Assessment of optimal strategies in a two-patch dengue transmission model with seasonality.
Directory of Open Access Journals (Sweden)
Jung Eun Kim
Full Text Available Emerging and re-emerging dengue fever has posed serious problems to public health officials in many tropical and subtropical countries. Continuous traveling in seasonally varying areas makes it more difficult to control the spread of dengue fever. In this work, we consider a two-patch dengue model that can capture the movement of host individuals between and within patches using a residence-time matrix. A previous two-patch dengue model without seasonality is extended by adding host demographics and seasonal forcing in the transmission rates. We investigate the effects of human movement and seasonality on the two-patch dengue transmission dynamics. Motivated by the recent Peruvian dengue data in jungle/rural areas and coast/urban areas, our model mimics the seasonal patterns of dengue outbreaks in two patches. The roles of seasonality and residence-time configurations are highlighted in terms of the seasonal reproduction number and cumulative incidence. Moreover, optimal control theory is employed to identify and evaluate patch-specific control measures aimed at reducing dengue prevalence in the presence of seasonality. Our findings demonstrate that optimal patch-specific control strategies are sensitive to seasonality and residence-time scenarios. Targeting only the jungle (or endemic is as effective as controlling both patches under weak coupling or symmetric mobility. However, focusing on intervention for the city (or high density areas turns out to be optimal when two patches are strongly coupled with asymmetric mobility.
Revisiting a two-patch SIS model with infection during transport.
Arino, Julien; Sun, Chengjun; Yang, Wei
2016-03-01
We incorporate parameter heterogeneity in a two-patch susceptible-infectious-susceptible (SIS) epidemic model with infection during transport and prove that the disease-free and endemic equilibria are globally asymptotically stable when the basic reproduction number [Formula: see text] and [Formula: see text], respectively. We find that infection during transport increases the possibility that the disease persists in both patches and amplifies prevalence when disease is present. We then study the effect of a perfect unilateral exit screening programme. Finally, we compare numerically the effects of using different incidence functions for infection within and while travelling between patches, and find that using mass action incidence to model infection during transport has the effect of maintaining disease prevalence at a higher level compared with when standard incidence is used. © The Authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Directory of Open Access Journals (Sweden)
Abdias Laohombé
2014-01-01
Full Text Available A two-patch model, SEi1,…,EinIiLi, i=1,2, is used to analyze the spread of tuberculosis, with an arbitrary number n of latently infected compartments in each patch. A fraction of infectious individuals that begun their treatment will not return to the hospital for the examination of sputum. This fact usually occurs in sub-Saharan Africa, due to many reasons. The model incorporates migrations from one patch to another. The existence and uniqueness of the associated equilibria are discussed. A Lyapunov function is used to show that when the basic reproduction ratio is less than one, the disease-free equilibrium is globally and asymptotically stable. When it is greater than one, there exists at least one endemic equilibrium. The local stability of endemic equilibria can be illustrated using numerical simulations. Numerical simulation results are provided to illustrate the theoretical results and analyze the influence of lost sight individuals.
Lismawati, Eka; Respatiwulan; Widyaningsih, Purnami
2017-06-01
The SIS epidemic model describes the pattern of disease spread with characteristics that recovered individuals can be infected more than once. The number of susceptible and infected individuals every time follows the discrete time Markov process. It can be represented by the discrete time Markov chains (DTMC) SIS. The DTMC SIS epidemic model can be developed for two pathogens in two patches. The aims of this paper are to reconstruct and to apply the DTMC SIS epidemic model with two pathogens in two patches. The model was presented as transition probabilities. The application of the model obtain that the number of susceptible individuals decreases while the number of infected individuals increases for each pathogen in each patch.
A periodic two-patch SIS model with time delay and transport-related infection.
Liu, Junli; Bai, Zhenguo; Zhang, Tailei
2018-01-21
In this paper, we propose a periodic SIS epidemic model with time delay and transport-related infection in a patchy environment. The basic reproduction number R 0 is derived which determines the global dynamics of the model system: if R 0 1. Numerical simulations are performed to confirm the analytical results and to explore the dependence of R 0 on the transport-related infection parameters and the amplitude of fluctuations. Copyright © 2017 Elsevier Ltd. All rights reserved.
Lanchier, Nicolas
2017-01-01
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...
Greenwood, Priscilla E
2016-01-01
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...
Cushman, John H.
1987-04-01
In a recent review article, G. Sposito et al. (1986) examined the various stochastic theories which are concerned with transport of solutes in porous media. In this short note we expand on their discussion to include several topics which had been omitted. We begin by looking at two definitions of probability theory and their relation to the concept of an ensemble. An REV ensemble of soils is defined and examined. The concept of ergodicity is reviewed, and it is pointed out that most stochastic models are theoretically unverifiable. The relationship between scale of measurement and stochasticity is briefly reviewed, and an equation that combines the two concepts is presented.
Stochastic Models of Evolution
Bezruchko, Boris P.; Smirnov, Dmitry A.
To continue the discussion of randomness given in Sect. 2.2.1, we briefly touch on stochastic models of temporal evolution (random processes). They can be specified either via explicit definition of their statistical properties (probability density functions, correlation functions, etc., Sects. 4.1, 4.2 and 4.3) or via stochastic difference or differential equations. Some of the most widely known equations, their properties and applications are discussed in Sects. 4.4 and 4.5.
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence. Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine...
Stochasticity Modeling in Memristors
Naous, Rawan
2015-10-26
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Identifiability in stochastic models
1992-01-01
The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.
Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P
2008-01-01
Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...
Stochastic ontogenetic growth model
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
Statistical validation of stochastic models
Energy Technology Data Exchange (ETDEWEB)
Hunter, N.F. [Los Alamos National Lab., NM (United States). Engineering Science and Analysis Div.; Barney, P.; Paez, T.L. [Sandia National Labs., Albuquerque, NM (United States). Experimental Structural Dynamics Dept.; Ferregut, C.; Perez, L. [Univ. of Texas, El Paso, TX (United States). Dept. of Civil Engineering
1996-12-31
It is common practice in structural dynamics to develop mathematical models for system behavior, and the authors are now capable of developing stochastic models, i.e., models whose parameters are random variables. Such models have random characteristics that are meant to simulate the randomness in characteristics of experimentally observed systems. This paper suggests a formal statistical procedure for the validation of mathematical models of stochastic systems when data taken during operation of the stochastic system are available. The statistical characteristics of the experimental system are obtained using the bootstrap, a technique for the statistical analysis of non-Gaussian data. The authors propose a procedure to determine whether or not a mathematical model is an acceptable model of a stochastic system with regard to user-specified measures of system behavior. A numerical example is presented to demonstrate the application of the technique.
Multiplier Models in Stochastic DEA
Directory of Open Access Journals (Sweden)
Mahnaz Mirbolouki
2014-05-01
Full Text Available Data Envelopment Analysis (DEA is a data-oriented performance evaluation method which has treated data as being deterministic. Throughout applications managers may encounter the data which are not recognized deterministically. In this paper a deterministic version of stochastic CCR multiplier model based on chance constrained programming approach is presented. The advantage of this method is that the stochastic essence of input-output variables has been taken into account. Using numerical example, we will demonstrate how this method works.
Stochastic models: theory and simulation.
Energy Technology Data Exchange (ETDEWEB)
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
The Probability of Extinction of Infectious Salmon Anemia Virus in One and Two Patches.
Milliken, Evan
2017-12-01
Single-type and multitype branching processes have been used to study the dynamics of a variety of stochastic birth-death type phenomena in biology and physics. Their use in epidemiology goes back to Whittle's study of a susceptible-infected-recovered (SIR) model in the 1950s. In the case of an SIR model, the presence of only one infectious class allows for the use of single-type branching processes. Multitype branching processes allow for multiple infectious classes and have latterly been used to study metapopulation models of disease. In this article, we develop a continuous time Markov chain (CTMC) model of infectious salmon anemia virus in two patches, two CTMC models in one patch and companion multitype branching process (MTBP) models. The CTMC models are related to deterministic models which inform the choice of parameters. The probability of extinction is computed for the CTMC via numerical methods and approximated by the MTBP in the supercritical regime. The stochastic models are treated as toy models, and the parameter choices are made to highlight regions of the parameter space where CTMC and MTBP agree or disagree, without regard to biological significance. Partial extinction events are defined and their relevance discussed. A case is made for calculating the probability of such events, noting that MTBPs are not suitable for making these calculations.
Stochastic model in microwave propagation
International Nuclear Information System (INIS)
Ranfagni, A.; Mugnai, D.
2011-01-01
Further experimental results of delay time in microwave propagation are reported in the presence of a lossy medium (wood). The measurements show that the presence of a lossy medium makes the propagation slightly superluminal. The results are interpreted on the basis of a stochastic (or path integral) model, showing how this model is able to describe each kind of physical system in which multi-path trajectories are present. -- Highlights: ► We present new experimental results on electromagnetic “anomalous” propagation. ► We apply a path integral theoretical model to wave propagation. ► Stochastic processes and multi-path trajectories in propagation are considered.
Stochastic models of cell motility
DEFF Research Database (Denmark)
Gradinaru, Cristian
2012-01-01
Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new...... interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic...... models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental...
Stochastic models for atmospheric dispersion
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2003-01-01
Simple stochastic differential equation models have been applied by several researchers to describe the dispersion of tracer particles in the planetary atmospheric boundary layer and to form the basis for computer simulations of particle paths. To obtain the drift coefficient, empirical vertical...... positions close to the boundaries. Different rules have been suggested in the literature with justifications based on simulation studies. Herein the relevant stochastic differential equation model is formulated in a particular way. The formulation is based on the marginal transformation of the position...... dependent particle velocity into a position independent Gaussian velocity. Boundary conditions are obtained from Itos rule of stochastic differentiation. The model directly point at a canonical rule of reflection for the approximating random walk with finite time step. This reflection rule is different from...
Birch regeneration: a stochastic model
William B. Leak
1968-01-01
The regeneration of a clearcutting with paper or yellow birch is expressed as an elementary stochastic (probabalistic) model that is computationally similar to an absorbing Markov chain. In the general case, the model contains 29 states beginning with the development of a flower (ament) and terminating with the abortion of a flower or seed, or the development of an...
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Stochastic Modelling of Hydrologic Systems
DEFF Research Database (Denmark)
Jonsdottir, Harpa
2007-01-01
In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains an introduct......In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains...... an introduction and an overview of the papers published. Then an introduction to basic concepts in hydrology along with a description of hydrological data is given. Finally an introduction to stochastic modelling is given. The second part contains the research papers. In the research papers the stochastic methods...... are described, as at the time of publication these methods represent new contribution to hydrology. The second part also contains additional description of software used and a brief introduction to stiff systems. The system in one of the papers is stiff....
Stochastic modeling of soil salinity
Suweis, S.; Rinaldo, A.; Zee, van der S.E.A.T.M.; Daly, E.; Maritan, A.
2010-01-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The long term probability density functions of salt mass and
Stochastic and deterministic trend models
Estela Bee Dagum; Camilo Dagum
2008-01-01
In this paper we provide an overview of some trend models formulated for global and local estimation. Global trend models are based on the assumption that the trend or nonstationary mean of a time series can be approximated closely by simple functions of time over the entire span of the series. The most common representation of deterministic and stochastic trend are introduced. In particular, for the former we analyze polynomial and transcendental functions, whereas for the latter we assume t...
Stochastic Models of Soil Denitrification
Parkin, T. B.; Robinson, J. A.
1989-01-01
Soil denitrification is a highly variable process that appears to be lognormally distributed. This variability is manifested by large sample coefficients of variation for replicate estimates of soil core denitrification rates. Deterministic models for soil denitrification have been proposed in the past, but none of these models predicts the approximate lognormality exhibited by natural denitrification rate estimates. In this study, probabilistic (stochastic) models were developed to understand how positively skewed distributions for field denitrification rate estimates result from the combined influences of variables known to affect denitrification. Three stochastic models were developed to describe the distribution of measured soil core denitrification rates. The driving variables used for all the models were denitrification enzyme activity and CO2 production rates. The three models were distinguished by the functional relationships combining these driving variables. The functional relationships used were (i) a second-order model (model 1), (ii) a second-order model with a threshold (model 2), and (iii) a second-order saturation model (model 3). The parameters of the models were estimated by using 12 separate data sets (24 replicates per set), and their abilities to predict denitrification rate distributions were evaluated by using three additional independent data sets of 180 replicates each. Model 2 was the best because it produced distributions of denitrification rate which were not significantly different (P > 0.1) from distributions of measured denitrification rates. The generality of this model is unknown, but it accurately predicted the mean denitrification rates and accounted for the stochastic nature of this variable at the site studied. The approach used in this study may be applicable to other areas of ecological research in which accounting for the high spatial variability of microbiological processes is of interest. PMID:16347838
Research on nonlinear stochastic dynamical price model
International Nuclear Information System (INIS)
Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng
2008-01-01
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies
Stochastic Models for Carcinogenesis
1961-01-01
Court Brown and Doll [3] on patients irradiated for ankylosing spondylitis . In their data, however, the peak incidence of leukemia occurred as soon as...and AploAtic Anaemia in Patients Irra- diated for Ankylosing Spondylitis , Special Report Series, Medical Research Council, No. 295, London, Her...function D(u). The possibilities are, of course, wide, and we shall not attempt any general treatment of such a model, although some particular cases will be
Stochastic Still Water Response Model
DEFF Research Database (Denmark)
Friis-Hansen, Peter; Ditlevsen, Ove Dalager
2002-01-01
water bending moment is compared to statistics from available regression formulas. It is found that the suggested model predicts a coefficient of variation of the maximum still water bending moment that is a factor of two to three times lower than that obtained by use of the regression formula. It turns......In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...
Stochastic Models of Human Errors
Elshamy, Maged; Elliott, Dawn M. (Technical Monitor)
2002-01-01
Humans play an important role in the overall reliability of engineering systems. More often accidents and systems failure are traced to human errors. Therefore, in order to have meaningful system risk analysis, the reliability of the human element must be taken into consideration. Describing the human error process by mathematical models is a key to analyzing contributing factors. Therefore, the objective of this research effort is to establish stochastic models substantiated by sound theoretic foundation to address the occurrence of human errors in the processing of the space shuttle.
Stochastic Subspace Modelling of Turbulence
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Pedersen, B. J.; Nielsen, Søren R.K.
2009-01-01
positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order......, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.......Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper...
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
Sequential neural models with stochastic layers
DEFF Research Database (Denmark)
Fraccaro, Marco; Sønderby, Søren Kaae; Paquet, Ulrich
2016-01-01
How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural...... generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over...
Stochastic models for cell division
Stukalin, Evgeny; Sun, Sean
2013-03-01
The probability of cell division per unit time strongly depends of age of cells, i.e., time elapsed since their birth. The theory of cell populations in the age-time representation is systematically applied for modeling cell division for different spreads in generation times. We use stochastic simulations to address the same issue at the level of individual cells. Our approach unlike deterministic theory enables to analyze the size fluctuations of cell colonies at different growth conditions (in the absence and in the presence of cell death, for initially synchronized and asynchronous cell populations, for conditions of restricted growth). We find the simple quantitative relation between the asymptotic values of relative size fluctuations around mean values for initially synchronized cell populations under growth and the coefficients of variation of generation times. Effect of initial age distribution for asynchronous growth of cell cultures is also studied by simulations. The influence of constant cell death on fluctuations of sizes of cell populations is found to be essential even for small cell death rates, i.e., for realistic growth conditions. The stochastic model is generalized for biologically relevant case that involves both cell reproduction and cell differentiation.
Stochastic models of technology diffusion
Energy Technology Data Exchange (ETDEWEB)
Horner, S.M.
1978-01-01
Simple stochastic models of epidemics have often been employed by economists and sociologists in the study of the diffusion of information or new technology. In the present theoretical inquiry the properties of a family of models related to these epidemic processes are investigated, and use of the results in the study of technical change phenomena is demonstrated. A moving limit to the level of productivity of capital is hypothesized, the exact increment is determined exogenously by basic or applied research carried on outside the industry. It is this level of latent productivity (LPRO) which fills the role of the ''disease'' which ''spreads'' through the industry. In the single advance models, LPRO is assumed to have moved forward at some point in time, after which an individual firm may advance to the limit by virtue of its own research and development or through imitation of the successful efforts of another firm. In the recurrent advance models, LPRO is assumed to increase at either a constant absolute or relative rate. The firms, in the course of their research and imitation efforts, follow behind LPRO. Using the methods of stochastic processes, it is shown that these models are equivalent to ergodic Markov chains. Based on an assumption of constant intensity of R and D effort, it is shown how the single and recurrent advance models reflect on Joseph Schumpeter's hypothesis that more concentrated industries tend to be more technologically advanced than less concentrated. The results corroborate the weakest version of the hypothesis: monopoly prices need not be higher than competitive prices.
CAM Stochastic Volatility Model for Option Pricing
Directory of Open Access Journals (Sweden)
Wanwan Huang
2016-01-01
Full Text Available The coupled additive and multiplicative (CAM noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks of the model. We also derive an approximation for the characteristic function of the model.
Stochastic hyperfine interactions modeling library
Zacate, Matthew O.; Evenson, William E.
2011-04-01
The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A can be neglected. Program summaryProgram title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mössbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When
From Complex to Simple: Interdisciplinary Stochastic Models
Mazilu, D. A.; Zamora, G.; Mazilu, I.
2012-01-01
We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique ap...
Consistent Stochastic Modelling of Meteocean Design Parameters
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Sterndorff, M. J.
2000-01-01
Consistent stochastic models of metocean design parameters and their directional dependencies are essential for reliability assessment of offshore structures. In this paper a stochastic model for the annual maximum values of the significant wave height, and the associated wind velocity, current...
Stochastic modeling of soil salinity
Suweis, S.; Porporato, A. M.; Daly, E.; van der Zee, S.; Maritan, A.; Rinaldo, A.
2010-12-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The equations for the probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equations to a single stochastic differential equation (generalized Langevin equation) driven by multiplicative Poisson noise. Generalized Langevin equations with multiplicative white Poisson noise pose the usual Ito (I) or Stratonovich (S) prescription dilemma. Different interpretations lead to different results and then choosing between the I and S prescriptions is crucial to describe correctly the dynamics of the model systems. We show how this choice can be determined by physical information about the timescales involved in the process. We also show that when the multiplicative noise is at most linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We then apply these results to the generalized Langevin equation that drives the salt mass dynamics. The stationary analytical solutions for the probability density functions of salt mass and concentration provide insight on the interplay of the main soil, plant and climate parameters responsible for long term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in longterm soil salinization trends, with significant consequences, e.g. for climate change impacts on rain fed agriculture.
Stochastic Models of Polymer Systems
2016-01-01
published in non-peer-reviewed journals (N/A for none) The dynamics of stochastic gradient algorithms (submitted); Noisy Hegselmann- Krause Systems...algorithms for big data applications. (2) We studied stochastic dynamics of polymer systems in the mean field limit. (3) We studied noisy Hegselmann- Krause
Stochastic Modelling and Analysis of Warehouse Operations
Y. Gong (Yeming)
2009-01-01
textabstractThis thesis has studied stochastic models and analysis of warehouse operations. After an overview of stochastic research in warehouse operations, we explore the following topics. Firstly, we search optimal batch sizes in a parallel-aisle warehouse with online order arrivals. We employ a
Temperature stochastic modeling and weather derivatives pricing ...
African Journals Online (AJOL)
... over a sufficient period to apply a stochastic process that describes the evolution of the temperature. A numerical example of a swap contract pricing is presented, using an approximation formula as well as Monte Carlo simulations. Keywords: Weather derivatives, temperature stochastic model, Monte Carlo simulation.
Stochastic models of intracellular transport
Bressloff, Paul C.
2013-01-09
The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an overdamped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of adenosine triphosphate hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review a wide range of analytical methods and models of intracellular transport is presented. In the case of diffusive transport, narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion are considered. In the case of active transport, Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean-field approximations are considered. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures. © 2013 American Physical Society.
Stochastic biomathematical models with applications to neuronal modeling
Batzel, Jerry; Ditlevsen, Susanne
2013-01-01
Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.
Modeling and analysis of stochastic systems
Kulkarni, Vidyadhar G
2011-01-01
Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edi
Numerical Simulation of the Heston Model under Stochastic Correlation
Directory of Open Access Journals (Sweden)
Long Teng
2017-12-01
Full Text Available Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.
Modelling and application of stochastic processes
1986-01-01
The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...
A stochastic SIS epidemic model with vaccination
Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming
2017-11-01
In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.
Moment Closure for the Stochastic Logistic Model
National Research Council Canada - National Science Library
Singh, Abhyudai; Hespanha, Joao P
2006-01-01
..., which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model...
Stochastic modeling for environmental stress screening
Cha, Ji Hwan; Finkelstein, Maxim
2014-01-01
Environmental stress screening (ESS) of manufactured items is used to reduce the occurrence of future failures that are caused by latent defects by eliminating the items with these defects. Some practical descriptions of the relevant ESS procedures can be found in the literature; however, the appropriate stochastic modeling and the corresponding thorough analysis have not been reported. In this paper we develop a stochastic model for the ESS, analyze the effect of this operation o...
A stochastic model of enzyme kinetics
Stefanini, Marianne; Newman, Timothy; McKane, Alan
2003-10-01
Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.
Modelling Cow Behaviour Using Stochastic Automata
DEFF Research Database (Denmark)
Jónsson, Ragnar Ingi
This report covers an initial study on the modelling of cow behaviour using stochastic automata with the aim of detecting lameness. Lameness in cows is a serious problem that needs to be dealt with because it results in less profitable production units and in reduced quality of life...... for the affected livestock. By featuring training data consisting of measurements of cow activity, three different models are obtained, namely an autonomous stochastic automaton, a stochastic automaton with coinciding state and output and an autonomous stochastic automaton with coinciding state and output, all...... of which describe the cows' activity in the two regarded behavioural scenarios, non-lame and lame. Using the experimental measurement data the different behavioural relations for the two regarded behavioural scenarios are assessed. The three models comprise activity within last hour, activity within last...
Computer Aided Continuous Time Stochastic Process Modelling
DEFF Research Database (Denmark)
Kristensen, N.R.; Madsen, Henrik; Jørgensen, Sten Bay
2001-01-01
A grey-box approach to process modelling that combines deterministic and stochastic modelling is advocated for identification of models for model-based control of batch and semi-batch processes. A computer-aided tool designed for supporting decision-making within the corresponding modelling cycle...
Stochastic Wake Modelling Based on POD Analysis
Directory of Open Access Journals (Sweden)
David Bastine
2018-03-01
Full Text Available In this work, large eddy simulation data is analysed to investigate a new stochastic modeling approach for the wake of a wind turbine. The data is generated by the large eddy simulation (LES model PALM combined with an actuator disk with rotation representing the turbine. After applying a proper orthogonal decomposition (POD, three different stochastic models for the weighting coefficients of the POD modes are deduced resulting in three different wake models. Their performance is investigated mainly on the basis of aeroelastic simulations of a wind turbine in the wake. Three different load cases and their statistical characteristics are compared for the original LES, truncated PODs and the stochastic wake models including different numbers of POD modes. It is shown that approximately six POD modes are enough to capture the load dynamics on large temporal scales. Modeling the weighting coefficients as independent stochastic processes leads to similar load characteristics as in the case of the truncated POD. To complete this simplified wake description, we show evidence that the small-scale dynamics can be captured by adding to our model a homogeneous turbulent field. In this way, we present a procedure to derive stochastic wake models from costly computational fluid dynamics (CFD calculations or elaborated experimental investigations. These numerically efficient models provide the added value of possible long-term studies. Depending on the aspects of interest, different minimalized models may be obtained.
Stochastic Modeling of Traffic Air Pollution
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
2014-01-01
In this paper, modeling of traffic air pollution is discussed with special reference to infrastructures. A number of subjects related to health effects of air pollution and the different types of pollutants are briefly presented. A simple model for estimating the social cost of traffic related air...... and using simple Monte Carlo techniques to obtain a stochastic estimate of the costs of traffic air pollution for infrastructures....... pollution is derived. Several authors have published papers on this very complicated subject, but no stochastic modelling procedure have obtained general acceptance. The subject is discussed basis of a deterministic model. However, it is straightforward to modify this model to include uncertain parameters...
Stochastic differential equation model to Prendiville processes
International Nuclear Information System (INIS)
Granita; Bahar, Arifah
2015-01-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution
Stochastic differential equation model to Prendiville processes
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Level Crossing Methods in Stochastic Models
Brill, Percy H
2008-01-01
Since its inception in 1974, the level crossing approach for analyzing a large class of stochastic models has become increasingly popular among researchers. This volume traces the evolution of level crossing theory for obtaining probability distributions of state variables and demonstrates solution methods in a variety of stochastic models including: queues, inventories, dams, renewal models, counter models, pharmacokinetics, and the natural sciences. Results for both steady-state and transient distributions are given, and numerous examples help the reader apply the method to solve problems fa
Infinite-degree-corrected stochastic block model
DEFF Research Database (Denmark)
Herlau, Tue; Schmidt, Mikkel Nørgaard; Mørup, Morten
2014-01-01
In stochastic block models, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman [Karrer and Newman...... corrected stochastic block model as a nonparametric Bayesian model, incorporating a parameter to control the amount of degree correction that can then be inferred from data. Additionally, our formulation yields principled ways of inferring the number of groups as well as predicting missing links...
Stochastic volatility models and Kelvin waves
International Nuclear Information System (INIS)
Lipton, Alex; Sepp, Artur
2008-01-01
We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics
Weather Derivatives and Stochastic Modelling of Temperature
Directory of Open Access Journals (Sweden)
Fred Espen Benth
2011-01-01
Full Text Available We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.
Stochastic Modelling Of The Repairable System
Directory of Open Access Journals (Sweden)
Andrzejczak Karol
2015-11-01
Full Text Available All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible. When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.
