varying parameters, we demonstrated that the GRL algorithm can predict an animal's choice behaviors as efficiently as the best Markov model. The results suggest the usefulness of the GRL for the model-based analysis of neural processes involved in decision making.
Mathematical Modeling on Open Limestone Channel
Bandstra, Joel; Wu, Naiyi
2014-01-01
Acid mine drainage (AMD) is the outflow of acidic water from metal mines or coal mines. When exposed to air and water, metal sulfides from the deposits of the mines are oxidized and produce acid, metal ions and sulfate, which lower the pH value of the water. An open limestone channel (OLC) is a passive and low cost way to neutralize AMD. The dissolution of calcium into the water increases the pH value of the solution. A differential equation model is numerically solved to predict the variation of concentration of each species in the OLC solution. The diffusion of Calcium due to iron precipitates is modeled by a linear equation. The results give the variation of pH value and the concentration of Calcium.
The possibilities of a modelling perspective for school mathematics
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Dirk Wessels
2009-09-01
complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem. Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has deﬁnitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to ﬁnding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full beneﬁt of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future.