Some recent developments in stochastic volatility modelling
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Nicolato, Elisa; Shephard, N.
2002-01-01
This paper reviews and puts in context some of our recent work on stochastic volatility (SV) modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and SV, (ii) OU based volatility models, (iii) exact option pricing, (iv) realized power variation...
Compositional Modelling of Stochastic Hybrid Systems
Strubbe, S.N.
2005-01-01
In this thesis we present a modelling framework for compositional modelling of stochastic hybrid systems. Hybrid systems consist of a combination of continuous and discrete dynamics. The state space of a hybrid system is hybrid in the sense that it consists of a continuous component and a discrete
Stochastic models for turbulent reacting flows
Energy Technology Data Exchange (ETDEWEB)
Kerstein, A. [Sandia National Laboratories, Livermore, CA (United States)
1993-12-01
The goal of this program is to develop and apply stochastic models of various processes occurring within turbulent reacting flows in order to identify the fundamental mechanisms governing these flows, to support experimental studies of these flows, and to further the development of comprehensive turbulent reacting flow models.
Predicting Footbridge Response using Stochastic Load Models
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2013-01-01
Walking parameters such as step frequency, pedestrian mass, dynamic load factor, etc. are basically stochastic, although it is quite common to adapt deterministic models for these parameters. The present paper considers a stochastic approach to modeling the action of pedestrians, but when doing so...... decisions need to be made in terms of statistical distributions of walking parameters and in terms of the parameters describing the statistical distributions. The paper explores how sensitive computations of bridge response are to some of the decisions to be made in this respect. This is useful...
A Stochastic Model for Malaria Transmission Dynamics
Directory of Open Access Journals (Sweden)
Rachel Waema Mbogo
2018-01-01
Full Text Available Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis. In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp. The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.
Stochastic resonance in biological nonlinear evolution models
Dunkel, Jörn; Hilbert, Stefan; Schimansky-Geier, Lutz; Hänggi, Peter
2004-05-01
We investigate stochastic resonance in the nonlinear, one-dimensional Fisher-Eigen model (FEM), which represents an archetypal model for biological evolution based on a global coupling scheme. In doing so we consider different periodically driven fitness functions which govern the evolution of a biological phenotype population. For the case of a simple harmonic fitness function we are able to derive the exact analytic solution for the asymptotic probability density. A distinct feature of this solution is a phase lag between the driving signal and the linear response of the system. Furthermore, for more complex systems a general perturbation theory (linear response approximation) is put forward. Using the latter approach, we investigate stochastic resonance in terms of the spectral amplification measure for a quadratic, a quartic single-peaked, and for a bistable fitness function. Our analytical results are also compared with those of detailed numerical simulations. Our findings vindicate that stochastic resonance does occur in these nonlinear, globally coupled biological systems.
A Stochastic Cobweb Dynamical Model
Directory of Open Access Journals (Sweden)
Serena Brianzoni
2008-01-01
_,__0__1, and the forward predictor with probability (1−, so that the expected price at time is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.
Stochastic resonance in models of neuronal ensembles
International Nuclear Information System (INIS)
Chialvo, D.R.; Longtin, A.; Mueller-Gerkin, J.
1997-01-01
Two recently suggested mechanisms for the neuronal encoding of sensory information involving the effect of stochastic resonance with aperiodic time-varying inputs are considered. It is shown, using theoretical arguments and numerical simulations, that the nonmonotonic behavior with increasing noise of the correlation measures used for the so-called aperiodic stochastic resonance (ASR) scenario does not rely on the cooperative effect typical of stochastic resonance in bistable and excitable systems. Rather, ASR with slowly varying signals is more properly interpreted as linearization by noise. Consequently, the broadening of the open-quotes resonance curveclose quotes in the multineuron stochastic resonance without tuning scenario can also be explained by this linearization. Computation of the input-output correlation as a function of both signal frequency and noise for the model system further reveals conditions where noise-induced firing with aperiodic inputs will benefit from stochastic resonance rather than linearization by noise. Thus, our study clarifies the tuning requirements for the optimal transduction of subthreshold aperiodic signals. It also shows that a single deterministic neuron can perform as well as a network when biased into a suprathreshold regime. Finally, we show that the inclusion of a refractory period in the spike-detection scheme produces a better correlation between instantaneous firing rate and input signal. copyright 1997 The American Physical Society
Stochastic linear programming models, theory, and computation
Kall, Peter
2011-01-01
This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...
Normal Forms for Reduced Stochastic Climate Models
Franzke, C.; Majda, A.; Crommelin, D.
2009-04-01
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high-dimensional climate models is an important topic for low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from applied mathematics are utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. The use of a few Empirical Orthogonal Functions (EOF) depending on observational data to span the low-frequency subspace requires the assessment of dyad interactions besides the more familiar triads in the interaction between the low- and high-frequency subspaces of the dynamics. It will be shown that the dyad and multiplicative triad interactions combine with the climatological linear operator interactions to simultaneously produce both strong nonlinear dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. For a single low-frequency variable the dyad interactions and climatological linear operator alone produce a normal form with CAM noise from advection of the large-scales by the small scales and simultaneously strong cubic damping. This normal form should prove useful for developing systematic regression fitting strategies for stochastic models of climate data. The validity of the one and two dimensional normal forms will be presented. Also the analytical PDF form for one-dimensional reduced models will be derived. This PDF can exhibit power-law decay only over a limited range and its ultimate decay is determined by the cubic damping. This cubic damping produces a Gaussian tail.
Stochastic Growth Models with No Discounting
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2007-01-01
Roč. 15, č. 4 (2007), s. 88-98 ISSN 0572-3043 R&D Projects: GA ČR(CZ) GA402/06/0990; GA ČR GA402/05/0115 Institutional research plan: CEZ:AV0Z10750506 Keywords : economic dynamics * stochastic version of the Ramsey growth model * Markov decision processes Subject RIV: AH - Economics
A Stochastic Dynamic Model of Computer Viruses
Directory of Open Access Journals (Sweden)
Chunming Zhang
2012-01-01
Full Text Available A stochastic computer virus spread model is proposed and its dynamic behavior is fully investigated. Specifically, we prove the existence and uniqueness of positive solutions, and the stability of the virus-free equilibrium and viral equilibrium by constructing Lyapunov functions and applying Ito's formula. Some numerical simulations are finally given to illustrate our main results.
Modeling animal movements using stochastic differential equations
Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie
2004-01-01
We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...
Stochastic models for road traffic control
Kovács, P.
2016-01-01
In this dissertation we make use of the theories of stochastic processes and operations research to develop models and methods to be applied for the analysis and control of road traffic networks. Within this field three subjects are considered: individual routing, urban traffic light networks and
Vulnerability in a Stochastic Dynamic Model
Elbers, Chris; Gunning, Jan Willem
2003-01-01
Most measures of vulnerability are a-theoretic and essentially static. In this paper we use a stochastic Ramsey model to find a household's optimal welfare and we measure vulnerability as the shortfall from the welfare attained if the household consumed permanently at the poverty line. The results
Stochastic Modeling Of Wind Turbine Drivetrain Components
DEFF Research Database (Denmark)
Rafsanjani, Hesam Mirzaei; Sørensen, John Dalsgaard
2014-01-01
reliable components are needed for wind turbine. In this paper focus is on reliability of critical components in drivetrain such as bearings and shafts. High failure rates of these components imply a need for more reliable components. To estimate the reliability of these components, stochastic models...
Stochastic models of intracellular calcium signals
Energy Technology Data Exchange (ETDEWEB)
Rüdiger, Sten, E-mail: sten.ruediger@physik.hu-berlin.de
2014-01-10
Cellular signaling operates in a noisy environment shaped by low molecular concentrations and cellular heterogeneity. For calcium release through intracellular channels–one of the most important cellular signaling mechanisms–feedback by liberated calcium endows fluctuations with critical functions in signal generation and formation. In this review it is first described, under which general conditions the environment makes stochasticity relevant, and which conditions allow approximating or deterministic equations. This analysis provides a framework, in which one can deduce an efficient hybrid description combining stochastic and deterministic evolution laws. Within the hybrid approach, Markov chains model gating of channels, while the concentrations of calcium and calcium binding molecules (buffers) are described by reaction–diffusion equations. The article further focuses on the spatial representation of subcellular calcium domains related to intracellular calcium channels. It presents analysis for single channels and clusters of channels and reviews the effects of buffers on the calcium release. For clustered channels, we discuss the application and validity of coarse-graining as well as approaches based on continuous gating variables (Fokker–Planck and chemical Langevin equations). Comparison with recent experiments substantiates the stochastic and spatial approach, identifies minimal requirements for a realistic modeling, and facilitates an understanding of collective channel behavior. At the end of the review, implications of stochastic and local modeling for the generation and properties of cell-wide release and the integration of calcium dynamics into cellular signaling models are discussed.
Stochastic modelling of migration from polyolefins
Helmroth, I.E.; Varekamp, C.; Dekker, M.
2005-01-01
A method is presented to predict diffusion coefficients in polyolefins using stochastic modelling. A large number of experimental diffusion coefficients, published in the literature as one dataset, was used to derive probability distributions of diffusion coefficients in the polymers low-density
Stochastic forward and inverse groundwater flow and solute transport modeling
Janssen, G.M.C.M.
2008-01-01
Keywords: calibration, inverse modeling, stochastic modeling, nonlinear biodegradation, stochastic-convective, advective-dispersive, travel time, network design, non-Gaussian distribution, multimodal distribution, representers
This thesis offers three new approaches that contribute
Stochastic models in reliability and maintenance
2002-01-01
Our daily lives can be maintained by the high-technology systems. Computer systems are typical examples of such systems. We can enjoy our modern lives by using many computer systems. Much more importantly, we have to maintain such systems without failure, but cannot predict when such systems will fail and how to fix such systems without delay. A stochastic process is a set of outcomes of a random experiment indexed by time, and is one of the key tools needed to analyze the future behavior quantitatively. Reliability and maintainability technologies are of great interest and importance to the maintenance of such systems. Many mathematical models have been and will be proposed to describe reliability and maintainability systems by using the stochastic processes. The theme of this book is "Stochastic Models in Reliability and Main tainability. " This book consists of 12 chapters on the theme above from the different viewpoints of stochastic modeling. Chapter 1 is devoted to "Renewal Processes," under which cla...
Dynamic optimization deterministic and stochastic models
Hinderer, Karl; Stieglitz, Michael
2016-01-01
This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.
Model predictive control classical, robust and stochastic
Kouvaritakis, Basil
2016-01-01
For the first time, a textbook that brings together classical predictive control with treatment of up-to-date robust and stochastic techniques. Model Predictive Control describes the development of tractable algorithms for uncertain, stochastic, constrained systems. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closed-loop stability and performance. Moving on to robust predictive control, the text explains how similar guarantees may be obtained for cases in which the model describing the system dynamics is subject to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are considered and the state of the art in computationally tractable methods based on uncertainty tubes presented for systems with additive model uncertainty. Finally, the tube framework is also applied to model predictive control problems involving hard or probabilistic constraints for the cases of multiplic...
Stochastic text models for music categorization
Pérez Sancho, Carlos; Rizo Valero, David; Iñesta Quereda, José Manuel
2008-01-01
Music genre meta-data is of paramount importance for the organization of music repositories. People use genre in a natural way when entering a music store or looking into music collections. Automatic genre classification has become a popular topic in music information retrieval research. This work brings to symbolic music recognition some technologies, like the stochastic language models, already successfully applied to text categorization. In this work we model chord progressions and melodie...
Stochastic models for atomic clocks
Barnes, J. A.; Jones, R. H.; Tryon, P. V.; Allan, D. W.
1983-01-01
For the atomic clocks used in the National Bureau of Standards Time Scales, an adequate model is the superposition of white FM, random walk FM, and linear frequency drift for times longer than about one minute. The model was tested on several clocks using maximum likelihood techniques for parameter estimation and the residuals were acceptably random. Conventional diagnostics indicate that additional model elements contribute no significant improvement to the model even at the expense of the added model complexity.
Stochastic Spectral Descent for Discrete Graphical Models
International Nuclear Information System (INIS)
Carlson, David; Hsieh, Ya-Ping; Collins, Edo; Carin, Lawrence; Cevher, Volkan
2015-01-01
Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted as gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.
Brain-inspired Stochastic Models and Implementations
Al-Shedivat, Maruan
2015-05-12
One of the approaches to building artificial intelligence (AI) is to decipher the princi- ples of the brain function and to employ similar mechanisms for solving cognitive tasks, such as visual perception or natural language understanding, using machines. The recent breakthrough, named deep learning, demonstrated that large multi-layer networks of arti- ficial neural-like computing units attain remarkable performance on some of these tasks. Nevertheless, such artificial networks remain to be very loosely inspired by the brain, which rich structures and mechanisms may further suggest new algorithms or even new paradigms of computation. In this thesis, we explore brain-inspired probabilistic mechanisms, such as neural and synaptic stochasticity, in the context of generative models. The two questions we ask here are: (i) what kind of models can describe a neural learning system built of stochastic components? and (ii) how can we implement such systems e ̆ciently? To give specific answers, we consider two well known models and the corresponding neural architectures: the Naive Bayes model implemented with a winner-take-all spiking neural network and the Boltzmann machine implemented in a spiking or non-spiking fashion. We propose and analyze an e ̆cient neuromorphic implementation of the stochastic neu- ral firing mechanism and study the e ̄ects of synaptic unreliability on learning generative energy-based models implemented with neural networks.
Stochastic Modelling of Energy Systems
DEFF Research Database (Denmark)
Andersen, Klaus Kaae
2001-01-01
In this thesis dynamic models of typical components in Danish heating systems are considered. Emphasis is made on describing and evaluating mathematical methods for identification of such models, and on presentation of component models for practical applications. The thesis consists of seven...... of component models, such as e.g. heat exchanger and valve models, adequate for system simulations. Furthermore, the thesis demonstrates and discusses the advantages and disadvantages of using statistical methods in conjunction with physical knowledge in establishing adequate component models of heating...... research papers (case studies) together with a summary report. Each case study takes it's starting point in typical heating system components and both, the applied mathematical modelling methods and the application aspects, are considered. The summary report gives an introduction to the scope...
Solvable stochastic dealer models for financial markets
Yamada, Kenta; Takayasu, Hideki; Ito, Takatoshi; Takayasu, Misako
2009-05-01
We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects: the self-modulation of transaction intervals and a forecasting tendency, which uses a moving average of the latest market price changes. Based on the present microscopic model of markets, we find a quantitative relation with market potential forces, which have recently been discovered in the study of market price modeling based on random walks.
Mixed effects in stochastic differential equation models
DEFF Research Database (Denmark)
Ditlevsen, Susanne; De Gaetano, Andrea
2005-01-01
maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes......maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes...
Fuzzy Stochastic Optimization Theory, Models and Applications
Wang, Shuming
2012-01-01
Covering in detail both theoretical and practical perspectives, this book is a self-contained and systematic depiction of current fuzzy stochastic optimization that deploys the fuzzy random variable as a core mathematical tool to model the integrated fuzzy random uncertainty. It proceeds in an orderly fashion from the requisite theoretical aspects of the fuzzy random variable to fuzzy stochastic optimization models and their real-life case studies. The volume reflects the fact that randomness and fuzziness (or vagueness) are two major sources of uncertainty in the real world, with significant implications in a number of settings. In industrial engineering, management and economics, the chances are high that decision makers will be confronted with information that is simultaneously probabilistically uncertain and fuzzily imprecise, and optimization in the form of a decision must be made in an environment that is doubly uncertain, characterized by a co-occurrence of randomness and fuzziness. This book begins...
Stochastic Model Checking of the Stochastic Quality Calculus
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin
2015-01-01
The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input...
Stochastic Modelling of Seafloor Morphology
1990-06-01
year of a grad students life into one of the most enjoyable. I also thank Mom, Dad, Barbi , Ellie, Robbie, Dick and Jean, Trudy and Will, Grandma and...1981; 1986] and Sinton et al. [ 19831 on the basis of variations in crystal fractionation throughout the evolution of the Galapagos 95.50 W...propagator. It is also consistent with the tectonic model proposed by Kleinrock and Hey [1989] for the evolution of the same propagator. In their model
Stochastic models for time series
Doukhan, Paul
2018-01-01
This book presents essential tools for modelling non-linear time series. The first part of the book describes the main standard tools of probability and statistics that directly apply to the time series context to obtain a wide range of modelling possibilities. Functional estimation and bootstrap are discussed, and stationarity is reviewed. The second part describes a number of tools from Gaussian chaos and proposes a tour of linear time series models. It goes on to address nonlinearity from polynomial or chaotic models for which explicit expansions are available, then turns to Markov and non-Markov linear models and discusses Bernoulli shifts time series models. Finally, the volume focuses on the limit theory, starting with the ergodic theorem, which is seen as the first step for statistics of time series. It defines the distributional range to obtain generic tools for limit theory under long or short-range dependences (LRD/SRD) and explains examples of LRD behaviours. More general techniques (central limit ...
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...
A stochastic model for quantum measurement
International Nuclear Information System (INIS)
Budiyono, Agung
2013-01-01
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic process with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary action. We apply the statistical model to stochastically modify a classical mechanical model for the measurement of physical quantities reproducing the prediction of quantum mechanics. The system+apparatus always has a definite configuration at all times, as in classical mechanics, fluctuating randomly following a continuous trajectory. On the other hand, the wavefunction and quantum mechanical Hermitian operator corresponding to the physical quantity arise formally as artificial mathematical constructs. During a single measurement, the wavefunction of the whole system+apparatus evolves according to a Schrödinger equation and the configuration of the apparatus acts as the pointer of the measurement so that there is no wavefunction collapse. We will also show that while the outcome of each single measurement event does not reveal the actual value of the physical quantity prior to measurement, its average in an ensemble of identical measurements is equal to the average of the actual value of the physical quantity prior to measurement over the distribution of the configuration of the system. (paper)
A stochastic model for the financial market with discontinuous prices
Directory of Open Access Journals (Sweden)
Leda D. Minkova
1996-01-01
Full Text Available This paper models some situations occurring in the financial market. The asset prices evolve according to a stochastic integral equation driven by a Gaussian martingale. A portfolio process is constrained in such a way that the wealth process covers some obligation. A solution to a linear stochastic integral equation is obtained in a class of cadlag stochastic processes.
Modelling conjugation with stochastic differential equations.
Philipsen, K R; Christiansen, L E; Hasman, H; Madsen, H
2010-03-07
Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared to the model without plate conjugation. The modelling approach described in this article can be applied generally when modelling dynamical systems. 2009 Elsevier Ltd. All rights reserved.
Stochastic Model of TCP SYN Attacks
Simona Ramanauskaitė; Antanas Čenys
2011-01-01
A great proportion of essential services are moving into internet space making the threat of DoS attacks even more actual. To estimate the real risk of some kind of denial of service (DoS) attack in real world is difficult, but mathematical and software models make this task easier. In this paper we overview the ways of implementing DoS attack models and offer a stochastic model of SYN flooding attack. It allows evaluating the potential threat of SYN flooding attacks, taking into account both...
Hidden Symmetries of Stochastic Models
Directory of Open Access Journals (Sweden)
Boyka Aneva
2007-05-01
Full Text Available In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a $SU_q(n$ quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the $SU_q(n$ symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.
Stochastic hyperelastic modeling considering dependency of material parameters
Caylak, Ismail; Penner, Eduard; Dridger, Alex; Mahnken, Rolf
2018-03-01
This paper investigates the uncertainty of a hyperelastic model by treating random material parameters as stochastic variables. For its stochastic discretization a polynomial chaos expansion (PCE) is used. An important aspect in our work is the consideration of stochastic dependencies in the stochastic modeling of Ogden's material model. To this end, artificial experiments are generated using the auto-regressive moving average process based on real experiments. The parameter identification for all data provides statistics of Ogden's material parameters, which are subsequently used for stochastic modeling. Stochastic dependencies are incorporated into the PCE using a Nataf transformation from dependent distributed random variables to independent standard normal distributed ones. The representative numerical example shows that our proposed method adequately takes into account the stochastic dependencies of Ogden's material parameters.
Stochastic Optimization of Wind Turbine Power Factor Using Stochastic Model of Wind Power
DEFF Research Database (Denmark)
Chen, Peiyuan; Siano, Pierluigi; Bak-Jensen, Birgitte
2010-01-01
This paper proposes a stochastic optimization algorithm that aims to minimize the expectation of the system power losses by controlling wind turbine (WT) power factors. This objective of the optimization is subject to the probability constraints of bus voltage and line current requirements....... The optimization algorithm utilizes the stochastic models of wind power generation (WPG) and load demand to take into account their stochastic variation. The stochastic model of WPG is developed on the basis of a limited autoregressive integrated moving average (LARIMA) model by introducing a crosscorrelation...... structure to the LARIMA model. The proposed stochastic optimization is carried out on a 69-bus distribution system. Simulation results confirm that, under various combinations of WPG and load demand, the system power losses are considerably reduced with the optimal setting of WT power factor as compared...
Models of the stochastic activity of neurones
Holden, Arun Vivian
1976-01-01
These notes have grown from a series of seminars given at Leeds between 1972 and 1975. They represent an attempt to gather together the different kinds of model which have been proposed to account for the stochastic activity of neurones, and to provide an introduction to this area of mathematical biology. A striking feature of the electrical activity of the nervous system is that it appears stochastic: this is apparent at all levels of recording, ranging from intracellular recordings to the electroencephalogram. The chapters start with fluctuations in membrane potential, proceed through single unit and synaptic activity and end with the behaviour of large aggregates of neurones: L have chgaen this seque~~e\\/~~';uggest that the interesting behaviourr~f :the nervous system - its individuality, variability and dynamic forms - may in part result from the stochastic behaviour of its components. I would like to thank Dr. Julio Rubio for reading and commenting on the drafts, Mrs. Doris Beighton for producing the fin...
Modelling Evolutionary Algorithms with Stochastic Differential Equations.
Heredia, Jorge Pérez
2017-11-20
There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.
Modeling stochastic frontier based on vine copulas
Constantino, Michel; Candido, Osvaldo; Tabak, Benjamin M.; da Costa, Reginaldo Brito
2017-11-01
This article models a production function and analyzes the technical efficiency of listed companies in the United States, Germany and England between 2005 and 2012 based on the vine copula approach. Traditional estimates of the stochastic frontier assume that data is multivariate normally distributed and there is no source of asymmetry. The proposed method based on vine copulas allow us to explore different types of asymmetry and multivariate distribution. Using data on product, capital and labor, we measure the relative efficiency of the vine production function and estimate the coefficient used in the stochastic frontier literature for comparison purposes. This production vine copula predicts the value added by firms with given capital and labor in a probabilistic way. It thereby stands in sharp contrast to the production function, where the output of firms is completely deterministic. The results show that, on average, S&P500 companies are more efficient than companies listed in England and Germany, which presented similar average efficiency coefficients. For comparative purposes, the traditional stochastic frontier was estimated and the results showed discrepancies between the coefficients obtained by the application of the two methods, traditional and frontier-vine, opening new paths of non-linear research.
Stochastic differential equations used to model conjugation
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo
be split into measurement noise and system noise. The system noise is used to compensate for those biological processes not explicitly described by the model. Many authors model conjugation by a simple mass action model first proposed by Levin et al. (1979). Also Michaelis-Menten dependence...... by an experiment conducted with E. faecium. In addition, we suggest that a 3rd order time-delay must be included in the model to account for the delay before a newly conjugated plasmid is expressed. A ML estimate of the parameters based on experimental data is found using the software CTSM. The conjugation rate......Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...
Modeling and Prediction Using Stochastic Differential Equations
DEFF Research Database (Denmark)
Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp
2016-01-01
deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs......) for modeling and forecasting. It is argued that this gives models and predictions which better reflect reality. The SDE approach also offers a more adequate framework for modeling and a number of efficient tools for model building. A software package (CTSM-R) for SDE-based modeling is briefly described....... that describes the variation between subjects. The ODE setup implies that the variation for a single subject is described by a single parameter (or vector), namely the variance (covariance) of the residuals. Furthermore the prediction of the states is given as the solution to the ODEs and hence assumed...
Stochastic Load Models and Footbridge Response
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2015-01-01
Pedestrians may cause vibrations in footbridges and these vibrations may potentially be annoying. This calls for predictions of footbridge vibration levels and the paper considers a stochastic approach to modeling the action of pedestrians assuming walking parameters such as step frequency......, pedestrian mass, dynamic load factor, etc. to be random variables. By this approach a probability distribution function of bridge response is calculated. The paper explores how sensitive estimates of probability distribution functions of bridge response are to some of the decisions to be made when modelling...
Can Household Benefit from Stochastic Programming Models?
DEFF Research Database (Denmark)
Rasmussen, Kourosh Marjani; Madsen, Claus A.; Poulsen, Rolf
2014-01-01
The Danish mortgage market is large and sophisticated. However, most Danish mortgage banks advise private home-owners based on simple, if sensible, rules of thumb. In recent years a number of papers (from Nielsen and Poulsen in J Econ Dyn Control 28:1267–1289, 2004 over Rasmussen and Zenios in J...... Risk 10:1–18, 2007 to Pedersen et al. in Ann Oper Res, 2013) have suggested a model-based, stochastic programming approach to mortgage choice. This paper gives an empirical comparison of performance over the period 2000–2010 of the rules of thumb to the model-based strategies. While the rules of thumb...
Modelling the stochastic behaviour of primary nucleation.
Maggioni, Giovanni Maria; Mazzotti, Marco
2015-01-01
We study the stochastic nature of primary nucleation and how it manifests itself in a crystallisation process at different scales and under different operating conditions. Such characteristics of nucleation are evident in many experiments where detection times of crystals are not identical, despite identical experimental conditions, but instead are distributed around an average value. While abundant experimental evidence has been reported in the literature, a clear theoretical understanding and an appropriate modelling of this feature is still missing. In this contribution, we present two models describing a batch cooling crystallisation, where the interplay between stochastic nucleation and deterministic crystal growth is described differently in each. The nucleation and growth rates of the two models are estimated by a comprehensive set of measurements of paracetamol crystallisation from aqueous solution in a 1 mL vessel [Kadam et al., Chemical Engineering Science, 2012, 72, 10-19]. Both models are applied to the cooling crystallisation process above under different operating conditions, i.e. different volumes, initial concentrations, cooling rates. The advantages and disadvantages of the two approaches are illustrated and discussed, with particular reference to their use across scales of nucleation rate measured in very small crystallisers.
Sensitivity Study of Stochastic Walking Load Models
DEFF Research Database (Denmark)
Pedersen, Lars; Frier, Christian
2010-01-01
is to employ a stochastic load model accounting for mean values and standard deviations for the walking load parameters, and to use this as a basis for estimation of structural response. This, however, requires decisions to be made in terms of statistical istributions and their parameters, and the paper...... investigates whether statistical distributions of bridge response are sensitive to some of the decisions made by the engineer doing the analyses. For the paper a selected part of potential influences are examined and footbridge responses are extracted using Monte-Carlo simulations and focus is on estimating...
A stochastic model of AIDS and condom use
Dalal, Nirav; Greenhalgh, David; Mao, Xuerong
2007-01-01
In this paper we introduce stochasticity into a model of AIDS and condom use via the technique of parameter perturbation which is standard in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as desired in any population dynamics. We also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment. Our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system.
Scalable inference for stochastic block models
Peng, Chengbin
2017-12-08
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of "big data," traditional inference algorithms for such a model are increasingly limited due to their high time complexity and poor scalability. In this paper, we propose a multi-stage maximum likelihood approach to recover the latent parameters of the stochastic block model, in time linear with respect to the number of edges. We also propose a parallel algorithm based on message passing. Our algorithm can overlap communication and computation, providing speedup without compromising accuracy as the number of processors grows. For example, to process a real-world graph with about 1.3 million nodes and 10 million edges, our algorithm requires about 6 seconds on 64 cores of a contemporary commodity Linux cluster. Experiments demonstrate that the algorithm can produce high quality results on both benchmark and real-world graphs. An example of finding more meaningful communities is illustrated consequently in comparison with a popular modularity maximization algorithm.
Stochastic Model of TCP SYN Attacks
Directory of Open Access Journals (Sweden)
Simona Ramanauskaitė
2011-08-01
Full Text Available A great proportion of essential services are moving into internet space making the threat of DoS attacks even more actual. To estimate the real risk of some kind of denial of service (DoS attack in real world is difficult, but mathematical and software models make this task easier. In this paper we overview the ways of implementing DoS attack models and offer a stochastic model of SYN flooding attack. It allows evaluating the potential threat of SYN flooding attacks, taking into account both the legitimate system flow as well as the possible attack power. At the same time we can assess the effect of such parameters as buffer capacity, open connection storage in the buffer or filtering efficiency on the success of different SYN flooding attacks. This model can be used for other type of memory depletion denial of service attacks.Article in Lithuanian
Stochastic modeling of financial electricity contracts
International Nuclear Information System (INIS)
Benth, Fred Espen; Koekebakker, Steen
2008-01-01
We discuss the modeling of electricity contracts traded in many deregulated power markets. These forward/futures type contracts deliver (either physically or financially) electricity over a specified time period, and is frequently referred to as swaps since they in effect represent an exchange of fixed for floating electricity price. We propose to use the Heath-Jarrow-Morton approach to model swap prices since the notion of a spot price is not easily defined in these markets. For general stochastic dynamical models, we connect the spot price, the instantaneous-delivery forward price and the swap price, and analyze two different ways to apply the Heath-Jarrow-Morton approach to swap pricing: Either one specifies a dynamics for the non-existing instantaneous-delivery forwards and derives the implied swap dynamics, or one models directly on the swaps. The former is shown to lead to quite complicated stochastic models for the swap price, even when the forward dynamics is simple. The latter has some theoretical problems due to a no-arbitrage condition that has to be satisfied for swaps with overlapping delivery periods. To overcome this problem, a practical modeling approach is analyzed. The market is supposed only to consist of non-overlapping swaps, and these are modelled directly. A thorough empirical study is performed using data collected from Nord Pool. Our investigations demonstrate that it is possible to state reasonable models for the swap price dynamics which is analytically tractable for risk management and option pricing purposes, however, this is an area of further research. (author)
Stochastic modeling of thermal fatigue crack growth
Radu, Vasile
2015-01-01
The book describes a systematic stochastic modeling approach for assessing thermal-fatigue crack-growth in mixing tees, based on the power spectral density of temperature fluctuation at the inner pipe surface. It shows the development of a frequency-temperature response function in the framework of single-input, single-output (SISO) methodology from random noise/signal theory under sinusoidal input. The frequency response of stress intensity factor (SIF) is obtained by a polynomial fitting procedure of thermal stress profiles at various instants of time. The method, which takes into account the variability of material properties, and has been implemented in a real-world application, estimates the probabilities of failure by considering a limit state function and Monte Carlo analysis, which are based on the proposed stochastic model. Written in a comprehensive and accessible style, this book presents a new and effective method for assessing thermal fatigue crack, and it is intended as a concise and practice-or...
Hopf bifurcation of the stochastic model on business cycle
International Nuclear Information System (INIS)
Xu, J; Wang, H; Ge, G
2008-01-01
A stochastic model on business cycle was presented in thas paper. Simplifying the model through the quasi Hamiltonian theory, the Ito diffusion process was obtained. According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired. Solving the stationary FPK equation and analyzing the stationary probability density, the stochastic Hopf bifurcation was explained. The result indicated that the change of parameter awas the key factor to the appearance of the stochastic Hopf bifurcation
Stochastic stability and bifurcation in a macroeconomic model
International Nuclear Information System (INIS)
Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei
2007-01-01
On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis
Stochastic inverse problems: Models and metrics
International Nuclear Information System (INIS)
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-01-01
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds
Stochastic inverse problems: Models and metrics
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-03-01
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds.
Stochastic inverse problems: Models and metrics
Energy Technology Data Exchange (ETDEWEB)
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim [Victor Technologies, LLC, Bloomington, IN 47407-7706 (United States); Aldrin, John C. [Computational Tools, Gurnee, IL 60031 (United States); Annis, Charles [Statistical Engineering, Palm Beach Gardens, FL 33418 (United States); Knopp, Jeremy S. [Air Force Research Laboratory (AFRL/RXCA), Wright Patterson AFB, OH 45433-7817 (United States)
2015-03-31
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds.
Stochastic simplified modelling of abrasive waterjet footprints
Torrubia, P. Lozano; Axinte, D. A.
2016-01-01
Abrasive micro-waterjet processing is a non-conventional machining method that can be used to manufacture complex shapes in difficult-to-cut materials. Predicting the effect of the jet on the surface for a given set of machine parameters is a key element of controlling the process. However, the noise of the process is significant, making it difficult to design reliable jet-path strategies that produce good quality parts via controlled-depth milling. The process is highly unstable and has a strong random component that can affect the quality of the workpiece, especially in the case of controlled-depth milling. This study describes a method to predict the variability of the jet footprint for different jet feed speeds. A stochastic partial differential equation is used to describe the etched surface as the jet is moved over it, assuming that the erosion process can be divided into two main components: a deterministic part that corresponds to the average erosion of the jet and a stochastic part that accounts for the noise generated at different stages of the process. The model predicts the variability of the trench profiles to within less than 8%. These advances could enable abrasive micro-waterjet technology to be a suitable technology for controlled-depth milling. PMID:27118905
Optimal information diffusion in stochastic block models.
Curato, Gianbiagio; Lillo, Fabrizio
2016-09-01
We use the linear threshold model to study the diffusion of information on a network generated by the stochastic block model. We focus our analysis on a two-community structure where the initial set of informed nodes lies only in one of the two communities and we look for optimal network structures, i.e., those maximizing the asymptotic extent of the diffusion. We find that, constraining the mean degree and the fraction of initially informed nodes, the optimal structure can be assortative (modular), core-periphery, or even disassortative. We then look for minimal cost structures, i.e., those for which a minimal fraction of initially informed nodes is needed to trigger a global cascade. We find that the optimal networks are assortative but with a structure very close to a core-periphery graph, i.e., a very dense community linked to a much more sparsely connected periphery.
Stochastic Modeling and Analysis of Power System with Renewable Generation
DEFF Research Database (Denmark)
Chen, Peiyuan
. With the increasing number of wind turbines (WTs) connected to distribution systems, network operators are concerned about how such a stochastic generation affects power losses of the network. Furthermore, the operators need to estimate how much and when the stochastic generation can reduce the loading of substation...... be achieved through a probabilistic analysis that takes into account the stochastic behavior of wind power generation (WPG) and load demand. Such a probabilistic analysis may help network operators to cut down the cost associated with system planning. Thus, the objective of this thesis is to develop...... stochastic models of renewable generation and load demand for the optimal operation and planning of modern distribution systems through a probabilistic approach. On the basis of statistical data, stochastic models of WPG, load and combined heat and power (CHP) generation are developed. The stochastic wind...
An adaptive stochastic model for financial markets
International Nuclear Information System (INIS)
Hernández, Juan Antonio; Benito, Rosa Marı´a; Losada, Juan Carlos
2012-01-01
An adaptive stochastic model is introduced to simulate the behavior of real asset markets. The model adapts itself by changing its parameters automatically on the basis of the recent historical data. The basic idea underlying the model is that a random variable uniformly distributed within an interval with variable extremes can replicate the histograms of asset returns. These extremes are calculated according to the arrival of new market information. This adaptive model is applied to the daily returns of three well-known indices: Ibex35, Dow Jones and Nikkei, for three complete years. The model reproduces the histograms of the studied indices as well as their autocorrelation structures. It produces the same fat tails and the same power laws, with exactly the same exponents, as in the real indices. In addition, the model shows a great adaptation capability, anticipating the volatility evolution and showing the same volatility clusters observed in the assets. This approach provides a novel way to model asset markets with internal dynamics which changes quickly with time, making it impossible to define a fixed model to fit the empirical observations.
Review of "Stochastic Modelling for Systems Biology" by Darren Wilkinson
Directory of Open Access Journals (Sweden)
Bullinger Eric
2006-12-01
Full Text Available Abstract "Stochastic Modelling for Systems Biology" by Darren Wilkinson introduces the peculiarities of stochastic modelling in biology. This book is particularly suited to as a textbook or for self-study, and for readers with a theoretical background.
Estimation of Stochastic Volatility Models by Nonparametric Filtering
DEFF Research Database (Denmark)
Kanaya, Shin; Kristensen, Dennis
2016-01-01
/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases...
A stochastic modeling of recurrent measles epidemic | Kassem ...
African Journals Online (AJOL)
A simple stochastic mathematical model is developed and investigated for the dynamics of measles epidemic. The model, which is a multi-dimensional diffusion process, includes susceptible individuals, latent (exposed), infected and removed individuals. Stochastic effects are assumed to arise in the process of infection of ...
Approximate models for broken clouds in stochastic radiative transfer theory
International Nuclear Information System (INIS)
Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas
2014-01-01
This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models
Interplanetary Alfvenic fluctuations: A stochastic model
International Nuclear Information System (INIS)
Barnes, A.
1981-01-01
The strong alignment of the average directions of minimum magnetic variance and mean magnetic field in interplanetary Alfvenic fluctuations is inconsistent with the usual wave-propagation models. We investigate the concept of minimum variance for nonplanar Alfvenic fluctuations in which the field direction varies stochastically. It is found that the tendency of the minimum variance and mean field directions to be aligned may be purely a consequence of the randomness of the field direction. In particular, a well-defined direction of minimum variance does not imply that the fluctuations are necessarily planar. The fluctuation power spectrum is a power law for frequencies much higher than the inverse of the correlation time. The probability distribution of directions a randomly fluctuating field of constant magnitude is calculated. A new approach for observational studies of interplanetary fluctuations is suggested
Spatial Stochastic Point Models for Reservoir Characterization
Energy Technology Data Exchange (ETDEWEB)
Syversveen, Anne Randi
1997-12-31
The main part of this thesis discusses stochastic modelling of geology in petroleum reservoirs. A marked point model is defined for objects against a background in a two-dimensional vertical cross section of the reservoir. The model handles conditioning on observations from more than one well for each object and contains interaction between objects, and the objects have the correct length distribution when penetrated by wells. The model is developed in a Bayesian setting. The model and the simulation algorithm are demonstrated by means of an example with simulated data. The thesis also deals with object recognition in image analysis, in a Bayesian framework, and with a special type of spatial Cox processes called log-Gaussian Cox processes. In these processes, the logarithm of the intensity function is a Gaussian process. The class of log-Gaussian Cox processes provides flexible models for clustering. The distribution of such a process is completely characterized by the intensity and the pair correlation function of the Cox process. 170 refs., 37 figs., 5 tabs.
Stochastic dynamical models for ecological regime shifts
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Jacob; Madsen, Henrik
phytoplankton and benthic vegetation with feedback mechanisms is formulated, and it is demonstrated that bistability can occur for specific parameter settings. When stochastic input and stochastic propagation of the states are applied on the system regime shifts occur more frequently, and the threshold...
Stochastic modeling of sunshine number data
Energy Technology Data Exchange (ETDEWEB)
Brabec, Marek, E-mail: mbrabec@cs.cas.cz [Department of Nonlinear Modeling, Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodarenskou vezi 2, 182 07 Prague 8 (Czech Republic); Paulescu, Marius [Physics Department, West University of Timisoara, V. Parvan 4, 300223 Timisoara (Romania); Badescu, Viorel [Candida Oancea Institute, Polytechnic University of Bucharest, Spl. Independentei 313, 060042 Bucharest (Romania)
2013-11-13
In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar
Stochastic modeling of sunshine number data
International Nuclear Information System (INIS)
Brabec, Marek; Paulescu, Marius; Badescu, Viorel
2013-01-01
In this paper, we will present a unified statistical modeling framework for estimation and forecasting sunshine number (SSN) data. Sunshine number has been proposed earlier to describe sunshine time series in qualitative terms (Theor Appl Climatol 72 (2002) 127-136) and since then, it was shown to be useful not only for theoretical purposes but also for practical considerations, e.g. those related to the development of photovoltaic energy production. Statistical modeling and prediction of SSN as a binary time series has been challenging problem, however. Our statistical model for SSN time series is based on an underlying stochastic process formulation of Markov chain type. We will show how its transition probabilities can be efficiently estimated within logistic regression framework. In fact, our logistic Markovian model can be relatively easily fitted via maximum likelihood approach. This is optimal in many respects and it also enables us to use formalized statistical inference theory to obtain not only the point estimates of transition probabilities and their functions of interest, but also related uncertainties, as well as to test of various hypotheses of practical interest, etc. It is straightforward to deal with non-homogeneous transition probabilities in this framework. Very importantly from both physical and practical points of view, logistic Markov model class allows us to test hypotheses about how SSN dependents on various external covariates (e.g. elevation angle, solar time, etc.) and about details of the dynamic model (order and functional shape of the Markov kernel, etc.). Therefore, using generalized additive model approach (GAM), we can fit and compare models of various complexity which insist on keeping physical interpretation of the statistical model and its parts. After introducing the Markovian model and general approach for identification of its parameters, we will illustrate its use and performance on high resolution SSN data from the Solar
Stochastic growth logistic model with aftereffect for batch fermentation process
International Nuclear Information System (INIS)
Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md
2014-01-01
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits
Gompertzian stochastic model with delay effect to cervical cancer growth
International Nuclear Information System (INIS)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah
2015-01-01
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits
Stochastic growth logistic model with aftereffect for batch fermentation process
Energy Technology Data Exchange (ETDEWEB)
Rosli, Norhayati; Ayoubi, Tawfiqullah [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah; Rahman, Haliza Abdul [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia); Salleh, Madihah Md [Department of Biotechnology Industry, Faculty of Biosciences and Bioengineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2014-06-19
In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.
Gompertzian stochastic model with delay effect to cervical cancer growth
Energy Technology Data Exchange (ETDEWEB)
Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor and UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2015-02-03
In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.
2011-05-12
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
A stochastic model for early placental development.
Cotter, Simon L
2014-08-01
In the human, placental structure is closely related to placental function and consequent pregnancy outcome. Studies have noted abnormal placental shape in small-for-gestational-age infants which extends to increased lifetime risk of cardiovascular disease. The origins and determinants of placental shape are incompletely understood and are difficult to study in vivo. In this paper, we model the early development of the human placenta, based on the hypothesis that this is driven by a chemoattractant effect emanating from proximal spiral arteries in the decidua. We derive and explore a two-dimensional stochastic model, and investigate the effects of loss of spiral arteries in regions near to the cord insertion on the shape of the placenta. This model demonstrates that disruption of spiral arteries can exert profound effects on placental shape, particularly if this is close to the cord insertion. Thus, placental shape reflects the underlying maternal vascular bed. Abnormal placental shape may reflect an abnormal uterine environment, predisposing to pregnancy complications. Through statistical analysis of model placentas, we are able to characterize the probability that a given placenta grew in a disrupted environment, and even able to distinguish between different disruptions.
Stochastic modelling of two-phase flows including phase change
International Nuclear Information System (INIS)
Hurisse, O.; Minier, J.P.
2011-01-01
Stochastic modelling has already been developed and applied for single-phase flows and incompressible two-phase flows. In this article, we propose an extension of this modelling approach to two-phase flows including phase change (e.g. for steam-water flows). Two aspects are emphasised: a stochastic model accounting for phase transition and a modelling constraint which arises from volume conservation. To illustrate the whole approach, some remarks are eventually proposed for two-fluid models. (authors)
On the small-time behavior of stochastic logistic models
Directory of Open Access Journals (Sweden)
Dung Tien Nguyen
2017-09-01
Full Text Available In this paper we investigate the small-time behaviors of the solution to a stochastic logistic model. The obtained results allow us to estimate the number of individuals in the population and can be used to study stochastic prey-predator systems.
A probabilistic graphical model based stochastic input model construction
International Nuclear Information System (INIS)
Wan, Jiang; Zabaras, Nicholas
2014-01-01
Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media
Stochastic modeling of virus capsid assembly pathways
Schwartz, Russell
2009-03-01
Virus capsids have become a key model system for understanding self-assembly due to their high complexity, robust and efficient assembly processes, and experimental tractability. Our ability to directly examine and manipulate capsid assembly kinetics in detail nonetheless remains limited, creating a need for computer models that can infer experimentally inaccessible features of the assembly process and explore the effects of hypothetical manipulations on assembly trajectories. We have developed novel algorithms for stochastic simulation of capsid assembly [1,2] that allow us to model capsid assembly over broad parameter spaces [3]. We apply these methods to study the nature of assembly pathway control in virus capsids as well as their sensitivity to assembly conditions and possible experimental interventions. [4pt] [1] F. Jamalyaria, R. Rohlfs, and R. Schwartz. J Comp Phys 204, 100 (2005). [0pt] [2] N. Misra and R. Schwartz. J Chem Phys 129, in press (2008). [0pt] [3] B. Sweeney, T. Zhang, and R. Schwartz. Biophys J 94, 772 (2008).
Stochastic Modeling of Reinforced Concrete Structures Exposed to Chloride Attack
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Frier, Christian
2003-01-01
concentration and reinforcement cover depth are modeled by stochastic fields. The paper contains a description of the parameters to be included in a stochastic model and a proposal for the information needed to obtain values for the parameters in order to be ab le to perform reliability investigations...... the reinforcement exceeds a critical threshold value. In the present paper a stochastic model is described by which the chloride content in a reinforced concrete structure can be estimated. The chloride ingress is modeled by a 2-dimensional diffusion process and the diffusion coefficient, surface chloride...
A hierarchical stochastic model for bistable perception.
Directory of Open Access Journals (Sweden)
Stefan Albert
2017-11-01
Full Text Available Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM, which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group
A hierarchical stochastic model for bistable perception.
Albert, Stefan; Schmack, Katharina; Sterzer, Philipp; Schneider, Gaby
2017-11-01
Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM) for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM), which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group differences to
Stochastic modeling of wetland-groundwater systems
Bertassello, Leonardo Enrico; Rao, P. Suresh C.; Park, Jeryang; Jawitz, James W.; Botter, Gianluca
2018-02-01
Modeling and data analyses were used in this study to examine the temporal hydrological variability in geographically isolated wetlands (GIWs), as influenced by hydrologic connectivity to shallow groundwater, wetland bathymetry, and subject to stochastic hydro-climatic forcing. We examined the general case of GIWs coupled to shallow groundwater through exfiltration or infiltration across wetland bottom. We also examined limiting case with the wetland stage as the local expression of the shallow groundwater. We derive analytical expressions for the steady-state probability density functions (pdfs) for wetland water storage and stage using few, scaled, physically-based parameters. In addition, we analyze the hydrologic crossing time properties of wetland stage, and the dependence of the mean hydroperiod on climatic and wetland morphologic attributes. Our analyses show that it is crucial to account for shallow groundwater connectivity to fully understand the hydrologic dynamics in wetlands. The application of the model to two different case studies in Florida, jointly with a detailed sensitivity analysis, allowed us to identify the main drivers of hydrologic dynamics in GIWs under different climate and morphologic conditions.
Stochastic Watershed Models for Risk Based Decision Making
Vogel, R. M.
2017-12-01
Over half a century ago, the Harvard Water Program introduced the field of operational or synthetic hydrology providing stochastic streamflow models (SSMs), which could generate ensembles of synthetic streamflow traces useful for hydrologic risk management. The application of SSMs, based on streamflow observations alone, revolutionized water resources planning activities, yet has fallen out of favor due, in part, to their inability to account for the now nearly ubiquitous anthropogenic influences on streamflow. This commentary advances the modern equivalent of SSMs, termed `stochastic watershed models' (SWMs) useful as input to nearly all modern risk based water resource decision making approaches. SWMs are deterministic watershed models implemented using stochastic meteorological series, model parameters and model errors, to generate ensembles of streamflow traces that represent the variability in possible future streamflows. SWMs combine deterministic watershed models, which are ideally suited to accounting for anthropogenic influences, with recent developments in uncertainty analysis and principles of stochastic simulation
Boundary effects on population dynamics in stochastic lattice Lotka-Volterra models
Heiba, Bassel; Chen, Sheng; Täuber, Uwe C.
2018-02-01
We investigate spatially inhomogeneous versions of the stochastic Lotka-Volterra model for predator-prey competition and coexistence by means of Monte Carlo simulations on a two-dimensional lattice with periodic boundary conditions. To study boundary effects for this paradigmatic population dynamics system, we employ a simulation domain split into two patches: Upon setting the predation rates at two distinct values, one half of the system resides in an absorbing state where only the prey survives, while the other half attains a stable coexistence state wherein both species remain active. At the domain boundary, we observe a marked enhancement of the predator population density. The predator correlation length displays a minimum at the boundary, before reaching its asymptotic constant value deep in the active region. The frequency of the population oscillations appears only very weakly affected by the existence of two distinct domains, in contrast to their attenuation rate, which assumes its largest value there. We also observe that boundary effects become less prominent as the system is successively divided into subdomains in a checkerboard pattern, with two different reaction rates assigned to neighboring patches. When the domain size becomes reduced to the scale of the correlation length, the mean population densities attain values that are very similar to those in a disordered system with randomly assigned reaction rates drawn from a bimodal distribution.
Model selection for integrated pest management with stochasticity.
Akman, Olcay; Comar, Timothy D; Hrozencik, Daniel
2018-04-07
In Song and Xiang (2006), an integrated pest management model with periodically varying climatic conditions was introduced. In order to address a wider range of environmental effects, the authors here have embarked upon a series of studies resulting in a more flexible modeling approach. In Akman et al. (2013), the impact of randomly changing environmental conditions is examined by incorporating stochasticity into the birth pulse of the prey species. In Akman et al. (2014), the authors introduce a class of models via a mixture of two birth-pulse terms and determined conditions for the global and local asymptotic stability of the pest eradication solution. With this work, the authors unify the stochastic and mixture model components to create further flexibility in modeling the impacts of random environmental changes on an integrated pest management system. In particular, we first determine the conditions under which solutions of our deterministic mixture model are permanent. We then analyze the stochastic model to find the optimal value of the mixing parameter that minimizes the variance in the efficacy of the pesticide. Additionally, we perform a sensitivity analysis to show that the corresponding pesticide efficacy determined by this optimization technique is indeed robust. Through numerical simulations we show that permanence can be preserved in our stochastic model. Our study of the stochastic version of the model indicates that our results on the deterministic model provide informative conclusions about the behavior of the stochastic model. Copyright © 2017 Elsevier Ltd. All rights reserved.
Determining Reduced Order Models for Optimal Stochastic Reduced Order Models
Energy Technology Data Exchange (ETDEWEB)
Bonney, Matthew S. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Brake, Matthew R.W. [Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2015-08-01
The use of parameterized reduced order models(PROMs) within the stochastic reduced order model (SROM) framework is a logical progression for both methods. In this report, five different parameterized reduced order models are selected and critiqued against the other models along with truth model for the example of the Brake-Reuss beam. The models are: a Taylor series using finite difference, a proper orthogonal decomposition of the the output, a Craig-Bampton representation of the model, a method that uses Hyper-Dual numbers to determine the sensitivities, and a Meta-Model method that uses the Hyper-Dual results and constructs a polynomial curve to better represent the output data. The methods are compared against a parameter sweep and a distribution propagation where the first four statistical moments are used as a comparison. Each method produces very accurate results with the Craig-Bampton reduction having the least accurate results. The models are also compared based on time requirements for the evaluation of each model where the Meta- Model requires the least amount of time for computation by a significant amount. Each of the five models provided accurate results in a reasonable time frame. The determination of which model to use is dependent on the availability of the high-fidelity model and how many evaluations can be performed. Analysis of the output distribution is examined by using a large Monte-Carlo simulation along with a reduced simulation using Latin Hypercube and the stochastic reduced order model sampling technique. Both techniques produced accurate results. The stochastic reduced order modeling technique produced less error when compared to an exhaustive sampling for the majority of methods.
On changes of measure in stochastic volatility models
Directory of Open Access Journals (Sweden)
Bernard Wong
2006-01-01
models. This had led many researchers to “assume the condition away,” even though the condition is not innocuous, and nonsensical results can occur if it is in fact not satisfied. We provide an applicable theorem to check the conditions for a general class of Markovian stochastic volatility models. As an example we will also provide a detailed analysis of the Stein and Stein and Heston stochastic volatility models.
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Directory of Open Access Journals (Sweden)
A. Valor
2013-01-01
Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.
Medium Term Hydroelectric Production Planning - A Multistage Stochastic Optimization Model
Directory of Open Access Journals (Sweden)
BITA ANALUI
2014-06-01
Full Text Available Multistage stochastic programming is a key technology for making decisions over time in an uncertain environment. One of the promising areas in which this technology is implementable, is medium term planning of electricity production and trading where decision makers are typically faced with uncertain parameters (such as future demands and market prices that can be described by stochastic processes in discrete time. We apply this methodology to hydrosystem operation assuming random electricity prices and random inflows to the reservoir system. After describing the multistage stochastic model a simple case study is presented. In particular we use the model for pricing an electricity delivery contract in the framework of indifference pricing.
Some Remarks on Stochastic Versions of the Ramsey Growth Model
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2012-01-01
Roč. 19, č. 29 (2012), s. 139-152 ISSN 1212-074X R&D Projects: GA ČR GAP402/10/1610; GA ČR GAP402/10/0956; GA ČR GAP402/11/0150 Institutional support: RVO:67985556 Keywords : Economic dynamics * Ramsey growth model with disturbance * stochastic dynamic programming * multistage stochastic programs Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2013/E/sladky-some remarks on stochastic versions of the ramsey growth model.pdf
Stochastic models for predicting pitting corrosion damage of HLRW containers
International Nuclear Information System (INIS)
Henshall, G.A.
1991-10-01
Stochastic models for predicting aqueous pitting corrosion damage of high-level radioactive-waste containers are described. These models could be used to predict the time required for the first pit to penetrate a container and the increase in the number of breaches at later times, both of which would be useful in the repository system performance analysis. Monte Carlo implementations of the stochastic models are described, and predictions of induction time, survival probability and pit depth distributions are presented. These results suggest that the pit nucleation probability decreases with exposure time and that pit growth may be a stochastic process. The advantages and disadvantages of the stochastic approach, methods for modeling the effects of environment, and plans for future work are discussed
Asymptotic and transient analysis of stochastic core ecosystem models
Directory of Open Access Journals (Sweden)
Thomas C. Gard
2000-07-01
Full Text Available General results on ultimate boundedness and exit probability estimates for stochastic differential equations are applied to investigate asymptotic and transient properties of models of plankton-fish dynamics in uncertain environments
Logics and Models for Stochastic Analysis Beyond Markov Chains
DEFF Research Database (Denmark)
Zeng, Kebin
form of discrete PH distributions as computational vehicle on measuring the performance of concurrent wireless sensor networks. Secondly, choosing stochastic process algebras as a widely accepted formalism, we study the compositionality of continuous PH distributions in order to support modelling...
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Valor, A.; Caleyo, F.; Alfonso, L.; Velázquez, J. C.; Hallen, J. M.
2013-01-01
The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure ...
A Jump-Diffusion Model with Stochastic Volatility and Durations
DEFF Research Database (Denmark)
Wei, Wei; Pelletier, Denis
Market microstructure theories suggest that the durations between transactions carry information about volatility. This paper puts forward a model featuring stochastic volatility, stochastic conditional duration, and jumps to analyze high frequency returns and durations. Durations affect price...... jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We adopt a bivariate Ornstein-Ulenbeck process to model intraday volatility and conditional duration. We develop a MCMC algorithm for the inference on irregularly spaced multivariate processes with jumps...
On the Stochastic Dynamics of a Social Epidemics Model
Directory of Open Access Journals (Sweden)
Xun-Yang Wang
2017-01-01
Full Text Available Alcohol abuse is a major social problem, which has caused a lot of damages or hidden dangers to the individual and the society. In this paper, with random factors of alcoholism considered in mortality rate of compartment populations, we formulate a stochastic alcoholism model according to compartment theory of infectious disease. Based on this model, we investigate the long-term stochastic dynamics behaviors of two equilibria of the corresponding deterministic model and point out the effect of random disturbance on the stability of the system. We find that when R0≤1, we get the estimation between the trajectory of stochastic system and E0=(Π/μs,0,0,0 in the average in time with respect to the disturbance intensity, while when R0>1, stochastic system is ergodic and has the unique stationary distribution. Finally, we carry out numerical simulations to support the corresponding theoretical results.
Stochastic dynamic programming model for optimal resource ...
Indian Academy of Sciences (India)
M Bhuvaneswari
2018-04-11
Apr 11, 2018 ... containers, doctors, nurses, cash and stocks. Similarly, the uncertainty may have different characterizations in these applications. An approximate stochastic dynamic programming (SDP) [3] allows nodes with a number of possible actions with clear strategies for devising an effective decision on optimal ...
Composed particle model in stochastic electrodynamics
International Nuclear Information System (INIS)
Brunini, S.A.
1985-01-01
We analyse the statistical properties of the non-relativistic motion of a particle that has two constituents having finite nasses and charges. The main interaction is in contact with thermal and zero point radiation of Stochastic Electrodynamics. (M.W.O.) [pt
Multivariate moment closure techniques for stochastic kinetic models
Energy Technology Data Exchange (ETDEWEB)
Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
A complementarity model for solving stochastic natural gas market equilibria
International Nuclear Information System (INIS)
Zhuang Jifang; Gabriel, Steven A.
2008-01-01
This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each player in which the first-stage decisions relate to long-term contracts and the second-stage decisions relate to spot market activities for three seasons. Besides showing that such a market model is an instance of a MiCP, we provide theoretical results concerning long-term and spot market prices and solve the resulting MiCP for a small yet representative market. We also note an interesting observation for the value of the stochastic solution for non-optimization problems
A complementarity model for solving stochastic natural gas market equilibria
International Nuclear Information System (INIS)
Jifang Zhuang; Gabriel, S.A.
2008-01-01
This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each player in which the first-stage decisions relate to long-term contracts and the second-stage decisions relate to spot market activities for three seasons. Besides showing that such a market model is an instance of a MiCP, we provide theoretical results concerning long-term and spot market prices and solve the resulting MiCP for a small yet representative market. We also note an interesting observation for the value of the stochastic solution for non-optimization problems. (author)
Tsunamis: stochastic models of occurrence and generation mechanisms
Geist, Eric L.; Oglesby, David D.
2014-01-01
The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.
Stochastic bifurcation in a model of love with colored noise
Yue, Xiaokui; Dai, Honghua; Yuan, Jianping
2015-07-01
In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.
Directory of Open Access Journals (Sweden)
Elston Timothy C
2004-03-01
Full Text Available Abstract Background Intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks. Results We have developed the software package Biochemical Network Stochastic Simulator (BioNetS for efficientlyand accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solvesthe appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS. Conclusions We have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.
Analysis of stochastic effects in Kaldor-type business cycle discrete model
Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna
2016-07-01
We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions ;chaos-order; is discussed.
Analysis of stochastic model for nonlinear volcanic dynamics
Alexandrov, D. V.; Bashkirtseva, I. A.; Ryashko, L. B.
2015-01-01
Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al.~(2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for a solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories ar...
Analysis of stochastic model for non-linear volcanic dynamics
D. Alexandrov; I. Bashkirtseva; L. Ryashko
2014-01-01
Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al. (2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random ...
A Stochastic Continuous Time Model for Microgrid Energy Management
Heymann, Benjamin; Frédéric Bonnans, J; Silva, Francisco; Jimenez, Guillermo
2016-01-01
International audience; We propose a novel stochastic control formulation for the microgrid energy management problem and extend previous works on continuous time rolling horizon strategy to uncertain demand. We modelize the demand dynamics with a stochastic differential equation. We decompose this dynamics into three terms: an average drift, a time-dependent mean-reversion term and a Brownian noise. We use BOCOPHJB for the numerical simulations. This optimal control toolbox implements a semi...
Analysis of dynamic regimes in stochastically forced Kaldor model
International Nuclear Information System (INIS)
Bashkirtseva, Irina; Ryazanova, Tatyana; Ryashko, Lev
2015-01-01
We consider the business cycle Kaldor model forced by random noise. Detailed parametric analysis of deterministic system is carried out and zones of coexisting stable equilibrium and stable limit cycle are found. Noise-induced transitions between these attractors are studied using stochastic sensitivity function technique and confidence domains method. Critical values of noise intensity corresponding to noise-induced transitions “equilibrium → cycle” and “cycle → equilibrium” are estimated. Dominants in combined stochastic regimes are discussed.
The multivariate supOU stochastic volatility model
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole; Stelzer, Robert
structure of the volatility, the log returns, as well as their "squares" are discussed in detail. Moreover, we give several examples in which long memory effects occur and study how the model as well as the simple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations......Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order....... In particular, the models are shown to be preserved under invertible linear transformations. Finally, we discuss how (sup)OU stochastic volatility models can be combined with a factor modelling approach....
Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models
International Nuclear Information System (INIS)
Eyink, Gregory L.
2009-01-01
We prove that smooth solutions of nonideal (viscous and resistive) incompressible magnetohydrodynamic (MHD) equations satisfy a stochastic law of flux conservation. This property implies that the magnetic flux through a surface is equal to the average of the magnetic fluxes through an ensemble of surfaces advected backward in time by the plasma velocity perturbed with a random white noise. Our result is an analog of the well-known Alfven theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein and Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the nonideal MHD equations but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall MHD and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux conservation remains stochastic in that limit.
Modeling ion channel dynamics through reflected stochastic differential equations.
Dangerfield, Ciara E; Kay, David; Burrage, Kevin
2012-05-01
Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks.
Stochastic models to simulate paratuberculosis in dairy herds
DEFF Research Database (Denmark)
Nielsen, Søren Saxmose; Weber, M.F.; Kudahl, Anne Margrethe Braad
2011-01-01
Stochastic simulation models are widely accepted as a means of assessing the impact of changes in daily management and the control of different diseases, such as paratuberculosis, in dairy herds. This paper summarises and discusses the assumptions of four stochastic simulation models and their use...... the models are somewhat different in their underlying principles and do put slightly different values on the different strategies, their overall findings are similar. Therefore, simulation models may be useful in planning paratuberculosis strategies in dairy herds, although as with all models caution...
Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations
Christensen, H. M.; Dawson, A.; Palmer, T.
2017-12-01
Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.
Deterministic and stochastic CTMC models from Zika disease transmission
Zevika, Mona; Soewono, Edy
2018-03-01
Zika infection is one of the most important mosquito-borne diseases in the world. Zika virus (ZIKV) is transmitted by many Aedes-type mosquitoes including Aedes aegypti. Pregnant women with the Zika virus are at risk of having a fetus or infant with a congenital defect and suffering from microcephaly. Here, we formulate a Zika disease transmission model using two approaches, a deterministic model and a continuous-time Markov chain stochastic model. The basic reproduction ratio is constructed from a deterministic model. Meanwhile, the CTMC stochastic model yields an estimate of the probability of extinction and outbreaks of Zika disease. Dynamical simulations and analysis of the disease transmission are shown for the deterministic and stochastic models.
Stochastic model of forecasting spare parts demand
Directory of Open Access Journals (Sweden)
Ivan S. Milojević
2012-01-01
Full Text Available If demand is known for the whole planning period (complete information, then this type of demand or a supply system is deterministic. In the simplest cases, the demand per time unit is constant. If demand levels change over time following a precisely determined and pre-known principle, this type of demand is also classified as deterministic. This quality of demand is very rare. In most cases demand is the product of a process, for example TMS maintenance, whose progression cannot be predicted due to a number of factors influencing the process and causing random demand changes. In this case, a supply system must function according to the complete information and with a certain degree of uncertainty. In cases when demand may be defined by some of the laws of the probability theory, we are talking about stochastic demand and a stochastic supply system. Demand can be described by mathematical expectation, mathematical expectation and standard deviation, probability distribution or as a random process. However, there is usually a need for the most complex description, i.e. the complex random process because both intensity of demand and the probability distribution change during the observed intervals. The level of temporal (dynamic series is traditionally considered as a complex phenomenon consisting of four components: - basic tendency of phenomenon development - cyclical impact (long-term, 'ancient' - seasonal effects - random fluctuations. The basic tendency of phenomenon development means a long-term evolution of phenomena. A function that expresses the trajectory of changes of the basic tendency of a phenomenon development in the form of the equation is called a trend. Often, the trend involves time regression; i.e. the coefficients of the proposed functions are often determined by the least squares method. To roughly determine the coefficients of the proposed function, the sum of three and three-point methods are also used. After checking the
Electricity Market Stochastic Dynamic Model and Its Mean Stability Analysis
Directory of Open Access Journals (Sweden)
Zhanhui Lu
2014-01-01
Full Text Available Based on the deterministic dynamic model of electricity market proposed by Alvarado, a stochastic electricity market model, considering the random nature of demand sides, is presented in this paper on the assumption that generator cost function and consumer utility function are quadratic functions. The stochastic electricity market model is a generalization of the deterministic dynamic model. Using the theory of stochastic differential equations, stochastic process theory, and eigenvalue techniques, the determining conditions of the mean stability for this electricity market model under small Gauss type random excitation are provided and testified theoretically. That is, if the demand elasticity of suppliers is nonnegative and the demand elasticity of consumers is negative, then the stochastic electricity market model is mean stable. It implies that the stability can be judged directly by initial data without any computation. Taking deterministic electricity market data combined with small Gauss type random excitation as numerical samples to interpret random phenomena from a statistical perspective, the results indicate the conclusions above are correct, valid, and practical.
On impulsive integrated pest management models with stochastic effects.
Akman, Olcay; Comar, Timothy D; Hrozencik, Daniel
2015-01-01
We extend existing impulsive differential equation models for integrated pest management (IPM) by including stage structure for both predator and prey as well as by adding stochastic elements in the birth rate of the prey. Based on our model, we propose an approach that incorporates various competing stochastic components. This approach enables us to select a model with optimally determined weights for maximum accuracy and precision in parameter estimation. This is significant in the case of IPM because the proposed model accommodates varying unknown environmental and climatic conditions, which affect the resources needed for pest eradication.
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.
Stochastic evolutions of dynamic traffic flow modeling and applications
Chen, Xiqun (Michael); Shi, Qixin
2015-01-01
This book reveals the underlying mechanisms of complexity and stochastic evolutions of traffic flows. Using Eulerian and Lagrangian measurements, the authors propose lognormal headway/spacing/velocity distributions and subsequently develop a Markov car-following model to describe drivers’ random choices concerning headways/spacings, putting forward a stochastic fundamental diagram model for wide scattering flow-density points. In the context of highway onramp bottlenecks, the authors present a traffic flow breakdown probability model and spatial-temporal queuing model to improve the stability and reliability of road traffic flows. This book is intended for researchers and graduate students in the fields of transportation engineering and civil engineering.
INFERENCE AND SENSITIVITY IN STOCHASTIC WIND POWER FORECAST MODELS.
Elkantassi, Soumaya
2017-10-03
Reliable forecasting of wind power generation is crucial to optimal control of costs in generation of electricity with respect to the electricity demand. Here, we propose and analyze stochastic wind power forecast models described by parametrized stochastic differential equations, which introduce appropriate fluctuations in numerical forecast outputs. We use an approximate maximum likelihood method to infer the model parameters taking into account the time correlated sets of data. Furthermore, we study the validity and sensitivity of the parameters for each model. We applied our models to Uruguayan wind power production as determined by historical data and corresponding numerical forecasts for the period of March 1 to May 31, 2016.
Stochastic description of heterogeneities of permeability within groundwater flow models
International Nuclear Information System (INIS)
Cacas, M.C.; Lachassagne, P.; Ledoux, E.; Marsily, G. de
1991-01-01
In order to model radionuclide migration in the geosphere realistically at the field scale, the hydrogeologist needs to be able to simulate groundwater flow in heterogeneous media. Heterogeneity of the medium can be described using a stochastic approach, that affects the way in which a flow model is formulated. In this paper, we discuss the problems that we have encountered in modelling both continuous and fractured media. The stochastic approach leads to a methodology that enables local measurements of permeability to be integrated into a model which gives a good prediction of groundwater flow on a regional scale. 5 Figs.; 8 Refs
Reconstructing nonlinear dynamic models of gene regulation using stochastic sampling
Directory of Open Access Journals (Sweden)
Reinelt Gerhard
2009-12-01
Full Text Available Abstract Background The reconstruction of gene regulatory networks from time series gene expression data is one of the most difficult problems in systems biology. This is due to several reasons, among them the combinatorial explosion of possible network topologies, limited information content of the experimental data with high levels of noise, and the complexity of gene regulation at the transcriptional, translational and post-translational levels. At the same time, quantitative, dynamic models, ideally with probability distributions over model topologies and parameters, are highly desirable. Results We present a novel approach to infer such models from data, based on nonlinear differential equations, which we embed into a stochastic Bayesian framework. We thus address both the stochasticity of experimental data and the need for quantitative dynamic models. Furthermore, the Bayesian framework allows it to easily integrate prior knowledge into the inference process. Using stochastic sampling from the Bayes' posterior distribution, our approach can infer different likely network topologies and model parameters along with their respective probabilities from given data. We evaluate our approach on simulated data and the challenge #3 data from the DREAM 2 initiative. On the simulated data, we study effects of different levels of noise and dataset sizes. Results on real data show that the dynamics and main regulatory interactions are correctly reconstructed. Conclusions Our approach combines dynamic modeling using differential equations with a stochastic learning framework, thus bridging the gap between biophysical modeling and stochastic inference approaches. Results show that the method can reap the advantages of both worlds, and allows the reconstruction of biophysically accurate dynamic models from noisy data. In addition, the stochastic learning framework used permits the computation of probability distributions over models and model parameters
Stochastic Approximation Methods for Latent Regression Item Response Models
von Davier, Matthias; Sinharay, Sandip
2010-01-01
This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariates…
A stochastic dynamic programming model for stream water quality ...
Indian Academy of Sciences (India)
This paper deals with development of a seasonal fraction-removal policy model for waste load allocation in streams addressing uncertainties due to randomness and fuzziness. A stochastic dynamic programming (SDP) model is developed to arrive at the steady-state seasonal fraction-removal policy. A fuzzy decision model ...
A Hierarchical Latent Stochastic Differential Equation Model for Affective Dynamics
Oravecz, Zita; Tuerlinckx, Francis; Vandekerckhove, Joachim
2011-01-01
In this article a continuous-time stochastic model (the Ornstein-Uhlenbeck process) is presented to model the perpetually altering states of the core affect, which is a 2-dimensional concept underlying all our affective experiences. The process model that we propose can account for the temporal changes in core affect on the latent level. The key…
Effects of Stochastic Traffic Flow Model on Expected System Performance
2012-12-01
feasible. 2.2.2 Brownian Bridge Stochastic Path Model Like the linear model, the Brownian bridge ( Karlin and Taylor 1981) model uses the idea of...IEEE Computer Vision and Pattern Recog- nition Workshop, Piscataway, New Jersey: Institute of Electrical and Electronics Engineers, Inc. Karlin , S
Stochastic models for some meteorological outcomes in Niger Delta ...
African Journals Online (AJOL)
In this paper, stochastic models based on autoregressive integrated moving average models of various orders and its seasonalized versions are presented, with a view to identifying the optimal model for some meteorological outcomes in some cities in Niger Delta region of Nigeria, using Normalized Bayesian Information ...
Introduction to modeling and analysis of stochastic systems
Kulkarni, V G
2011-01-01
This is an introductory-level text on stochastic modeling. It is suited for undergraduate students in engineering, operations research, statistics, mathematics, actuarial science, business management, computer science, and public policy. It employs a large number of examples to teach the students to use stochastic models of real-life systems to predict their performance, and use this analysis to design better systems. The book is devoted to the study of important classes of stochastic processes: discrete and continuous time Markov processes, Poisson processes, renewal and regenerative processes, semi-Markov processes, queueing models, and diffusion processes. The book systematically studies the short-term and the long-term behavior, cost/reward models, and first passage times. All the material is illustrated with many examples, and case studies. The book provides a concise review of probability in the appendix. The book emphasizes numerical answers to the problems. A collection of MATLAB programs to accompany...
Distributed parallel computing in stochastic modeling of groundwater systems.
Dong, Yanhui; Li, Guomin; Xu, Haizhen
2013-03-01
Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.
Deterministic and stochastic models for middle east respiratory syndrome (MERS)
Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning
2018-03-01
World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.
A stochastic model for intermittent search strategies
International Nuclear Information System (INIS)
Benichou, O; Coppey, M; Moreau, M; Suet, P H; Voituriez, R
2005-01-01
It is often necessary, in scientific or everyday life problems, to find a randomly hidden target. What is then the optimal strategy to reach it as rapidly as possible? In this article, we develop a stochastic theory for intermittent search behaviours, which are often observed: the searcher alternates phases of intensive search and slow motion with fast displacements. The first results of this theory have already been announced recently. Here we provide a detailed presentation of the theory, as well as the full derivation of the results. Furthermore, we explicitly discuss the minimization of the time needed to find the target
On the Robustness of Temporal Properties for Stochastic Models
Directory of Open Access Journals (Sweden)
Ezio Bartocci
2013-08-01
Full Text Available Stochastic models such as Continuous-Time Markov Chains (CTMC and Stochastic Hybrid Automata (SHA are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity inherent in biological processes. A classical question in formal modelling with clear relevance to biological modelling is the model checking problem. i.e. calculate the probability that a behaviour, expressed for instance in terms of a certain temporal logic formula, may occur in a given stochastic process. However, one may not only be interested in the notion of satisfiability, but also in the capacity of a system to mantain a particular emergent behaviour unaffected by the perturbations, caused e.g. from extrinsic noise, or by possible small changes in the model parameters. To address this issue, researchers from the verification community have recently proposed several notions of robustness for temporal logic providing suitable definitions of distance between a trajectory of a (deterministic dynamical system and the boundaries of the set of trajectories satisfying the property of interest. The contributions of this paper are twofold. First, we extend the notion of robustness to stochastic systems, showing that this naturally leads to a distribution of robustness scores. By discussing two examples, we show how to approximate the distribution of the robustness score and its key indicators: the average robustness and the conditional average robustness. Secondly, we show how to combine these indicators with the satisfaction probability to address the system design problem, where the goal is to optimize some control parameters of a stochastic model in order to best maximize robustness of the desired specifications.
The critical domain size of stochastic population models.
Reimer, Jody R; Bonsall, Michael B; Maini, Philip K
2017-02-01
Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.
Stochastic reduced order models for inverse problems under uncertainty.
Warner, James E; Aquino, Wilkins; Grigoriu, Mircea D
2015-03-01
This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well.
The role of residence times in two-patch dengue transmission dynamics and optimal strategies.
Lee, Sunmi; Castillo-Chavez, Carlos
2015-06-07
The reemergence and geographical dispersal of vector-borne diseases challenge global health experts around the world and in particular, dengue poses increasing difficulties in the Americas, due in part to explosive urban and semi-urban growth, increases of within and between region mobility, the absence of a vaccine, and the limited resources available for public health services. In this work, a simple deterministic two-patch model is introduced to assess the impact of dengue transmission dynamics in heterogeneous environments. The two-patch system models the movement (e.g. urban versus rural areas residence times) of individuals between and within patches/environments using residence-time matrices with entries that budget within and between host patch relative residence times, under the assumption that only the human budgets their residence time across regions. Three scenarios are considered: (i) resident hosts in Patch i visit patch j, where i≠j but not the other way around, a scenario referred to as unidirectional motion; (ii) symmetric bi-directional motion; and (iii) asymmetric bi-directional motion. Optimal control theory is used to identify and evaluate patch-specific control measures aimed at reducing dengue prevalence in humans and vectors at a minimal cost. Optimal policies are computed under different residence-matrix configurations mentioned above as well as transmissibility scenarios characterized by the magnitude of the basic reproduction number. Optimal patch-specific polices can ameliorate the impact of epidemic outbreaks substantially when the basic reproduction number is moderate. The final patch-specific epidemic size variation increases as the residence time matrix moves away from the symmetric case (asymmetry). As expected, the patch where individuals spend most of their time or in the patch where transmissibility is higher tend to support larger patch-specific final epidemic sizes. Hence, focusing on intervention that target areas where
Stochastic processes analysis in nuclear reactor using ARMA models
International Nuclear Information System (INIS)
Zavaljevski, N.
1990-01-01
The analysis of ARMA model derived from general stochastic state equations of nuclear reactor is given. The dependence of ARMA model parameters on the main physical characteristics of RB nuclear reactor in Vinca is presented. Preliminary identification results are presented, observed discrepancies between theory and experiment are explained and the possibilities of identification improvement are anticipated. (author)
Powering stochastic reliability models by discrete event simulation
DEFF Research Database (Denmark)
Kozine, Igor; Wang, Xiaoyun
2012-01-01
it difficult to find a solution to the problem. The power of modern computers and recent developments in discrete-event simulation (DES) software enable to diminish some of the drawbacks of stochastic models. In this paper we describe the insights we have gained based on using both Markov and DES models...
Dynamic two state stochastic models for ecological regime shifts
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Carstensen, Niels Jacob; Madsen, Henrik
2009-01-01
A simple non-linear stochastic two state, discrete-time model is presented. The interaction between benthic and pelagic vegetation in aquatic ecosystems subject to changing external nutrient loading is described by the nonlinear functions. The dynamical behavior of the deterministic part of the m......A simple non-linear stochastic two state, discrete-time model is presented. The interaction between benthic and pelagic vegetation in aquatic ecosystems subject to changing external nutrient loading is described by the nonlinear functions. The dynamical behavior of the deterministic part...
Reflected stochastic differential equation models for constrained animal movement
Hanks, Ephraim M.; Johnson, Devin S.; Hooten, Mevin B.
2017-01-01
Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modeling unconstrained animal movement. We present methods for simulation and inference based on augmenting the constrained movement path with a latent unconstrained path and illustrate this augmentation with a simulation example and an analysis of telemetry data from a Steller sea lion (Eumatopias jubatus) in southeast Alaska.
International Nuclear Information System (INIS)
Laurens, J.M.
1985-01-01
A computer code was written to model food chains in order to estimate the internal and external doses, for stochastic and non-stochastic effects, on humans (adults and infants). Results are given for 67 radionuclides, for unit concentration in water (1 Bq/L) and in atmosphere (1 Bq/m 3 )
Multi-scenario modelling of uncertainty in stochastic chemical systems
International Nuclear Information System (INIS)
Evans, R. David; Ricardez-Sandoval, Luis A.
2014-01-01
Uncertainty analysis has not been well studied at the molecular scale, despite extensive knowledge of uncertainty in macroscale systems. The ability to predict the effect of uncertainty allows for robust control of small scale systems such as nanoreactors, surface reactions, and gene toggle switches. However, it is difficult to model uncertainty in such chemical systems as they are stochastic in nature, and require a large computational cost. To address this issue, a new model of uncertainty propagation in stochastic chemical systems, based on the Chemical Master Equation, is proposed in the present study. The uncertain solution is approximated by a composite state comprised of the averaged effect of samples from the uncertain parameter distributions. This model is then used to study the effect of uncertainty on an isomerization system and a two gene regulation network called a repressilator. The results of this model show that uncertainty in stochastic systems is dependent on both the uncertain distribution, and the system under investigation. -- Highlights: •A method to model uncertainty on stochastic systems was developed. •The method is based on the Chemical Master Equation. •Uncertainty in an isomerization reaction and a gene regulation network was modelled. •Effects were significant and dependent on the uncertain input and reaction system. •The model was computationally more efficient than Kinetic Monte Carlo
The stochastic model of pitting corrosion of metals
You, Y. H.; Wang, B. R.; Hu, H. Y.
2017-12-01
Considering that pitting corrosion is a stochastic process, the purpose of this paper is to use stochastic theory to investigate the growth process of pitting corrosion of metals. Based on the mechanism of pit growth and nonequilibrium statistical theory, the time evolution equations of pit depth and corrosion rate are obtained, and the probability density function can be derived by solving Fock-Plank Equation. Subsequently, the failure probability or reliability of metals is calculated based on the weakest link model of pitting corrosion. Finally, the stochastic model is used on the aircraft aluminum alloy LD2. Furthermore, this methodology can be applied to analyze the reliability and predict the pitting life of metals.
Stochastic Climate Forcing for Ice-Sheet Models
Nuterman, Roman; Jochum, Markus
2017-04-01
Climate oscillations from glacial periods, with large parts of the continents covered with ice, to warm interglacials like the present one, are observed in various paleoclimatic records over the past few million years. According to Milankovitch theory, which is commonly assumed, these glacial cycles are linked to changes in insolation due to periodic changes of external earth-orbital forcing. However, this relationship is far from understood, because the insolation variations are so small that enhancing feedbacks must be at play. Moreover, there are several shortcomings in the Milankovitch theory: first, the duration of the glacial cycles changed at the so-called Mid-Pleistocene transition from 41,000 years to approximately 100,000 years and second, the interglacial of 400,000 years ago should not have happened. Thus, the current phasing and magnitude of the glacial cycles are far from being well understood and the external perturbation might only play a minor role in comparison to internal stochastic variations or internal oscillations. Although modern Ice-Sheet Models (ISM) are able to simulate evolution of ice-sheets at the entire glacial or interglacial time scales, the state-of-the-art Earth System Models (ESM) are too computationally expensive for such long integrations. Therefore, a constant climate forcing is usually used in the ice-sheet models. However, this approach does not take into account the stochastic nature of climate. At the same time, ESM models provide valuable information on natural climate variability, which then can be used for building stochastic climate models able to generate both continuous and discrete climate variables with stochastic atmospheric processes. In this study, we present a stochastic climate model, built from large sets of Community Earth System Model (CESM) integrations with both internal and external climate forcing, and able to generate synthetic climate forcing (such as temperature and precipitation fields) of any
Stochastic lattice model of synaptic membrane protein domains
Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A.
2017-05-01
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
Stochastic lattice model of synaptic membrane protein domains.
Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A
2017-05-01
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism
Directory of Open Access Journals (Sweden)
Jian Zhang
2017-01-01
Full Text Available A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.
Modeling a SI epidemic with stochastic transmission: hyperbolic incidence rate.
Christen, Alejandra; Maulén-Yañez, M Angélica; González-Olivares, Eduardo; Curé, Michel
2018-03-01
In this paper a stochastic susceptible-infectious (SI) epidemic model is analysed, which is based on the model proposed by Roberts and Saha (Appl Math Lett 12: 37-41, 1999), considering a hyperbolic type nonlinear incidence rate. Assuming the proportion of infected population varies with time, our new model is described by an ordinary differential equation, which is analogous to the equation that describes the double Allee effect. The limit of the solution of this equation (deterministic model) is found when time tends to infinity. Then, the asymptotic behaviour of a stochastic fluctuation due to the environmental variation in the coefficient of disease transmission is studied. Thus a stochastic differential equation (SDE) is obtained and the existence of a unique solution is proved. Moreover, the SDE is analysed through the associated Fokker-Planck equation to obtain the invariant measure when the proportion of the infected population reaches steady state. An explicit expression for invariant measure is found and we study some of its properties. The long time behaviour of deterministic and stochastic models are compared by simulations. According to our knowledge this incidence rate has not been previously used for this type of epidemic models.
Stochastic Modeling of Radioactive Material Releases
International Nuclear Information System (INIS)
Andrus, Jason; Pope, Chad
2015-01-01
Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculates the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was
Stochastic Modeling of Radioactive Material Releases
Energy Technology Data Exchange (ETDEWEB)
Andrus, Jason [Idaho National Lab. (INL), Idaho Falls, ID (United States); Pope, Chad [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
Nonreactor nuclear facilities operated under the approval authority of the U.S. Department of Energy use unmitigated hazard evaluations to determine if potential radiological doses associated with design basis events challenge or exceed dose evaluation guidelines. Unmitigated design basis events that sufficiently challenge dose evaluation guidelines or exceed the guidelines for members of the public or workers, merit selection of safety structures, systems, or components or other controls to prevent or mitigate the hazard. Idaho State University, in collaboration with Idaho National Laboratory, has developed a portable and simple to use software application called SODA (Stochastic Objective Decision-Aide) that stochastically calculates the radiation dose associated with hypothetical radiological material release scenarios. Rather than producing a point estimate of the dose, SODA produces a dose distribution result to allow a deeper understanding of the dose potential. SODA allows users to select the distribution type and parameter values for all of the input variables used to perform the dose calculation. SODA then randomly samples each distribution input variable and calculates the overall resulting dose distribution. In cases where an input variable distribution is unknown, a traditional single point value can be used. SODA was developed using the MATLAB coding framework. The software application has a graphical user input. SODA can be installed on both Windows and Mac computers and does not require MATLAB to function. SODA provides improved risk understanding leading to better informed decision making associated with establishing nuclear facility material-at-risk limits and safety structure, system, or component selection. It is important to note that SODA does not replace or compete with codes such as MACCS or RSAC, rather it is viewed as an easy to use supplemental tool to help improve risk understanding and support better informed decisions. The work was
Response spectrum analysis of a stochastic seismic model
International Nuclear Information System (INIS)
Kimura, Koji; Sakata, Masaru; Takemoto, Shinichiro.
1990-01-01
The stochastic response spectrum approach is presented for predicting the dynamic behavior of structures to earthquake excitation expressed by a random process, one of whose sample functions can be regarded as a recorded strong-motion earthquake accelerogram. The approach consists of modeling recorded ground motion by a random process and the root-mean-square response (rms) analysis of a single-degree-of-freedom system by using the moment equations method. The stochastic response spectrum is obtained as a plot of the maximum rms response versus the natural period of the system and is compared with the conventional response spectrum. (author)
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
S. Peiris (Shelton); M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility
Stochastic Modelling and Optimization of Complex Infrastructure Systems
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
In this paper it is shown that recent progress in stochastic modelling and optimization in combination with advanced computer systems has now made it possible to improve the design and the maintenance strategies for infrastructure systems. The paper concentrates on highway networks and single large...
Optimal Tax Reduction by Depreciation : A Stochastic Model
Berg, M.; De Waegenaere, A.M.B.; Wielhouwer, J.L.
1996-01-01
This paper focuses on the choice of a depreciation method, when trying to minimize the expected value of the present value of future tax payments.In a quite general model that allows for stochastic future cash- ows and a tax structure with tax brackets, we determine the optimal choice between the
A stochastic model for forecast consumption in master scheduling
Weeda, P.J.; Weeda, P.J.
1994-01-01
This paper describes a stochastic model for the reduction of the initial forecast in the Master Schedule (MS) of an MRP system during progress of time by the acceptance of customer orders. Results are given for the expectation and variance of the number of yet unknown deliveries as a function of
Stochastic model of thin market with an indivisible commodity
Czech Academy of Sciences Publication Activity Database
Šmíd, Martin
2005-01-01
Roč. 13, č. 1 (2005), s. 94-100 ISSN 0572-3043 R&D Projects: GA ČR GA402/04/1294 Institutional research plan: CEZ:AV0Z10750506 Keywords : thin market * market price * stochastic models Subject RIV: AH - Economics
Time Ordering in Frontal Lobe Patients: A Stochastic Model Approach
Magherini, Anna; Saetti, Maria Cristina; Berta, Emilia; Botti, Claudio; Faglioni, Pietro
2005-01-01
Frontal lobe patients reproduced a sequence of capital letters or abstract shapes. Immediate and delayed reproduction trials allowed the analysis of short- and long-term memory for time order by means of suitable Markov chain stochastic models. Patients were as proficient as healthy subjects on the immediate reproduction trial, thus showing spared…
Integrated Human Behavior Modeling and Stochastic Control (IHBMSC)
2014-08-01
angle, dwell time, workload). For a 50% target density scenario where the operator discrimination task is fairly difficult, the integrated human ... behavior model and stochastic controller (IHBMSC) was shown to reduce the FA rate from 35% to 5%. Also, the IHBMSC performance was found to be quite robust for lower target densities (5%) and different operators.
Probability density estimation in stochastic environmental models using reverse representations
Van den Berg, E.; Heemink, A.W.; Lin, H.X.; Schoenmakers, J.G.M.
2003-01-01
The estimation of probability densities of variables described by systems of stochastic dierential equations has long been done using forward time estimators, which rely on the generation of realizations of the model, forward in time. Recently, an estimator based on the combination of forward and
Model tracking dual stochastic controller design under irregular internal noises
International Nuclear Information System (INIS)
Lee, Jong Bok; Heo, Hoon; Cho, Yun Hyun; Ji, Tae Young
2006-01-01
Although many methods about the control of irregular external noise have been introduced and implemented, it is still necessary to design a controller that will be more effective and efficient methods to exclude for various noises. Accumulation of errors due to model tracking, internal noises (thermal noise, shot noise and l/f noise) that come from elements such as resistor, diode and transistor etc. in the circuit system and numerical errors due to digital process often destabilize the system and reduce the system performance. New stochastic controller is adopted to remove those noises using conventional controller simultaneously. Design method of a model tracking dual controller is proposed to improve the stability of system while removing external and internal noises. In the study, design process of the model tracking dual stochastic controller is introduced that improves system performance and guarantees robustness under irregular internal noises which can be created internally. The model tracking dual stochastic controller utilizing F-P-K stochastic control technique developed earlier is implemented to reveal its performance via simulation
Stochastic models in risk theory and management accounting
Brekelmans, R.C.M.
2000-01-01
This thesis deals with stochastic models in two fields: risk theory and management accounting. Firstly, two extensions of the classical risk process are analyzed. A method is developed that computes bounds of the probability of ruin for the classical risk rocess extended with a constant interest
A simple stochastic weather generator for ecological modeling
A.G. Birt; M.R. Valdez-Vivas; R.M. Feldman; C.W. Lafon; D. Cairns; R.N. Coulson; M. Tchakerian; W. Xi; Jim Guldin
2010-01-01
Stochastic weather generators are useful tools for exploring the relationship between organisms and their environment. This paper describes a simple weather generator that can be used in ecological modeling projects. We provide a detailed description of methodology, and links to full C++ source code (http://weathergen.sourceforge.net) required to implement or modify...
Stochastic disturbance rejection in model predictive control by randomized algorithms
Batina, Ivo; Stoorvogel, Antonie Arij; Weiland, Siep
2001-01-01
In this paper we consider model predictive control with stochastic disturbances and input constraints. We present an algorithm which can solve this problem approximately but with arbitrary high accuracy. The optimization at each time step is a closed loop optimization and therefore takes into
Hydrological modeling using a multi-site stochastic weather generator
Weather data is usually required at several locations over a large watershed, especially when using distributed models for hydrological simulations. In many applications, spatially correlated weather data can be provided by a multi-site stochastic weather generator which considers the spatial correl...
Application of a stochastic modelling framework to characterize the ...
Indian Academy of Sciences (India)
Home; Journals; Sadhana; Volume 36; Issue 4. Application of a stochastic modelling framework to characterize the inﬂuence of different oxide scales on the solid particle erosion behaviour of boiler grade steel. S K Das. Volume 36 Issue 4 August 2011 pp 425-440 ...
Latent Stochastic Actor Oriented Models for Relational Event Data
2012-03-15
L-SAOMs for Relational Events Latent Stochastic Actor Oriented Models for Relational Event Data J.A. Lospinoso12 J.H. Koskinen2 T.A.B. Snijders2......PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) US
A stochastic large deformation model for computational anatomy
DEFF Research Database (Denmark)
Arnaudon, Alexis; Holm, Darryl D.; Pai, Akshay Sadananda Uppinakudru
2017-01-01
In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation...
Stochastic finite-fault modelling of strong earthquakes in Narmada ...
Indian Academy of Sciences (India)
Stochastic finite fault modelling of strong earthquakes. 839. 1983). It has been widely used to predict the ground motion around the globe where earthquake recordings are scanty. The conventional point source approximation is unable to characterize key features of ground motions from large earthquakes, such as their ...
Stochastic volatility and stochastic leverage
DEFF Research Database (Denmark)
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
Parameter estimation in stochastic rainfall-runoff models
DEFF Research Database (Denmark)
Jonsdottir, Harpa; Madsen, Henrik; Palsson, Olafur Petur
2006-01-01
A parameter estimation method for stochastic rainfall-runoff models is presented. The model considered in the paper is a conceptual stochastic model, formulated in continuous-discrete state space form. The model is small and a fully automatic optimization is, therefore, possible for estimating all....... For a comparison the parameters are also estimated by an output error method, where the sum of squared simulation error is minimized. The former methodology is optimal for short-term prediction whereas the latter is optimal for simulations. Hence, depending on the purpose it is possible to select whether...... the parameter values are optimal for simulation or prediction. The data originates from Iceland and the model is designed for Icelandic conditions, including a snow routine for mountainous areas. The model demands only two input data series, precipitation and temperature and one output data series...
Stochastic Mixing Model with Power Law Decay of Variance
Fedotov, S.; Ihme, M.; Pitsch, H.
2003-01-01
Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.
Epigenetics and Evolution: Transposons and the Stochastic Epigenetic Modification Model
Sergio Branciamore; Andrei S. Rodin; Grigoriy Gogoshin; Arthur D. Riggs
2015-01-01
In addition to genetic variation, epigenetic variation and transposons can greatly affect the evolutionary fitnesses landscape and gene expression. Previously we proposed a mathematical treatment of a general epigenetic variation model that we called Stochastic Epigenetic Modification (SEM) model. In this study we follow up with a special case, the Transposon Silencing Model (TSM), with, once again, emphasis on quantitative treatment. We have investigated the evolutionary effects of epigeneti...
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik
2009-06-01
The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.
A stochastic model for colloid transport and deposition.
Bradford, S A; Toride, N
2007-01-01
Profiles of retained colloids in porous media have frequently been observed to be hyper-exponential or non-monotonic with transport depth under unfavorable attachment conditions, whereas filtration theory predicts an exponential profile. In this work we present a stochastic model for colloid transport and deposition that allows various hypotheses for such deviations to be tested. The model is based on the conventional advective dispersion equation that accounts for first-order kinetic deposition and release of colloids. One or two stochastic parameters can be considered in this model, including the deposition coefficient, the release coefficient, and the average pore water velocity. In the case of one stochastic parameter, the probability density function (PDF) is characterized using log-normal, bimodal log-normal, or a simple two species/region formulation. When two stochastic parameters are considered, then a joint log-normal PDF is employed. Simulation results indicated that variations in the deposition coefficient and the average pore water velocity can both produce hyper-exponential deposition profiles. Bimodal formulations for the PDF were also able to produce hyper-exponential profiles, but with much lower variances in the deposition coefficient. The shape of the deposition profile was found to be very sensitive to the correlation of deposition and release coefficients, and to the correlation of pore water velocity and deposition coefficient. Application of the developed stochastic model to a particular set of colloid transport and deposition data indicated that chemical heterogeneity of the colloid population could not fully explain the observed behavior. Alternative interpretations were therefore proposed based on variability of the pore size and the water velocity distributions.
Application of Stochastic Partial Differential Equations to Reservoir Property Modelling
Potsepaev, R.
2010-09-06
Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.
Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
Directory of Open Access Journals (Sweden)
J. Lévy Véhel
2013-09-01
Full Text Available Multifractional Brownian motion (mBm has proved to be a useful tool in various areas of geophysical modelling. Although a versatile model, mBm is of course not always an adequate one. We present in this work several other stochastic processes which could potentially be useful in geophysics. The first alternative type is that of self-regulating processes: these are models where the local regularity is a function of the amplitude, in contrast to mBm where it is tuned exogenously. We demonstrate the relevance of such models for digital elevation maps and for temperature records. We also briefly describe two other types of alternative processes, which are the counterparts of mBm and of self-regulating processes when the intensity of local jumps is considered in lieu of local regularity: multistable processes allow one to prescribe the local intensity of jumps in space/time, while this intensity is governed by the amplitude for self-stabilizing processes.
Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
Lévy Véhel, J.
2013-09-01
Multifractional Brownian motion (mBm) has proved to be a useful tool in various areas of geophysical modelling. Although a versatile model, mBm is of course not always an adequate one. We present in this work several other stochastic processes which could potentially be useful in geophysics. The first alternative type is that of self-regulating processes: these are models where the local regularity is a function of the amplitude, in contrast to mBm where it is tuned exogenously. We demonstrate the relevance of such models for digital elevation maps and for temperature records. We also briefly describe two other types of alternative processes, which are the counterparts of mBm and of self-regulating processes when the intensity of local jumps is considered in lieu of local regularity: multistable processes allow one to prescribe the local intensity of jumps in space/time, while this intensity is governed by the amplitude for self-stabilizing processes.
Modeling bacterial population growth from stochastic single-cell dynamics.
Alonso, Antonio A; Molina, Ignacio; Theodoropoulos, Constantinos
2014-09-01
A few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature for Escherichia coli, Listeria innocua, and Salmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to
Quantitative sociodynamics stochastic methods and models of social interaction processes
Helbing, Dirk
1995-01-01
Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioural changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics but they have very often proved their explanatory power in chemistry, biology, economics and the social sciences. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces the most important concepts from nonlinear dynamics (synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches a very fundamental dynamic model is obtained which seems to open new perspectives in the social sciences. It includes many established models as special cases, e.g. the log...
Quantitative Sociodynamics Stochastic Methods and Models of Social Interaction Processes
Helbing, Dirk
2010-01-01
This new edition of Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioral changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics and mathematics, but they have very often proven their explanatory power in chemistry, biology, economics and the social sciences as well. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces important concepts from nonlinear dynamics (e.g. synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches, a fundamental dynamic model is obtained, which opens new perspectives in the social sciences. It includes many established models a...
Development of stochastic indicator models of lithology, Yucca Mountain, Nevada
International Nuclear Information System (INIS)
Rautman, C.A.; Robey, T.H.
1994-01-01
Indicator geostatistical techniques have been used to produce a number of fully three-dimensional stochastic simulations of large-scale lithologic categories at the Yucca Mountain site. Each realization reproduces the available drill hole data used to condition the simulation. Information is propagated away from each point of observation in accordance with a mathematical model of spatial continuity inferred through soft data taken from published geologic cross sections. Variations among the simulated models collectively represent uncertainty in the lithology at unsampled locations. These stochastic models succeed in capturing many major features of welded-nonwelded lithologic framework of Yucca Mountain. However, contacts between welded and nonwelded rock types for individual simulations appear more complex than suggested by field observation, and a number of probable numerical artifacts exist in these models. Many of the apparent discrepancies between the simulated models and the general geology of Yucca Mountain represent characterization uncertainty, and can be traced to the sparse site data used to condition the simulations. Several vertical stratigraphic columns have been extracted from the three-dimensional stochastic models for use in simplified total-system performance assessment exercises. Simple, manual adjustments are required to eliminate the more obvious simulation artifacts and to impose a secondary set of deterministic geologic features on the overall stratigraphic framework provided by the indictor models
Stochastic Differential Equation-Based Flexible Software Reliability Growth Model
Directory of Open Access Journals (Sweden)
P. K. Kapur
2009-01-01
Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.
The Stochastic Ising Model with the Mixed Boundary Conditions
Directory of Open Access Journals (Sweden)
Wang Jun
2009-01-01
Full Text Available Abstract We estimate the spectral gap of the two-dimensional stochastic Ising model for four classes of mixed boundary conditions. On a finite square, in the absence of an external field, two-sided estimates on the spectral gap for the first class of (weak positive boundary conditions are given. Further, at inverse temperatures , we will show lower bounds of the spectral gap of the Ising model for the other three classes mixed boundary conditions.
Stochastic Online Learning in Dynamic Networks under Unknown Models
2016-08-02
Stochastic Online Learning in Dynamic Networks under Unknown Models This research aims to develop fundamental theories and practical algorithms for...12211 Research Triangle Park, NC 27709-2211 Online learning , multi-armed bandit, dynamic networks REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S... Online Learning in Dynamic Networks under Unknown Models Report Title This research aims to develop fundamental theories and practical algorithms for
Dynamical behavior of a stochastic SVIR epidemic model with vaccination
Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir
2017-10-01
In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s 1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R˜0s > 1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.
Stochastic programming framework for Lithuanian pension payout modelling
Directory of Open Access Journals (Sweden)
Audrius Kabašinskas
2014-12-01
Full Text Available The paper provides a scientific approach to the problem of selecting a pension fund by taking into account some specific characteristics of the Lithuanian Republic (LR pension accumulation system. The decision making model, which can be used to plan a long-term pension accrual of the Lithuanian Republic (LR citizens, in an optimal way is presented. This model focuses on factors that influence the sustainability of the pension system selection under macroeconomic, social and demographic uncertainty. The model is formalized as a single stage stochastic optimization problem where the long-term optimal strategy can be obtained based on the possible scenarios generated for a particular participant. Stochastic programming methods allow including the pension fund rebalancing moment and direction of investment, and taking into account possible changes of personal income, changes of society and the global financial market. The collection of methods used to generate scenario trees was found useful to solve strategic planning problems.
A stochastic differential equation model for transcriptional regulatory networks
Directory of Open Access Journals (Sweden)
Quirk Michelle D
2007-05-01
Full Text Available Abstract Background This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets. The dynamics of the gene expression level are fitted via a stochastic differential equation model, yielding a set of specific regulators and their contribution. Results We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic differential equation model follows well the dynamic of the gene expression levels. Conclusion When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved models of the transcriptional regulatory networks.
Radio Channel Modelling Using Stochastic Propagation Graphs
DEFF Research Database (Denmark)
Pedersen, Troels; Fleury, Bernard Henri
2007-01-01
In this contribution the radio channel model proposed in [1] is extended to include multiple transmitters and receivers. The propagation environment is modelled using random graphs where vertices of a graph represent scatterers and edges model the wave propagation between scatterers. Furthermore...
Stochastic population dynamic models as probability networks
M.E. and D.C. Lee. Borsuk
2009-01-01
The dynamics of a population and its response to environmental change depend on the balance of birth, death and age-at-maturity, and there have been many attempts to mathematically model populations based on these characteristics. Historically, most of these models were deterministic, meaning that the results were strictly determined by the equations of the model and...
Stochastic modeling of central apnea events in preterm infants
Clark, Matthew T.; Delos, John B.; Lake, Douglas E.; Lee, Hoshik; Fairchild, Karen D.; Kattwinkel, John; Moorman, J. Randall
2016-01-01
Summary A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the NICU. It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 hours) to very unstable (with an average lifetime of 10 seconds). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm – stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events – may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge. PMID:26963049
Stochastic modeling of central apnea events in preterm infants
International Nuclear Information System (INIS)
Clark, Matthew T; Lake, Douglas E; Randall Moorman, J; Delos, John B; Lee, Hoshik; Fairchild, Karen D; Kattwinkel, John
2016-01-01
A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the neonatal intensive care unit (NICU). It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 h) to very unstable (with an average lifetime of 10 s). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm—stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events—may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge. (paper)
Data-driven stochastic modelling of zebrafish locomotion.
Zienkiewicz, Adam; Barton, David A W; Porfiri, Maurizio; di Bernardo, Mario
2015-11-01
In this work, we develop a data-driven modelling framework to reproduce the locomotion of fish in a confined environment. Specifically, we highlight the primary characteristics of the motion of individual zebrafish (Danio rerio), and study how these can be suitably encapsulated within a mathematical framework utilising a limited number of calibrated model parameters. Using data captured from individual zebrafish via automated visual tracking, we develop a model using stochastic differential equations and describe fish as a self propelled particle moving in a plane. Based on recent experimental evidence of the importance of speed regulation in social behaviour, we extend stochastic models of fish locomotion by introducing experimentally-derived processes describing dynamic speed regulation. Salient metrics are defined which are then used to calibrate key parameters of coupled stochastic differential equations, describing both speed and angular speed of swimming fish. The effects of external constraints are also included, based on experimentally observed responses. Understanding the spontaneous dynamics of zebrafish using a bottom-up, purely data-driven approach is expected to yield a modelling framework for quantitative investigation of individual behaviour in the presence of various external constraints or biological assays.
Stochastic modeling of central apnea events in preterm infants.
Clark, Matthew T; Delos, John B; Lake, Douglas E; Lee, Hoshik; Fairchild, Karen D; Kattwinkel, John; Moorman, J Randall
2016-04-01
A near-ubiquitous pathology in very low birth weight infants is neonatal apnea, breathing pauses with slowing of the heart and falling blood oxygen. Events of substantial duration occasionally occur after an infant is discharged from the neonatal intensive care unit (NICU). It is not known whether apneas result from a predictable process or from a stochastic process, but the observation that they occur in seemingly random clusters justifies the use of stochastic models. We use a hidden-Markov model to analyze the distribution of durations of apneas and the distribution of times between apneas. The model suggests the presence of four breathing states, ranging from very stable (with an average lifetime of 12 h) to very unstable (with an average lifetime of 10 s). Although the states themselves are not visible, the mathematical analysis gives estimates of the transition rates among these states. We have obtained these transition rates, and shown how they change with post-menstrual age; as expected, the residence time in the more stable breathing states increases with age. We also extrapolated the model to predict the frequency of very prolonged apnea during the first year of life. This paradigm-stochastic modeling of cardiorespiratory control in neonatal infants to estimate risk for severe clinical events-may be a first step toward personalized risk assessment for life threatening apnea events after NICU discharge.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
Directory of Open Access Journals (Sweden)
Shelton Peiris
2017-12-01
Full Text Available This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV components in order to develop the General Long Memory SV (GLMSV model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications.
Stochastic quantization of a topological quantum mechanical model
International Nuclear Information System (INIS)
Antunes, Sergio; Krein, Gastao; Menezes, Gabriel; Svaiter, Nami Fux
2011-01-01
Full text: Stochastic quantization of complex actions has been extensively studied in the literature. In these models, a Markovian Langevin equation is used in order to study the quantization of such systems. In such papers, the advantages of the Markovian stochastic quantization method were explored and exposed. However, many drawbacks of the method were also pointed out, such as instability of the simulations with absence of convergence and sometimes convergence to the wrong limit. Indeed, although several alternative methods have been proposed to deal with interesting physical systems where the action is complex, these approaches do not suggest any general way of solving the particular difficulties that arise in each situation. Here, we wish to make contributions to the program of stochastic quantization of theories with imaginary action by investigating the consequences of a non-Markovian stochastic quantization in a particular situation, namely a quantum mechanical topological action. We analyze the Markovian stochastic quantization for a topological quantum mechanical action which is analog to a Maxwell-Chern-Simons action in the Weyl gauge. Afterwards we consider a Langevin equation with memory kernel and Einstein's relations with colored noise. We show that convergence towards equilibrium is achieved in both regimes. We also sketch a simple numerical analysis to investigate the possible advantages of non-Markovian procedure over the usual Markovian quantization. Both retarded Green's function for the diffusion problem are considered in such analysis. We show that, although the results indicated that the effect of memory kernel, as usually expected, is to delay the convergence to equilibrium, non-Markovian systems imply a faster decay compared to Markovian ones as well as smoother convergence to equilibrium. (author)
Performance modeling, stochastic networks, and statistical multiplexing
Mazumdar, Ravi R
2013-01-01
This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of introducing an appropriate mathematical framework for modeling and analysis as well as understanding the phenomenon of statistical multiplexing. The models, techniques, and results presented form the core of traffic engineering methods used to design, control and allocate resources in communication networks.The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the importan
Stochastic models of solute transport in highly heterogeneous geologic media
Energy Technology Data Exchange (ETDEWEB)
Semenov, V.N.; Korotkin, I.A.; Pruess, K.; Goloviznin, V.M.; Sorokovikova, O.S.
2009-09-15
A stochastic model of anomalous diffusion was developed in which transport occurs by random motion of Brownian particles, described by distribution functions of random displacements with heavy (power-law) tails. One variant of an effective algorithm for random function generation with a power-law asymptotic and arbitrary factor of asymmetry is proposed that is based on the Gnedenko-Levy limit theorem and makes it possible to reproduce all known Levy {alpha}-stable fractal processes. A two-dimensional stochastic random walk algorithm has been developed that approximates anomalous diffusion with streamline-dependent and space-dependent parameters. The motivation for introducing such a type of dispersion model is the observed fact that tracers in natural aquifers spread at different super-Fickian rates in different directions. For this and other important cases, stochastic random walk models are the only known way to solve the so-called multiscaling fractional order diffusion equation with space-dependent parameters. Some comparisons of model results and field experiments are presented.
A Stochastic Operational Planning Model for Smart Power Systems
Directory of Open Access Journals (Sweden)
Sh. Jadid
2014-12-01
Full Text Available Smart Grids are result of utilizing novel technologies such as distributed energy resources, and communication technologies in power system to compensate some of its defects. Various power resources provide some benefits for operation domain however, power system operator should use a powerful methodology to manage them. Renewable resources and load add uncertainty to the problem. So, independent system operator should use a stochastic method to manage them. A Stochastic unit commitment is presented in this paper to schedule various power resources such as distributed generation units, conventional thermal generation units, wind and PV farms, and demand response resources. Demand response resources, interruptible loads, distributed generation units, and conventional thermal generation units are used to provide required reserve for compensating stochastic nature of various resources and loads. In the presented model, resources connected to distribution network can participate in wholesale market through aggregators. Moreover, a novel three-program model which can be used by aggregators is presented in this article. Loads and distributed generation can contract with aggregators by these programs. A three-bus test system and the IEEE RTS are used to illustrate usefulness of the presented model. The results show that ISO can manage the system effectively by using this model
Stochastic modelling in design of mechanical properties of nanometals
International Nuclear Information System (INIS)
Tengen, T.B.; Wejrzanowski, T.; Iwankiewicz, R.; Kurzydlowski, K.J.
2010-01-01
Polycrystalline nanometals are being fabricated through different processing routes and conditions. The consequence is that nanometals having the same mean grain size may have different grain size dispersion and, hence, may have different material properties. This has often led to conflicting reports from both theoretical and experimental findings about the evolutions of the mechanical properties of nanomaterials. The present paper employs stochastic model to study the impact of microstructure evolution during grain growth on the mechanical properties of polycrystalline nanometals. The stochastic model for grain growth and the stochastic model for changes in mechanical properties of nanomaterials are proposed. The model for the mechanical properties developed is tested on aluminium samples.Many salient features of the mechanical properties of the aluminium samples are revealed. The results show that the different mechanisms of grain growth impart different nature of response to the material mechanical properties. The conventional, homologous and anomalous temperature dependences of the yield stress have also been revealed to be due to different nature of interactions of the microstructures during evolution.
Introduction to stochastic models in biology
DEFF Research Database (Denmark)
Ditlevsen, Susanne; Samson, Adeline
2013-01-01
This chapter is concerned with continuous time processes, which are often modeled as a system of ordinary differential equations (ODEs). These models assume that the observed dynamics are driven exclusively by internal, deterministic mechanisms. However, real biological systems will always be exp...
On a Stochastic Model in Insurance
Indian Academy of Sciences (India)
2. Life insurance/pension insurance models are gen- erally described in terms of continuous time Markov processes with state space having only a finite number of elements; at least one state is absorbing, and cer- tain transitions may be disallowed. For example, in the simplest life insurance model there are only two states,.
Stochastic species abundance models involving special copulas
Huillet, Thierry E.
2018-01-01
Copulas offer a very general tool to describe the dependence structure of random variables supported by the hypercube. Inspired by problems of species abundances in Biology, we study three distinct toy models where copulas play a key role. In a first one, a Marshall-Olkin copula arises in a species extinction model with catastrophe. In a second one, a quasi-copula problem arises in a flagged species abundance model. In a third model, we study completely random species abundance models in the hypercube as those, not of product type, with uniform margins and singular. These can be understood from a singular copula supported by an inflated simplex. An exchangeable singular Dirichlet copula is also introduced, together with its induced completely random species abundance vector.
Stochastic population and epidemic models persistence and extinction
Allen, Linda J S
2015-01-01
This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix. These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics ...
Modeling and stochastic analysis of dynamic mechanisms of the perception
Pisarchik, A.; Bashkirtseva, I.; Ryashko, L.
2017-10-01
Modern studies in physiology and cognitive neuroscience consider a noise as an important constructive factor of the brain functionality. Under the adequate noise, the brain can rapidly access different ordered states, and provide decision-making by preventing deadlocks. Bistable dynamic models are often used for the study of the underlying mechanisms of the visual perception. In the present paper, we consider a bistable energy model subject to both additive and parametric noise. Using the catastrophe theory formalism and stochastic sensitivity functions technique, we analyze a response of the equilibria to noise, and study noise-induced transitions between equilibria. We demonstrate and analyse the effect of hysteresis squeezing when the intensity of noise is increased. Stochastic bifurcations connected with the suppression of oscillations by parametric noises are discussed.
An extension of clarke's model with stochastic amplitude flip processes
Hoel, Hakon
2014-07-01
Stochastic modeling is an essential tool for studying statistical properties of wireless channels. In multipath fading channel (MFC) models, the signal reception is modeled by a sum of wave path contributions, and Clarke\\'s model is an important example of such which has been widely accepted in many wireless applications. However, since Clarke\\'s model is temporally deterministic, Feng and Field noted that it does not model real wireless channels with time-varying randomness well. Here, we extend Clarke\\'s model to a novel time-varying stochastic MFC model with scatterers randomly flipping on and off. Statistical properties of the MFC model are analyzed and shown to fit well with real signal measurements, and a limit Gaussian process is derived from the model when the number of active wave paths tends to infinity. A second focus of this work is a comparison study of the error and computational cost of generating signal realizations from the MFC model and from its limit Gaussian process. By rigorous analysis and numerical studies, we show that in many settings, signal realizations are generated more efficiently by Gaussian process algorithms than by the MFC model\\'s algorithm. Numerical examples that strengthen these observations are also presented. © 2014 IEEE.
On a Versatile Stochastic Growth Model
Directory of Open Access Journals (Sweden)
Samiur Arif
2012-06-01
Full Text Available Growth phenomena are ubiquitous and pervasive not only in biology and the medical sciences, but also in economics, marketing and the computer and social sciences. We introduce a three-parameter version of the classic pure-birth process growth model when suitably instantiated, can be used to model growth phenomena in many seemingly unrelated application domains. We point out that the model is computationally attractive since it admits of conceptually simple, closed form solutions for the time-dependent probabilities.
GEMFsim: A Stochastic Simulator for the Generalized Epidemic Modeling Framework
Sahneh, Faryad Darabi; Vajdi, Aram; Shakeri, Heman; Fan, Futing; Scoglio, Caterina
2016-01-01
The recently proposed generalized epidemic modeling framework (GEMF) \\cite{sahneh2013generalized} lays the groundwork for systematically constructing a broad spectrum of stochastic spreading processes over complex networks. This article builds an algorithm for exact, continuous-time numerical simulation of GEMF-based processes. Moreover the implementation of this algorithm, GEMFsim, is available in popular scientific programming platforms such as MATLAB, R, Python, and C; GEMFsim facilitates ...
Genre classification using chords and stochastic language models
Pérez Sancho, Carlos; Rizo Valero, David; Iñesta Quereda, José Manuel
2009-01-01
Music genre meta-data is of paramount importance for the organisation of music repositories. People use genre in a natural way when entering a music store or looking into music collections. Automatic genre classification has become a popular topic in music information retrieval research both, with digital audio and symbolic data. This work focuses on the symbolic approach, bringing to music cognition some technologies, like the stochastic language models, already successfully applied to text ...
Stochastic model of Rayleigh-Taylor turbulent mixing
International Nuclear Information System (INIS)
Abarzhi, S.I.; Cadjan, M.; Fedotov, S.
2007-01-01
We propose a stochastic model to describe the random character of the dissipation process in Rayleigh-Taylor turbulent mixing. The parameter alpha, used conventionally to characterize the mixing growth-rate, is not a universal constant and is very sensitive to the statistical properties of the dissipation. The ratio between the rates of momentum loss and momentum gain is the statistic invariant and a robust parameter to diagnose with or without turbulent diffusion accounted for
Forecasting labour supply and population: An integrated stochastic model
Fuchs, Johann; Söhnlein, Doris; Weber, Brigitte; Weber, Enzo
2017-01-01
This paper presents a stochastic integrated model to forecast the German population and labour supply until 2060. Within a cohort-component approach, the population forecast applies principal components to birth, mortality, emigration and immigration rates. The labour force participation rates are estimated by means of an econometric time series approach. All time series are forecast by bootstrapping. This allows fully integrated simulations and the possibility to illustrate the uncertainties...
Dynamic analysis of a stochastic delayed rumor propagation model
Jia, Fangju; Lv, Guangying; Wang, Shuangfeng; Zou, Guang-an
2018-02-01
The rapid development of the Internet, especially the emergence of the social networks, has led rumor propagation into a new media era. In this paper, we are concerned with a stochastic delayed rumor propagation model. Firstly, we obtain the existence of the global solution. Secondly, sufficient conditions for extinction of the rumor are established. Lastly, the boundedness of solution is proved and some simulations are given to verify our results.
A stochastic modeling of isotope exchange reactions in glutamine synthetase
Kazmiruk, N. V.; Boronovskiy, S. E.; Nartsissov, Ya R.
2017-11-01
The model presented in this work allows simulation of isotopic exchange reactions at chemical equilibrium catalyzed by a glutamine synthetase. To simulate the functioning of the enzyme the algorithm based on the stochastic approach was applied. The dependence of exchange rates for 14C and 32P on metabolite concentration was estimated. The simulation results confirmed the hypothesis of the ascertained validity for preferred order random binding mechanism. Corresponding values of K0.5 were also obtained.
A stochastic model of gene expression including splicing events
Penim, Flávia Alexandra Mendes
2014-01-01
Tese de mestrado, Bioinformática e Biologia Computacional, Universidade de Lisboa, Faculdade de Ciências, 2014 Proteins carry out the great majority of the catalytic and structural work within an organism. The RNA templates used in their synthesis determines their identity, and this is dictated by which genes are transcribed. Therefore, gene expression is the fundamental determinant of an organism’s nature. The main objective of this thesis was to develop a stochastic computational model a...
Zacharuk, Matthias; Dolaptchiev, Stamen; Achatz, Ulrich; Timofeyev, Ilya
2017-04-01
Due to the finite spatial resolution in numerical atmospheric models, subgrid-scale (SGS) processes arise. A SGS parameterization of these excluded processes might improve the model on all scales. In this study we present a model derived parameterization of these processes for the one dimensional shallow water equations. To parameterize the SGS processes we choose the MTV stochastic mode reduction (Majda, Timofeyev, Vanden-Eijnden 2001, A mathematical framework for stochastic climate models. Commun. Pure Appl. Math., 54:891-974). For this the model is separated into fast and slow processes. Using the statistics of the fast processes, a SGS parameterization is found. To identify fast processes the state vector of the model is separated into two state vectors. One vector is the average of the full model state vector in a coarse grid cell. The other describes SGS processes which are defined as the deviation of the full state vector from the coarse cell average. If the SGS vector decorrelates faster in time than the coarse grid vector, the stochastic MTV SGS parameterization can be derived from the model equation, which is the advantage of this method compared to others. So far the method was successfully applied on the Burgers-equation (Dolaptchiev et al. 2013, Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation. Theor. Comp. Fluid Dyn., 27:297-317). To apply the method onto the one the dimensional shallow water equations, we choose a local approach of the fine variable self-interactions. With this, we are able to derive a local SGS parameterization using MTV's method leading to a closed model wrt. the coarse variable. We show, that this model is able to fix the energy decrease for high wave numbers which appears at the coarse resolution model with neglected SGS parameterization. In the future we plan to extend the model to two dimensions and multiple layers. Perspectively, the method can be used to derive a
Stochastic Models of Molecule Formation on Dust
Charnley, Steven; Wirstroem, Eva
2011-01-01
We will present new theoretical models for the formation of molecules on dust. The growth of ice mantles and their layered structure is accounted for and compared directly to observations through simulation of the expected ice absorption spectra
Advanced Stochastic Modeling of Railway Track Irregularities
Directory of Open Access Journals (Sweden)
Mengyi Zhu
2013-01-01
Full Text Available As an important interference source of railway vibration, track irregularity is studied in this paper. It is presented that irregularities in the vertical profile and alignment can be modeled as a Gaussian random process. The power spectral density (PSD of the irregularity is calculated and discussed. By analyzing the model, level-crossing properties as well as peak statistics are studied and compared with the observed data.
Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes
DEFF Research Database (Denmark)
Starke, Jens; Reichert, Christian; Eiswirth, Markus
2007-01-01
Three levels of modeling, microscopic, mesoscopic and macroscopic are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. It can......, such that in contrast to the microscopic model the spatial resolution is reduced. The derivation of deterministic limit equations is in correspondence with the successful description of experiments under low-pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena...
Deterministic geologic processes and stochastic modeling
International Nuclear Information System (INIS)
Rautman, C.A.; Flint, A.L.
1991-01-01
Recent outcrop sampling at Yucca Mountain, Nevada, has produced significant new information regarding the distribution of physical properties at the site of a potential high-level nuclear waste repository. Consideration of the spatial distribution of measured values and geostatistical measures of spatial variability indicates that there are a number of widespread deterministic geologic features at the site that have important implications for numerical modeling of such performance aspects as ground water flow and radionuclide transport. These deterministic features have their origin in the complex, yet logical, interplay of a number of deterministic geologic processes, including magmatic evolution; volcanic eruption, transport, and emplacement; post-emplacement cooling and alteration; and late-stage (diagenetic) alteration. Because of geologic processes responsible for formation of Yucca Mountain are relatively well understood and operate on a more-or-less regional scale, understanding of these processes can be used in modeling the physical properties and performance of the site. Information reflecting these deterministic geologic processes may be incorporated into the modeling program explicitly, using geostatistical concepts such as soft information, or implicitly, through the adoption of a particular approach to modeling. It is unlikely that any single representation of physical properties at the site will be suitable for all modeling purposes. Instead, the same underlying physical reality will need to be described many times, each in a manner conducive to assessing specific performance issues
Time-Weighted Balanced Stochastic Model Reduction
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Shaker, Hamid Reza
2011-01-01
A new relative error model reduction technique for linear time invariant (LTI) systems is proposed in this paper. Both continuous and discrete time systems can be reduced within this framework. The proposed model reduction method is mainly based upon time-weighted balanced truncation and a recently...... developed inner-outer factorization technique. Compared to the other analogous counterparts, the proposed method shows to provide more accurate results in terms of time weighted norms, when applied to different practical examples. The results are further illustrated by a numerical example....
Stochastic and Centrifuge Modelling of Jointed Rock
1990-08-31
Whitman D. Veneziano 0. Reyes G. Iglesia J. S. Lee I Sponsored by U.S. Air Force Air Force Office of Scientific Research Boiling Air Force Base Air...1b Maxmu Tensile Prnia StesVcos fSeie * t 30 Preextin- Frcue and -ne a Wine Crck Subec toUix.Cmrsie* tesi Vetia Direction- Noe Hg eniesteslee i oe...German sponsors, enhanced our modelling the model approach and led to a paper, "Trapdoor Experiments With Simulated Jointed Rock", Iglesia , et al., by
Uncertainty modelling of atmospheric dispersion by stochastic ...
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... Uncertainty; polynomial chaos expansion; fuzzy set theory; cumulative distribution function; uniform distribution; membership function. Abstract. The parameters associated to a environmental dispersion model may include different kinds of variability, imprecision and uncertainty. More often, it is seen that ...
Stochastic modelling of dynamical systems in biology
Pellin, Danilo
2017-01-01
In this thesis two relevant biological problems will be addressed from a statistical modelling perspective. The first regards the study of hematopoiesis, a still not well understood biological process rarely observable in humans due to technical and ethical reasons. Hematopoiesis is responsible for
STOCHASTIC MODELING OF INFLATION IN NIGERIA
African Journals Online (AJOL)
2006-04-04
Apr 4, 2006 ... In this paper, we adopt a time series approach in modeling inflation in Nig'eria using a four-decade data (1960- 1999) on consumer price index.. Logarithmic transformation was used to stabilize the variation in the data. On the whole four decades, a quadratic trend was obtained. This is also true with the ...
On a Stochastic Model in Insurance
Indian Academy of Sciences (India)
Insurance mathematics today is considered a part of applied probability theory. Main objectives are modelling of claims that arrive in an insurance business, and decide how premiums are to be charged to avoid ruin of the insurance company. GENERAL I ARTICLE various results and the heuristics can be appreciated.
Stochastic Modelling of Wireless Energy Transfer
Veilleux, Shaun; Almaghasilah, Ahmed; Abedi, Ali; Wilkerson, DeLisa
2017-01-01
This study investigates the efficiency of a new method of powering remote sensors by the means of wireless energy transfer. The increased use of sensors for data collection comes with the inherent cost of supplying power from sources such as power cables or batteries. Wireless energy transfer technology eliminates the need for power cables or periodic battery replacement. The time and cost of setting up or expanding a sensor network will be reduced while allowing sensors to be placed in areas where running power cables or battery replacement is not feasible. This paper models wireless channels for power and data separately. Smart scheduling for the data channel is proposed to avoid transmitting data on a noisy channel where the probability of data loss is high to improve power efficiency. Analytical models have been developed and verified using simulations.
Classical and quantum stochastic models of resistive and memristive circuits
Gough, John E.; Zhang, Guofeng
2017-07-01
The purpose of this paper is to examine stochastic Markovian models for circuits in phase space for which the drift term is equivalent to the standard circuit equations. In particular, we include dissipative components corresponding to both a resistor and a memristor in series. We obtain a dilation of the problem which is canonical in the sense that the underlying Poisson bracket structure is preserved under the stochastic flow. We do this first of all for standard Wiener noise but also treat the problem using a new concept of symplectic noise, where the Poisson structure is extended to the noise as well as the circuit variables, and in particular where we have canonically conjugate noises. Finally, we construct a dilation which describes the quantum mechanical analogue.
Stochastic sensitivity of a bistable energy model for visual perception
Pisarchik, Alexander N.; Bashkirtseva, Irina; Ryashko, Lev
2017-01-01
Modern trends in physiology, psychology and cognitive neuroscience suggest that noise is an essential component of brain functionality and self-organization. With adequate noise the brain as a complex dynamical system can easily access different ordered states and improve signal detection for decision-making by preventing deadlocks. Using a stochastic sensitivity function approach, we analyze how sensitive equilibrium points are to Gaussian noise in a bistable energy model often used for qualitative description of visual perception. The probability distribution of noise-induced transitions between two coexisting percepts is calculated at different noise intensity and system stability. Stochastic squeezing of the hysteresis range and its transition from positive (bistable regime) to negative (intermittency regime) are demonstrated as the noise intensity increases. The hysteresis is more sensitive to noise in the system with higher stability.
Stochastic modelling for financial bubbles and policy
Fry, John
2015-01-01
In this paper, we draw upon the close relationship between statistical physics and mathematical finance to develop a suite of models for financial bubbles and crashes. By modifying previous approaches, we are able to derive novel analytical formulae for evaluation problems and for the expected timing of future change points. In particular, we help to explain why previous approaches have systematically overstated the timing of changes in market regime. The list of potential empirical applicati...
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Energy Technology Data Exchange (ETDEWEB)
Dobay, M. P. D., E-mail: maria.pamela.david@physik.uni-muenchen.de; Alberola, A. Piera; Mendoza, E. R.; Raedler, J. O., E-mail: joachim.raedler@physik.uni-muenchen.de [Ludwig-Maximilians University, Faculty of Physics, Center for NanoScience (Germany)
2012-03-15
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
International Nuclear Information System (INIS)
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-01-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-03-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
A delay financial model with stochastic volatility; martingale method
Lee, Min-Ku; Kim, Jeong-Hoon; Kim, Joocheol
2011-08-01
In this paper, we extend a delayed geometric Brownian model by adding a stochastic volatility term, which is driven by a hidden process of fast mean reverting diffusion, to the delayed model. Combining a martingale approach and an asymptotic method, we develop a theory for option pricing under this hybrid model. The core result obtained by our work is a proof that a discounted approximate option price can be decomposed as a martingale part plus a small term. Subsequently, a correction effect on the European option price is demonstrated both theoretically and numerically for a good agreement with practical results.
Uncertainty quantification and stochastic modeling with Matlab
Souza de Cursi, Eduardo
2015-01-01
Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences. Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does no
Stochastic modelling for financial bubbles and policy
Directory of Open Access Journals (Sweden)
John Fry
2015-12-01
Full Text Available In this paper, we draw upon the close relationship between statistical physics and mathematical finance to develop a suite of models for financial bubbles and crashes. By modifying previous approaches, we are able to derive novel analytical formulae for evaluation problems and for the expected timing of future change points. In particular, we help to explain why previous approaches have systematically overstated the timing of changes in market regime. The list of potential empirical applications is deep and wide ranging, and includes contemporary housing bubbles, the Eurozone crisis and the Crash of 2008.
Stochastic Differential Equations in Artificial Pancreas Modelling
DEFF Research Database (Denmark)
Duun-Henriksen, Anne Katrine
Type 1 diabetes accounts for approximately 5% of the total diabetes population. It is caused by the destruction of insulin producing β-cells in the pancreas. Various treatment strategies are available today, some of which include advanced technological devices such as an insulin pump...... and a continuous glucose monitor (CGM). Despite these technological advances in the treatment of type 1 diabetes, the disease still poses an enormous and constant challenge for the patients. To obtain tight glucose control the patients are required to assess how much they will eat prior to the meal. They have...... the benefits and challenges by using SDEs compared to traditional methods on the basis of the results of the project. First of all, we designed a clinical study to obtain high quality data from type 1 diabetes patients to identify the models from. The study included the main factors influencing the glucose...
Stochastic Modelling of Past Volcanic Crises
Woo, Gordon
2017-04-01
It is customary to have continuous monitoring of volcanoes showing signs of unrest that might lead to an eruption threatening local populations. Despite scientific progress in estimating the probability of an eruption occurring, the concept of continuously tracking eruption probability remains a future aspiration for volcano risk analysts. During some recent major volcanic crises, attempts have been made to estimate the eruption probability in real time to support government decision-making. These include the possibility of an eruption of Katla linked with the eruption of Eyjafjallajökull in 2010, and the Santorini crisis of 2011-2012. However, once a crisis fades, interest in analyzing the probability that there might have been an eruption tends to wane. There is an inherent outcome bias well known to psychologists: if disaster was avoided, there is perceived to be little purpose in exploring scenarios where a disaster might have happened. Yet the better that previous periods of unrest are understood and modelled, the better that the risk associated with future periods of unrest will be quantified. Scenarios are counterfactual histories of the future. The task of quantifying the probability of an eruption for a past period of unrest should not be merely a statistical calculation, but should serve to elucidate and refine geophysical models of the eruptive processes. This is achieved by using a Bayesian Belief Network approach, in which monitoring observations are used to draw inferences on the underlying causal factors. Specifically, risk analysts are interested in identifying what dynamical perturbations might have tipped an unrest period in history over towards an eruption, and assessing what was the likelihood of such perturbations. Furthermore, in what ways might a historical volcano crisis have turned for the worse? Such important counterfactual questions are addressed in this paper.
Stochastic modelling of regional archaeomagnetic series
Hellio, G.; Gillet, N.; Bouligand, C.; Jault, D.
2014-11-01
We report a new method to infer continuous time-series of the declination, inclination and intensity of the magnetic field from archaeomagnetic data. Adopting a Bayesian perspective, we need to specify a priori knowledge about the time evolution of the magnetic field. It consists in a time correlation function that we choose to be compatible with present knowledge about the geomagnetic time spectra. The results are presented as distributions of possible values for the declination, inclination or intensity. We find that the methodology can be adapted to account for the age uncertainties of archaeological artefacts and we use Markov chain Monte Carlo to explore the possible dates of observations. We apply the method to intensity data sets from Mari, Syria and to intensity and directional data sets from Paris, France. Our reconstructions display more rapid variations than previous studies and we find that the possible values of geomagnetic field elements are not necessarily normally distributed. Another output of the model is better age estimates of archaeological artefacts.
A validation study of a stochastic model of human interaction
Burchfield, Mitchel Talmadge
The purpose of this dissertation is to validate a stochastic model of human interactions which is part of a developmentalism paradigm. Incorporating elements of ancient and contemporary philosophy and science, developmentalism defines human development as a progression of increasing competence and utilizes compatible theories of developmental psychology, cognitive psychology, educational psychology, social psychology, curriculum development, neurology, psychophysics, and physics. To validate a stochastic model of human interactions, the study addressed four research questions: (a) Does attitude vary over time? (b) What are the distributional assumptions underlying attitudes? (c) Does the stochastic model, {-}N{intlimitssbsp{-infty}{infty}}varphi(chi,tau)\\ Psi(tau)dtau, have utility for the study of attitudinal distributions and dynamics? (d) Are the Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein theories applicable to human groups? Approximately 25,000 attitude observations were made using the Semantic Differential Scale. Positions of individuals varied over time and the logistic model predicted observed distributions with correlations between 0.98 and 1.0, with estimated standard errors significantly less than the magnitudes of the parameters. The results bring into question the applicability of Fisherian research designs (Fisher, 1922, 1928, 1938) for behavioral research based on the apparent failure of two fundamental assumptions-the noninteractive nature of the objects being studied and normal distribution of attributes. The findings indicate that individual belief structures are representable in terms of a psychological space which has the same or similar properties as physical space. The psychological space not only has dimension, but individuals interact by force equations similar to those described in theoretical physics models. Nonlinear regression techniques were used to estimate Fermi-Dirac parameters from the data. The model explained a high degree
Modelling the heat dynamics of buildings using stochastic
DEFF Research Database (Denmark)
Andersen, Klaus Kaae; Madsen, Henrik
2000-01-01
This paper describes the continuous time modelling of the heat dynamics of a building. The considered building is a residential like test house divided into two test rooms with a water based central heating. Each test room is divided into thermal zones in order to describe both short and long term...... variations. Besides modelling the heat transfer between thermal zones, attention is put on modelling the heat input from radiators and solar radiation. The applied modelling procedure is based on collected building performance data and statistical methods. The statistical methods are used in parameter...... estimation and model validation, while physical knowledge is used in forming the model structure. The suggested lumped parameter model is thus based on thermodynamics and formulated as a system of stochastic differential equations. Due to the continuous time formulation the parameters of the model...
A stochastic surplus production model in continuous time
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte
2017-01-01
surplus production model in continuous time (SPiCT), which in addition to stock dynamics also models the dynamics of the fisheries. This enables error in the catch process to be reflected in the uncertainty of estimated model parameters and management quantities. Benefits of the continuous-time state......Surplus production modelling has a long history as a method for managing data-limited fish stocks. Recent advancements have cast surplus production models as state-space models that separate random variability of stock dynamics from error in observed indices of biomass. We present a stochastic...... and improve estimation of reference points relative to discrete-time analysis of aggregated annual data. Finally, subannual data from five North Sea stocks are analysed with particular focus on using residual analysis to diagnose model insufficiencies and identify necessary model extensions such as robust...
The stochastic resonance for the incidence function model of metapopulation
Li, Jiang-Cheng; Dong, Zhi-Wei; Zhou, Ruo-Wei; Li, Yun-Xian; Qian, Zhen-Wei
2017-06-01
A stochastic model with endogenous and exogenous periodicities is proposed in this paper on the basis of metapopulation dynamics to model the crop yield losses due to pests and diseases. The rationale is that crop yield losses occur because the physiology of the growing crop is negatively affected by pests and diseases in a dynamic way over time as crop both grows and develops. Metapopulation dynamics can thus be used to model the resultant crop yield losses. The stochastic metapopulation process is described by using the Simplified Incidence Function model (IFM). Compared to the original IFMs, endogenous and exogenous periodicities are considered in the proposed model to handle the cyclical patterns observed in pest infestations, diseases epidemics, and exogenous affecting factors such as temperature and rainfalls. Agricultural loss data in China are used to fit the proposed model. Experimental results demonstrate that: (1) Model with endogenous and exogenous periodicities is a better fit; (2) When the internal system fluctuations and external environmental fluctuations are negatively correlated, EIL or the cost of loss is monotonically increasing; when the internal system fluctuations and external environmental fluctuations are positively correlated, an outbreak of pests and diseases might occur; (3) If the internal system fluctuations and external environmental fluctuations are positively correlated, an optimal patch size can be identified which will greatly weaken the effects of external environmental influence and hence inhibit pest infestations and disease epidemics.
ARMA modelling of neutron stochastic processes with large measurement noise
International Nuclear Information System (INIS)
Zavaljevski, N.; Kostic, Lj.; Pesic, M.
1994-01-01
An autoregressive moving average (ARMA) model of the neutron fluctuations with large measurement noise is derived from langevin stochastic equations and validated using time series data obtained during prompt neutron decay constant measurements at the zero power reactor RB in Vinca. Model parameters are estimated using the maximum likelihood (ML) off-line algorithm and an adaptive pole estimation algorithm based on the recursive prediction error method (RPE). The results show that subcriticality can be determined from real data with high measurement noise using much shorter statistical sample than in standard methods. (author)
Optimizing ZigBee Security using Stochastic Model Checking
DEFF Research Database (Denmark)
Yuksel, Ender; Nielson, Hanne Riis; Nielson, Flemming
ZigBee is a fairly new but promising wireless sensor network standard that offers the advantages of simple and low resource communication. Nevertheless, security is of great concern to ZigBee, and enhancements are prescribed in the latest ZigBee specication: ZigBee-2007. In this technical report......, we identify an important gap in the specification on key updates, and present a methodology for determining optimal key update policies and security parameters. We exploit the stochastic model checking approach using the probabilistic model checker PRISM, and assess the security needs for realistic...
Stochastic modelling of non-stationary financial assets
Estevens, Joana; Rocha, Paulo; Boto, João P.; Lind, Pedro G.
2017-11-01
We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely, biology, medicine, and geology.
Dynamic analysis of a stochastic rumor propagation model
Jia, Fangju; Lv, Guangying
2018-01-01
The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. In this paper, we are concerned with a stochastic rumor propagation model. Sufficient conditions for extinction and persistence in the mean of the rumor are established. The threshold between persistence in the mean and extinction of the rumor is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.
Generation of a stochastic precipitation model for the tropical climate
Ng, Jing Lin; Abd Aziz, Samsuzana; Huang, Yuk Feng; Wayayok, Aimrun; Rowshon, MK
2017-06-01
A tropical country like Malaysia is characterized by intense localized precipitation with temperatures remaining relatively constant throughout the year. A stochastic modeling of precipitation in the flood-prone Kelantan River Basin is particularly challenging due to the high intermittency of precipitation events of the northeast monsoons. There is an urgent need to have long series of precipitation in modeling the hydrological responses. A single-site stochastic precipitation model that includes precipitation occurrence and an intensity model was developed, calibrated, and validated for the Kelantan River Basin. The simulation process was carried out separately for each station without considering the spatial correlation of precipitation. The Markov chains up to the fifth-order and six distributions were considered. The daily precipitation data of 17 rainfall stations for the study period of 1954-2013 were selected. The results suggested that second- and third-order Markov chains were suitable for simulating monthly and yearly precipitation occurrences, respectively. The fifth-order Markov chain resulted in overestimation of precipitation occurrences. For the mean, distribution, and standard deviation of precipitation amounts, the exponential, gamma, log-normal, skew normal, mixed exponential, and generalized Pareto distributions performed superiorly. However, for the extremes of precipitation, the exponential and log-normal distributions were better while the skew normal and generalized Pareto distributions tend to show underestimations. The log-normal distribution was chosen as the best distribution to simulate precipitation amounts. Overall, the stochastic precipitation model developed is considered a convenient tool to simulate the characteristics of precipitation in the Kelantan River Basin.
A stochastic phase-field model determined from molecular dynamics
von Schwerin, Erik
2010-03-17
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.
Stochastic modeling for river pollution of Sungai Perlis
International Nuclear Information System (INIS)
Yunus, Nurul Izzaty Mohd.; Rahman, Haliza Abd.; Bahar, Arifah
2015-01-01
River pollution has been recognized as a contributor to a wide range of health problems and disorders in human. It can pose health dangers to humans who come into contact with it, either directly or indirectly. Therefore, it is most important to measure the concentration of Biochemical Oxygen Demand (BOD) as a water quality parameter since the parameter has long been the basic means for determining the degree of water pollution in rivers. In this study, BOD is used as a parameter to estimate the water quality at Sungai Perlis. It has been observed that Sungai Perlis is polluted due to lack of management and improper use of resources. Therefore, it is of importance to model the Sungai Perlis water quality in order to describe and predict the water quality systems. The BOD concentration secondary data set is used which was extracted from the Drainage and Irrigation Department Perlis State website. The first order differential equation from Streeter – Phelps model was utilized as a deterministic model. Then, the model was developed into a stochastic model. Results from this study shows that the stochastic model is more adequate to describe and predict the BOD concentration and the water quality systems in Sungai Perlis by having smaller value of mean squared error (MSE)
Stochastic modeling for river pollution of Sungai Perlis
Energy Technology Data Exchange (ETDEWEB)
Yunus, Nurul Izzaty Mohd.; Rahman, Haliza Abd. [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia,81310 Johor Bahru, Johor (Malaysia); Bahar, Arifah [UTM-Centre of Industrial and Applied Mathematics (UTM-CIAM) Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)
2015-02-03
River pollution has been recognized as a contributor to a wide range of health problems and disorders in human. It can pose health dangers to humans who come into contact with it, either directly or indirectly. Therefore, it is most important to measure the concentration of Biochemical Oxygen Demand (BOD) as a water quality parameter since the parameter has long been the basic means for determining the degree of water pollution in rivers. In this study, BOD is used as a parameter to estimate the water quality at Sungai Perlis. It has been observed that Sungai Perlis is polluted due to lack of management and improper use of resources. Therefore, it is of importance to model the Sungai Perlis water quality in order to describe and predict the water quality systems. The BOD concentration secondary data set is used which was extracted from the Drainage and Irrigation Department Perlis State website. The first order differential equation from Streeter – Phelps model was utilized as a deterministic model. Then, the model was developed into a stochastic model. Results from this study shows that the stochastic model is more adequate to describe and predict the BOD concentration and the water quality systems in Sungai Perlis by having smaller value of mean squared error (MSE)
Stochastic modeling for river pollution of Sungai Perlis
Yunus, Nurul Izzaty Mohd.; Rahman, Haliza Abd.; Bahar, Arifah
2015-02-01
River pollution has been recognized as a contributor to a wide range of health problems and disorders in human. It can pose health dangers to humans who come into contact with it, either directly or indirectly. Therefore, it is most important to measure the concentration of Biochemical Oxygen Demand (BOD) as a water quality parameter since the parameter has long been the basic means for determining the degree of water pollution in rivers. In this study, BOD is used as a parameter to estimate the water quality at Sungai Perlis. It has been observed that Sungai Perlis is polluted due to lack of management and improper use of resources. Therefore, it is of importance to model the Sungai Perlis water quality in order to describe and predict the water quality systems. The BOD concentration secondary data set is used which was extracted from the Drainage and Irrigation Department Perlis State website. The first order differential equation from Streeter - Phelps model was utilized as a deterministic model. Then, the model was developed into a stochastic model. Results from this study shows that the stochastic model is more adequate to describe and predict the BOD concentration and the water quality systems in Sungai Perlis by having smaller value of mean squared error (MSE).
Combining Deterministic structures and stochastic heterogeneity for transport modeling
Zech, Alraune; Attinger, Sabine; Dietrich, Peter; Teutsch, Georg
2017-04-01
Contaminant transport in highly heterogeneous aquifers is extremely challenging and subject of current scientific debate. Tracer plumes often show non-symmetric but highly skewed plume shapes. Predicting such transport behavior using the classical advection-dispersion-equation (ADE) in combination with a stochastic description of aquifer properties requires a dense measurement network. This is in contrast to the available information for most aquifers. A new conceptual aquifer structure model is presented which combines large-scale deterministic information and the stochastic approach for incorporating sub-scale heterogeneity. The conceptual model is designed to allow for a goal-oriented, site specific transport analysis making use of as few data as possible. Thereby the basic idea is to reproduce highly skewed tracer plumes in heterogeneous media by incorporating deterministic contrasts and effects of connectivity instead of using unimodal heterogeneous models with high variances. The conceptual model consists of deterministic blocks of mean hydraulic conductivity which might be measured by pumping tests indicating values differing in orders of magnitudes. A sub-scale heterogeneity is introduced within every block. This heterogeneity can be modeled as bimodal or log-normal distributed. The impact of input parameters, structure and conductivity contrasts is investigated in a systematic manor. Furthermore, some first successful implementation of the model was achieved for the well known MADE site.
A spatially structured metapopulation model within a stochastic environment.
Smith, Andrew G
2017-09-01
Populations often exist, either by choice or by external pressure, in a fragmented way, referred to as a metapopulation. Typically, the dynamics accounted for within metapopulation models are assumed to be static. For example, patch occupancy models often assume that the colonisation and extinction rates do not change, while spatially structured models often assume that the rates of births, deaths and migrations do not depend on time. While some progress has been made when these dynamics are changing deterministically, less is known when the changes are stochastic. It can be quite common that the environment a population inhabits determines how these dynamics change over time. Changes to this environment can have a large impact on the survival probability of a population and such changes will often be stochastic. The typical metapopulation model allows for catastrophes that could eradicate most, if not all, individuals on an entire patch. It is this type of phenomenon that this article addresses. A Markov process is developed that models the number of individuals on each patch within a metapopulation. An approximation for the original model is presented in the form of a piecewise-deterministic Markov process and the approximation is analysed to present conditions for extinction. Copyright © 2017 Elsevier Inc. All rights reserved.
Stochastic Higher Spin Vertex Models on the Line
Corwin, Ivan; Petrov, Leonid
2016-04-01
We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain Markov dualities. Using this, for the systems started in step initial data, we write down nested contour integral formulas for moments and Fredholm determinant formulas for Laplace-type transforms. Taking various choices or limits of parameters, this family degenerates to many of the known exactly solvable models in the Kardar-Parisi-Zhang universality class, as well as leads to many new examples of such models. In particular, asymmetric simple exclusion process, the stochastic six-vertex model, q-totally asymmetric simple exclusion process and various directed polymer models all arise in this manner. Our systems are constructed from stochastic versions of the R-matrix related to the six-vertex model. One of the key tools used here is the fusion of R-matrices and we provide a probabilistic proof of this procedure.
Stochastic cellular automata model for wildland fire spread dynamics
International Nuclear Information System (INIS)
Maduro Almeida, Rodolfo; Macau, Elbert E N
2011-01-01
A stochastic cellular automata model for wildland fire spread under flat terrain and no-wind conditions is proposed and its dynamics is characterized and analyzed. One of three possible states characterizes each cell: vegetation cell, burning cell and burnt cell. The dynamics of fire spread is modeled as a stochastic event with an effective fire spread probability S which is a function of three probabilities that characterize: the proportion of vegetation cells across the lattice, the probability of a burning cell becomes burnt, and the probability of the fire spread from a burning cell to a neighboring vegetation cell. A set of simulation experiments is performed to analyze the effects of different values of the three probabilities in the fire pattern. Monte-Carlo simulations indicate that there is a critical line in the model parameter space that separates the set of parameters which a fire can propagate from those for which it cannot propagate. Finally, the relevance of the model is discussed under the light of computational experiments that illustrate the capability of the model catches both the dynamical and static qualitative properties of fire propagation.
Sampling from stochastic reservoir models constrained by production data
Energy Technology Data Exchange (ETDEWEB)
Hegstad, Bjoern Kaare
1997-12-31
When a petroleum reservoir is evaluated, it is important to forecast future production of oil and gas and to assess forecast uncertainty. This is done by defining a stochastic model for the reservoir characteristics, generating realizations from this model and applying a fluid flow simulator to the realizations. The reservoir characteristics define the geometry of the reservoir, initial saturation, petrophysical properties etc. This thesis discusses how to generate realizations constrained by production data, that is to say, the realizations should reproduce the observed production history of the petroleum reservoir within the uncertainty of these data. The topics discussed are: (1) Theoretical framework, (2) History matching, forecasting and forecasting uncertainty, (3) A three-dimensional test case, (4) Modelling transmissibility multipliers by Markov random fields, (5) Up scaling, (6) The link between model parameters, well observations and production history in a simple test case, (7) Sampling the posterior using optimization in a hierarchical model, (8) A comparison of Rejection Sampling and Metropolis-Hastings algorithm, (9) Stochastic simulation and conditioning by annealing in reservoir description, and (10) Uncertainty assessment in history matching and forecasting. 139 refs., 85 figs., 1 tab.
Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.
Ullah, M; Schmidt, H; Cho, K H; Wolkenhauer, O
2006-03-01
The analysis of complex biochemical networks is conducted in two popular conceptual frameworks for modelling. The deterministic approach requires the solution of ordinary differential equations (ODEs, reaction rate equations) with concentrations as continuous state variables. The stochastic approach involves the simulation of differential-difference equations (chemical master equations, CMEs) with probabilities as variables. This is to generate counts of molecules for chemical species as realisations of random variables drawn from the probability distribution described by the CMEs. Although there are numerous tools available, many of them free, the modelling and simulation environment MATLAB is widely used in the physical and engineering sciences. We describe a collection of MATLAB functions to construct and solve ODEs for deterministic simulation and to implement realisations of CMEs for stochastic simulation using advanced MATLAB coding (Release 14). The program was successfully applied to pathway models from the literature for both cases. The results were compared to implementations using alternative tools for dynamic modelling and simulation of biochemical networks. The aim is to provide a concise set of MATLAB functions that encourage the experimentation with systems biology models. All the script files are available from www.sbi.uni-rostock.de/ publications_matlab-paper.html.
Modelling biochemical reaction systems by stochastic differential equations with reflection.
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2016-05-07
In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.
Evapotranspiration Estimates for a Stochastic Soil-Moisture Model
Chaleeraktrakoon, Chavalit; Somsakun, Somrit
2009-03-01
Potential evapotranspiration is information that is necessary for applying a widely used stochastic model of soil moisture (I. Rodriguez Iturbe, A. Porporato, L. Ridolfi, V. Isham and D. R. Cox, Probabilistic modelling of water balance at a point: The role of climate, soil and vegetation, Proc. Roy. Soc. London A455 (1999) 3789-3805). An objective of the present paper is thus to find a proper estimate of the evapotranspiration for the stochastic model. This estimate is obtained by comparing the calculated soil-moisture distribution resulting from various techniques, such as Thornthwaite, Makkink, Jensen-Haise, FAO Modified Penman, and Blaney-Criddle, with an observed one. The comparison results using five sequences of daily soil-moisture for a dry season from November 2003 to April 2004 (Udornthani Province, Thailand) have indicated that all methods can be used if the weather information required is available. This is because their soil-moisture distributions are alike. In addition, the model is shown to have its ability in approximately describing the phenomenon at a weekly or biweekly time scale which is desirable for agricultural engineering applications.
Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory
Constable, George W. A.; McKane, Alan J.
2017-08-01
The relationship between the M -species stochastic Lotka-Volterra competition (SLVC) model and the M -allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the population size is large but finite, precise conditions are determined for the stochastic dynamics of the SLVC model to be mappable to the neutral Moran model, the Moran model with frequency-independent selection, and the Moran model with frequency-dependent selection (equivalently a game-theoretic formulation of the Moran model). We demonstrate how these mappings can be used to calculate extinction probabilities and the times until a species' extinction in the SLVC model.
Investment timing decisions in a stochastic duopoly model
Energy Technology Data Exchange (ETDEWEB)
Marseguerra, Giovanni [Istituto di Econometria e CRANEC, Universita Cattolica del Sacro Cuore di Milan (Italy)]. E-mail: giovanni.marseguerra@unicatt.it; Cortelezzi, Flavia [Dipartimento di Diritto ed Economia delle Persone e delle Imprese, Universita dell' Insubria (Italy)]. E-mail: flavia.cortelezzi@uninsubria.it; Dominioni, Armando [CORE-Catholique de Louvain la Neuve (Belgium)]. E-mail: dominioni@core.ucl.ac.be
2006-08-15
We investigate the role of strategic considerations on the optimal timing of investment when firms compete for a new market (e.g., the provision of an innovative product) under demand uncertainty. Within a continuous time model of stochastic oligopoly, we show that strategic considerations are likely to be of limited impact when the new product is radically innovative whilst the fear of a rival's entry may deeply affect firms' decisions whenever innovation is to some extent limited. The welfare analysis shows surprisingly that the desirability of the different market structures considered does not depend on the fixed entry cost.
Investment timing decisions in a stochastic duopoly model
International Nuclear Information System (INIS)
Marseguerra, Giovanni; Cortelezzi, Flavia; Dominioni, Armando
2006-01-01
We investigate the role of strategic considerations on the optimal timing of investment when firms compete for a new market (e.g., the provision of an innovative product) under demand uncertainty. Within a continuous time model of stochastic oligopoly, we show that strategic considerations are likely to be of limited impact when the new product is radically innovative whilst the fear of a rival's entry may deeply affect firms' decisions whenever innovation is to some extent limited. The welfare analysis shows surprisingly that the desirability of the different market structures considered does not depend on the fixed entry cost
Characterizing economic trends by Bayesian stochastic model specification search
DEFF Research Database (Denmark)
Grassi, Stefano; Proietti, Tommaso
on whether their parameters are fixed or evolutive. Stochastic model specification is carried out to discriminate two alternative hypotheses concerning the generation of trends: the trend-stationary hypothesis, on the one hand, for which the trend is a deterministic function of time and the short run...... dynamics are represented by a stationary autoregressive process; the difference-stationary hypothesis, on the other, according to which the trend results from the cumulation of the effects of random disturbances. We illustrate the methodology for a set of U.S. macroeconomic time series, which includes...
A stochastic large deformation model for computational anatomy
DEFF Research Database (Denmark)
Arnaudon, Alexis; Holm, Darryl D.; Pai, Akshay Sadananda Uppinakudru
2017-01-01
In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation...... Diffeomorphic Metric Mapping (LDDMM) framework. By accounting for randomness in a particular setup which is crafted to fit the geometrical properties of LDDMM, we formulate the template estimation problem for landmarks with noise and give two methods for efficiently estimating the parameters of the noise fields...
Brownian motion model with stochastic parameters for asset prices
Ching, Soo Huei; Hin, Pooi Ah
2013-09-01
The Brownian motion model may not be a completely realistic model for asset prices because in real asset prices the drift μ and volatility σ may change over time. Presently we consider a model in which the parameter x = (μ,σ) is such that its value x (t + Δt) at a short time Δt ahead of the present time t depends on the value of the asset price at time t + Δt as well as the present parameter value x(t) and m-1 other parameter values before time t via a conditional distribution. The Malaysian stock prices are used to compare the performance of the Brownian motion model with fixed parameter with that of the model with stochastic parameter.
Algorithmic detectability threshold of the stochastic block model
Kawamoto, Tatsuro
2018-03-01
The assumption that the values of model parameters are known or correctly learned, i.e., the Nishimori condition, is one of the requirements for the detectability analysis of the stochastic block model in statistical inference. In practice, however, there is no example demonstrating that we can know the model parameters beforehand, and there is no guarantee that the model parameters can be learned accurately. In this study, we consider the expectation-maximization (EM) algorithm with belief propagation (BP) and derive its algorithmic detectability threshold. Our analysis is not restricted to the community structure but includes general modular structures. Because the algorithm cannot always learn the planted model parameters correctly, the algorithmic detectability threshold is qualitatively different from the one with the Nishimori condition.
Stochastic modelling of groundwater flow at the WIPP site
International Nuclear Information System (INIS)
Cliffe, K.A.; Jackson, C.P.
1993-01-01
A stochastic approach to modelling the groundwater flow in the vicinity of the WIPP site in New Mexico is described. A geostatistical model of the transmissivity of the Culebra dolomite was constructed on the basis of experimental measurements. The uncertainty in various quantities of interest in a repository performance assessment, such as the time to travel to the boundary of the model domain, were studied using a Monte-Carlo technique. The results indicate that conditioning the transmissivity on the measured values can lead to a significant reduction in uncertainty. The issue of validation of statistical models is also addressed. Several statistical tests were applied to the models and it is suggested that hypothesis testing can be a useful technique for validation
Using Stochastic Model Checking to Provision Complex Business Services
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2012-01-01
We present a framework for modelling and analysis of real-world business workflows. Business processes regularly form the basis for the design of software services, and frequently display complex stochastic behaviour. The accurate evaluation of their qualitative aspects can allow for determining...... bounds on resources consumed during execution of business processes. Accurate resource provisioning is often central to ensuring the safe execution of a process. We first introduce a formalised core subset of the Business Process Modelling and Notation (BPMN), which we extend with probabilistic and non......-deterministic branching and reward annotations. We then develop an algorithm for the efficient translation of these models into the guarded command language used by the model checker PRISM, in turn enabling model checking of BPMN processes and allowing for the calculation of a wide range of quantitative properties...
The BDS Triple Frequency Pseudo-range Correlated Stochastic Model of Single Station Modeling Method
Directory of Open Access Journals (Sweden)
HUANG Lingyong
2017-05-01
Full Text Available In order to provide a reliable pseudo-range stochastic model, a method is studied to estimate the BDS triple-frequency pseudo-range related stochastic model based on three BDS triple-frequency pseudo-range minus carrier (GIF combinations using the data of a single station. In this algorithm, the low order polynomial fitting method is used to fit the GIF combination in order to eliminate the error and other constants except non pseudo noise at first. And then, multiple linear regression analysis method is used to model the stochastic function of three linearly independent GIF combinations. Finally the related stochastic model of the original BDS triple-frequency pseudo-range observations is obtained by linear transformation. The BDS triple-frequency data verification results show that this algorithm can get a single station related stochastic model of BDS triple-frequency pseudo-range observation, and it is advantageous to provide accurate stochastic model for navigation and positioning and integrity monitoring.
Development of the Stochastic Lung Model for Asthma
International Nuclear Information System (INIS)
Dobos, E.; Borbely-Kiss, I.; Kertesz, Zs.; Balashazy, I.
2005-01-01
Complete text of publication follows. The Stochastic Lung Model is a state-of-the-art tool for the investigation of the health impact of atmospheric aerosols. This model has already been tested and applied to calculate the deposition fractions of aerosols in different regions of the human respiratory tract. The health effects of inhaled aerosols may strongly depend on the distribution of deposition within the respiratory tract. In the current study three Asthma Models have been incorporated into the Stochastic Lung Deposition Code. A common new feature of these models is that the breathing cycle may be asymmetric. It means that the inspiration time, the expiration time and the two breath hold times are independent. And the code can simulate the mucus blockage, too. The main characteristics of the models are the followings: a) ASTHMA MODEL I: One input bronchial asthma factor is applied for the whole tracheobronchial region. The code multiplies all tracheobroncial diameters with this single value. b) ASTHMA MODEL II: Bronchial asthma factors have to be given for each bronchial generation as input data (21 values). The program multiplies the diameter of bronchi with these factors. c) ASTHMA MODEL III: Here, only the range of bronchial asthma factors are presented as input data and the code selects randomly the exact factors in pre-described airway generations. In this case the stochastic character appears in the Asthma Model, as well. As an example, Figure 1 shows the deposition fractions in the tracheobronchial and acinar regions of the human lung in the case of healthy and asthmatic adults at sitting breathing conditions as a function of particle size computed by Asthma Model I where the bronchial asthma factor was 30%. These models have been tested and compared for different types of asthma at various breathing conditions and in a wide range of particle sizes. The distribution of deposition in the characteristic regions of the respiratory tract have been computed
2013-09-30
picture of ENSO-driven autoregressive models for North Pacific SST variability, providing evidence that intermittent processes, such as variability of...intermittent aspects (i) and (ii) are achieved by developing a simple stochastic parameterization for the unresolved details of synoptic -scale...stochastic parameterization of synoptic scale activity to build a stochastic skeleton model for the MJO; this is the first low order model of the MJO which
A spatial stochastic programming model for timber and core area management under risk of fires
Yu Wei; Michael Bevers; Dung Nguyen; Erin Belval
2014-01-01
Previous stochastic models in harvest scheduling seldom address explicit spatial management concerns under the influence of natural disturbances. We employ multistage stochastic programming models to explore the challenges and advantages of building spatial optimization models that account for the influences of random stand-replacing fires. Our exploratory test models...
Simulation of nuclear plant operation into a stochastic energy production model
International Nuclear Information System (INIS)
Pacheco, R.L.
1983-04-01
A simulation model of nuclear plant operation is developed to fit into a stochastic energy production model. In order to improve the stochastic model used, and also reduce its computational time burdened by the aggregation of the model of nuclear plant operation, a study of tail truncation of the unsupplied demand distribution function has been performed. (E.G.) [pt
Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA
Energy Technology Data Exchange (ETDEWEB)
Thimmisetty, Charanraj A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Zhao, Wenju [Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing; Chen, Xiao [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Tong, Charles H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; White, Joshua A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Atmospheric, Earth and Energy Division
2017-10-18
Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.
Modeling energy price dynamics: GARCH versus stochastic volatility
International Nuclear Information System (INIS)
Chan, Joshua C.C.; Grant, Angelia L.
2016-01-01
We compare a number of GARCH and stochastic volatility (SV) models using nine series of oil, petroleum product and natural gas prices in a formal Bayesian model comparison exercise. The competing models include the standard models of GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, and t distributed and moving average innovations. We find that: (1) SV models generally compare favorably to their GARCH counterparts; (2) the jump component and t distributed innovations substantially improve the performance of the standard GARCH, but are unimportant for the SV model; (3) the volatility feedback channel seems to be superfluous; (4) the moving average component markedly improves the fit of both GARCH and SV models; and (5) the leverage effect is important for modeling crude oil prices—West Texas Intermediate and Brent—but not for other energy prices. Overall, the SV model with moving average innovations is the best model for all nine series. - Highlights: • We compare a variety of GARCH and SV models for fitting nine series of energy prices. • We find that SV models generally compare favorably to their GARCH counterparts. • The SV model with moving average innovations is the best model for all nine series.
Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage
Guo, Wenjuan; Cai, Yongli; Zhang, Qimin; Wang, Weiming
2018-02-01
This paper aims to study an SIS epidemic model with media coverage from a general deterministic model to a stochastic differential equation with environment fluctuation. Mathematically, we use the Markov semigroup theory to prove that the basic reproduction number R0s can be used to control the dynamics of stochastic system. Epidemiologically, we show that environment fluctuation can inhibit the occurrence of the disease, namely, in the case of disease persistence for the deterministic model, the disease still dies out with probability one for the stochastic model. So to a great extent the stochastic perturbation under media coverage affects the outbreak of the disease.
Stochastic Four-State Mechanochemical Model of F1-ATPase
International Nuclear Information System (INIS)
Wu Weixia; Zhan Yong; Zhao Tongjun; Han Yingrong; Chen Yafei
2010-01-01
F 1 -ATPase, a part of ATP synthase, can synthesize and hydrolyze ATP moleculars in which the central γ-subunit rotates inside the α 3 β 3 cylinder. A stochastic four-state mechanochemical coupling model of F 1 -ATPase is studied with the aid of the master equation. In this model, the ATP hydrolysis and synthesis are dependent on ATP, ADP, and Pi concentrations. The effects of ATP concentration, ADP concentration, and the external torque on the occupation probability of binding-state, the rotation rate and the diffusion coefficient of F 1 -ATPase are investigated. Moreover, the results from this model are compared with experiments. The mechanochemical mechanism F 1 -ATPase is qualitatively explained by the model. (general)
Stochastic hybrid model of spontaneous dendritic NMDA spikes
International Nuclear Information System (INIS)
Bressloff, Paul C; Newby, Jay M
2014-01-01
Following recent advances in imaging techniques and methods of dendritic stimulation, active voltage spikes have been observed in thin dendritic branches of excitatory pyramidal neurons, where the majority of synapses occur. The generation of these dendritic spikes involves both Na + ion channels and M-methyl-D-aspartate receptor (NMDAR) channels. During strong stimulation of a thin dendrite, the resulting high levels of glutamate, the main excitatory neurotransmitter in the central nervous system and an NMDA agonist, modify the current-voltage (I–V) characteristics of an NMDAR so that it behaves like a voltage-gated Na + channel. Hence, the NMDARs can fire a regenerative dendritic spike, just as Na + channels support the initiation of an action potential following membrane depolarization. However, the duration of the dendritic spike is of the order 100 ms rather than 1 ms, since it involves slow unbinding of glutamate from NMDARs rather than activation of hyperpolarizing K + channels. It has been suggested that dendritic NMDA spikes may play an important role in dendritic computations and provide a cellular substrate for short-term memory. In this paper, we consider a stochastic, conductance-based model of dendritic NMDA spikes, in which the noise originates from the stochastic opening and closing of a finite number of Na + and NMDA receptor ion channels. The resulting model takes the form of a stochastic hybrid system, in which membrane voltage evolves according to a piecewise deterministic dynamics that is coupled to a jump Markov process describing the opening and closing of the ion channels. We formulate the noise-induced initiation and termination of a dendritic spike in terms of a first-passage time problem, under the assumption that glutamate unbinding is negligible, which we then solve using a combination of WKB methods and singular perturbation theory. Using a stochastic phase-plane analysis we then extend our analysis to take proper account of the
A stochastic model of input effectiveness during irregular gamma rhythms.
Dumont, Grégory; Northoff, Georg; Longtin, André
2016-02-01
Gamma-band synchronization has been linked to attention and communication between brain regions, yet the underlying dynamical mechanisms are still unclear. How does the timing and amplitude of inputs to cells that generate an endogenously noisy gamma rhythm affect the network activity and rhythm? How does such "communication through coherence" (CTC) survive in the face of rhythm and input variability? We present a stochastic modelling approach to this question that yields a very fast computation of the effectiveness of inputs to cells involved in gamma rhythms. Our work is partly motivated by recent optogenetic experiments (Cardin et al. Nature, 459(7247), 663-667 2009) that tested the gamma phase-dependence of network responses by first stabilizing the rhythm with periodic light pulses to the interneurons (I). Our computationally efficient model E-I network of stochastic two-state neurons exhibits finite-size fluctuations. Using the Hilbert transform and Kuramoto index, we study how the stochastic phase of its gamma rhythm is entrained by external pulses. We then compute how this rhythmic inhibition controls the effectiveness of external input onto pyramidal (E) cells, and how variability shapes the window of firing opportunity. For transferring the time variations of an external input to the E cells, we find a tradeoff between the phase selectivity and depth of rate modulation. We also show that the CTC is sensitive to the jitter in the arrival times of spikes to the E cells, and to the degree of I-cell entrainment. We further find that CTC can occur even if the underlying deterministic system does not oscillate; quasicycle-type rhythms induced by the finite-size noise retain the basic CTC properties. Finally a resonance analysis confirms the relative importance of the I cell pacing for rhythm generation. Analysis of whole network behaviour, including computations of synchrony, phase and shifts in excitatory-inhibitory balance, can be further sped up by orders of
Zacharuk, Matthias; Stamen, Dolaptchiev; Ulrich, Achatz; Ilya, Timofeyev
2016-04-01
Due to the finite spatial resolution in numerical atmospheric models subgrid-scale (SGS) processes are excluded. A SGS parameterization of these excluded processes might improve the model on all scales. To parameterize the SGS processes we choose the MTV stochastic mode reduction (Majda, Timofeyev, Vanden-Eijnden 2001, A mathematical framework for stochastic climate models. Commun. Pure Appl. Math., 54:891-974). For this the model is separated into fast and slow processes. Using the statistics of the fast processes, a SGS parameterization is found. To identify fast processes the state vector of the model is separated into two state vectors. One vector is the average of the full model state vector in a coarse grid cell. The other describes SGS processes which are defined as the deviation of the full state vector from the coarse cell average. If the SGS vector decorrelates faster in time than the coarse grid vector, the interactions of SGS processes in the equation of the SGS processes are replaced by a local Ornstein-Uhlenbeck process. Afterwards the MTV SGS parameterization can be derived. This method was successfully applied on the Burgers-equation (Dolaptchiev et al. 2013, Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation. Theor. Comp. Fluid Dyn., 27:297-317). In this study we consider a more atmosphere like model and choose a model of the one dimensional shallow water equations (SWe). It will be shown, that the fine state vector decorrelates faster than the coarse state vector. Due to the non-polynomial form of the SWe in flux formulation an approximation of all 1/h (h = fluid depth) terms needs to be done, except of the interactions between coarse state vector to coarse state vector. It will be shown, that this approximation has only minor impact on the model results. In the following the model with the local Ornstein-Uhlenbeck process approximation of SGS interactions is analyzed and compared to the
Kulasiri, Don
2002-01-01
Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas ...
Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process
Turner, Douglas C.; Ladde, Gangaram S.
2018-03-01
Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.
Developing Itô stochastic differential equation models for neuronal signal transduction pathways.
Manninen, Tiina; Linne, Marja-Leena; Ruohonen, Keijo
2006-08-01
Mathematical modeling and simulation of dynamic biochemical systems are receiving considerable attention due to the increasing availability of experimental knowledge of complex intracellular functions. In addition to deterministic approaches, several stochastic approaches have been developed for simulating the time-series behavior of biochemical systems. The problem with stochastic approaches, however, is the larger computational time compared to deterministic approaches. It is therefore necessary to study alternative ways to incorporate stochasticity and to seek approaches that reduce the computational time needed for simulations, yet preserve the characteristic behavior of the system in question. In this work, we develop a computational framework based on the Itô stochastic differential equations for neuronal signal transduction networks. There are several different ways to incorporate stochasticity into deterministic differential equation models and to obtain Itô stochastic differential equations. Two of the developed models are found most suitable for stochastic modeling of neuronal signal transduction. The best models give stable responses which means that the variances of the responses with time are not increasing and negative concentrations are avoided. We also make a comparative analysis of different kinds of stochastic approaches, that is the Itô stochastic differential equations, the chemical Langevin equation, and the Gillespie stochastic simulation algorithm. Different kinds of stochastic approaches can be used to produce similar responses for the neuronal protein kinase C signal transduction pathway. The fine details of the responses vary slightly, depending on the approach and the parameter values. However, when simulating great numbers of chemical species, the Gillespie algorithm is computationally several orders of magnitude slower than the Itô stochastic differential equations and the chemical Langevin equation. Furthermore, the chemical
Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings
Cunha, Americo; Soize, Christian; Sampaio, Rubens
2015-11-01
This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bit-rock interaction model are taken into account using a parametric probabilistic approach. Numerical simulations have shown that the mechanical system of interest has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits.
The Prandtl-Tomlinson model of friction with stochastic driving
Jagla, E. A.
2018-01-01
We consider the classical Prandtl-Tomlinson model of a particle moving on a corrugated potential, pulled by a spring. In the usual situation in which pulling acts at constant velocity \\dotγ , the model displays an average friction force σ that relates to \\dotγ (for small \\dotγ) as \\dotγ˜ (σ-σ_c){\\hspace{0pt}}^β , where σc is a critical friction force. The possible values of β are well known in terms of the analytical properties of the corrugated potential. We study here the situation in which the pulling has, in addition to the constant velocity term, a stochastic term of mechanical origin. We analytically show how this term modifies the force-velocity dependence close to the critical force, and give the value of β in terms of the analytical properties of the corrugation potential and the scaling properties of the stochastic driving, encoded in the value of its Hurst exponent.
Outbreak and Extinction Dynamics in a Stochastic Ebola Model
Nieddu, Garrett; Bianco, Simone; Billings, Lora; Forgoston, Eric; Kaufman, James
A zoonotic disease is a disease that can be passed between animals and humans. In many cases zoonotic diseases can persist in the animal population even if there are no infections in the human population. In this case we call the infected animal population the reservoir for the disease. Ebola virus disease (EVD) and SARS are both notable examples of such diseases. There is little work devoted to understanding stochastic disease extinction and reintroduction in the presence of a reservoir. Here we build a stochastic model for EVD and explicitly consider the presence of an animal reservoir. Using a master equation approach and a WKB ansatz, we determine the associated Hamiltonian of the system. Hamilton's equations are then used to numerically compute the 12-dimensional optimal path to extinction, which is then used to estimate mean extinction times. We also numerically investigate the behavior of the model for dynamic population size. Our results provide an improved understanding of outbreak and extinction dynamics in diseases like EVD.
Stochastic Modeling and Optimization in a Microgrid: A Survey
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Hao Liang
2014-03-01
Full Text Available The future smart grid is expected to be an interconnected network of small-scale and self-contained microgrids, in addition to a large-scale electric power backbone. By utilizing microsources, such as renewable energy sources and combined heat and power plants, microgrids can supply electrical and heat loads in local areas in an economic and environment friendly way. To better adopt the intermittent and weather-dependent renewable power generation, energy storage devices, such as batteries, heat buffers and plug-in electric vehicles (PEVs with vehicle-to-grid systems can be integrated in microgrids. However, significant technical challenges arise in the planning, operation and control of microgrids, due to the randomness in renewable power generation, the buffering effect of energy storage devices and the high mobility of PEVs. The two-way communication functionalities of the future smart grid provide an opportunity to address these challenges, by offering the communication links for microgrid status information collection. However, how to utilize stochastic modeling and optimization tools for efficient, reliable and economic planning, operation and control of microgrids remains an open issue. In this paper, we investigate the key features of microgrids and provide a comprehensive literature survey on the stochastic modeling and optimization tools for a microgrid. Future research directions are also identified.
A stochastic model for speciation by mating preferences.
Coron, Camille; Costa, Manon; Leman, Hélène; Smadi, Charline
2018-05-01
Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the carrying capacity. Our results rely on a fine study of the stochastic process and of its deterministic limit in large population, which is given by a system of coupled nonlinear differential equations. Besides, we propose several generalisations of our model, and prove that our findings are robust for those generalisations.
Stochastic cellular automata model for stock market dynamics.
Bartolozzi, M; Thomas, A W
2004-04-01
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two-dimensional grid. Active traders are characterized by the decision to buy, sigma(i) (t)=+1, or sell, sigma(i) (t)=-1, a stock at a certain discrete time step. The remaining cells are inactive, sigma(i) (t)=0. The trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster. Extreme, intermittent events, such as crashes or bubbles, are triggered by a phase transition in the state of the bigger clusters present on the grid, where almost all the active traders come to share the same spin orientation. Most of the stylized aspects of the financial market time series, including multifractal proprieties, are reproduced by the model. A direct comparison is made with the daily closures of the S&P 500 index.
Stochastic cellular automata model for stock market dynamics
Bartolozzi, M.; Thomas, A. W.
2004-04-01
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two-dimensional grid. Active traders are characterized by the decision to buy, σi (t)=+1 , or sell, σi (t)=-1 , a stock at a certain discrete time step. The remaining cells are inactive, σi (t)=0 . The trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster. Extreme, intermittent events, such as crashes or bubbles, are triggered by a phase transition in the state of the bigger clusters present on the grid, where almost all the active traders come to share the same spin orientation. Most of the stylized aspects of the financial market time series, including multifractal proprieties, are reproduced by the model. A direct comparison is made with the daily closures of the S&P500 index.
Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling
Hackett-Jones, Emily J.
2012-04-17
Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations. © 2012 American Physical Society.
Nonlinear Stochastic Modelling of Antimicrobial resistance in Bacterial Populations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber
an important role for the evolution of resistance. When growing under stressed conditions, such as in the presence of antibiotics, mutators are considered to have an advantages in comparison to non-mutators. This has been supported by a mathematical model for competing growth between a mutator and a non......This thesis applies mathematical modelling and statistical methods to investigate the dynamics and mechanisms of bacterial evolution. More specifically it is concerned with the evolution of antibiotic resistance in bacteria populations, which is an increasing problem for the treatment of infections...... in humans and animals. To prevent the evolution and spread of resistance, there is a need for further understanding of its dynamics. A grey-box modelling approach based on stochastic differential equations is the main and innovative method applied to study bacterial systems in this thesis. Through...
A stochastic delay differential model of cerebral autoregulation.
Directory of Open Access Journals (Sweden)
Simona Panunzi
Full Text Available Mathematical models of the cardiovascular system and of cerebral autoregulation (CAR have been employed for several years in order to describe the time course of pressures and flows changes subsequent to postural changes. The assessment of the degree of efficiency of cerebral auto regulation has indeed importance in the prognosis of such conditions as cerebro-vascular accidents or Alzheimer. In the quest for a simple but realistic mathematical description of cardiovascular control, which may be fitted onto non-invasive experimental observations after postural changes, the present work proposes a first version of an empirical Stochastic Delay Differential Equations (SDDEs model. The model consists of a total of four SDDEs and two ancillary algebraic equations, incorporates four distinct delayed controls from the brain onto different components of the circulation, and is able to accurately capture the time course of mean arterial pressure and cerebral blood flow velocity signals, reproducing observed auto-correlated error around the expected drift.
A stochastic delay differential model of cerebral autoregulation.
Panunzi, Simona; D'Orsi, Laura; Iacoviello, Daniela; De Gaetano, Andrea
2015-01-01
Mathematical models of the cardiovascular system and of cerebral autoregulation (CAR) have been employed for several years in order to describe the time course of pressures and flows changes subsequent to postural changes. The assessment of the degree of efficiency of cerebral auto regulation has indeed importance in the prognosis of such conditions as cerebro-vascular accidents or Alzheimer. In the quest for a simple but realistic mathematical description of cardiovascular control, which may be fitted onto non-invasive experimental observations after postural changes, the present work proposes a first version of an empirical Stochastic Delay Differential Equations (SDDEs) model. The model consists of a total of four SDDEs and two ancillary algebraic equations, incorporates four distinct delayed controls from the brain onto different components of the circulation, and is able to accurately capture the time course of mean arterial pressure and cerebral blood flow velocity signals, reproducing observed auto-correlated error around the expected drift.
Stochastic effects in a discretized kinetic model of economic exchange
Bertotti, M. L.; Chattopadhyay, A. K.; Modanese, G.
2017-04-01
Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker-Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.
Excitability in a stochastic differential equation model for calcium puffs.
Rüdiger, S
2014-06-01
Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.
Prediction of interest rate using CKLS model with stochastic parameters
Energy Technology Data Exchange (ETDEWEB)
Ying, Khor Chia [Faculty of Computing and Informatics, Multimedia University, Jalan Multimedia, 63100 Cyberjaya, Selangor (Malaysia); Hin, Pooi Ah [Sunway University Business School, No. 5, Jalan Universiti, Bandar Sunway, 47500 Subang Jaya, Selangor (Malaysia)
2014-06-19
The Chan, Karolyi, Longstaff and Sanders (CKLS) model is a popular one-factor model for describing the spot interest rates. In this paper, the four parameters in the CKLS model are regarded as stochastic. The parameter vector φ{sup (j)} of four parameters at the (J+n)-th time point is estimated by the j-th window which is defined as the set consisting of the observed interest rates at the j′-th time point where j≤j′≤j+n. To model the variation of φ{sup (j)}, we assume that φ{sup (j)} depends on φ{sup (j−m)}, φ{sup (j−m+1)},…, φ{sup (j−1)} and the interest rate r{sub j+n} at the (j+n)-th time point via a four-dimensional conditional distribution which is derived from a [4(m+1)+1]-dimensional power-normal distribution. Treating the (j+n)-th time point as the present time point, we find a prediction interval for the future value r{sub j+n+1} of the interest rate at the next time point when the value r{sub j+n} of the interest rate is given. From the above four-dimensional conditional distribution, we also find a prediction interval for the future interest rate r{sub j+n+d} at the next d-th (d≥2) time point. The prediction intervals based on the CKLS model with stochastic parameters are found to have better ability of covering the observed future interest rates when compared with those based on the model with fixed parameters.
Estimation of some stochastic models used in reliability engineering
International Nuclear Information System (INIS)
Huovinen, T.
1989-04-01
The work aims to study the estimation of some stochastic models used in reliability engineering. In reliability engineering continuous probability distributions have been used as models for the lifetime of technical components. We consider here the following distributions: exponential, 2-mixture exponential, conditional exponential, Weibull, lognormal and gamma. Maximum likelihood method is used to estimate distributions from observed data which may be either complete or censored. We consider models based on homogeneous Poisson processes such as gamma-poisson and lognormal-poisson models for analysis of failure intensity. We study also a beta-binomial model for analysis of failure probability. The estimators of the parameters for three models are estimated by the matching moments method and in the case of gamma-poisson and beta-binomial models also by maximum likelihood method. A great deal of mathematical or statistical problems that arise in reliability engineering can be solved by utilizing point processes. Here we consider the statistical analysis of non-homogeneous Poisson processes to describe the failing phenomena of a set of components with a Weibull intensity function. We use the method of maximum likelihood to estimate the parameters of the Weibull model. A common cause failure can seriously reduce the reliability of a system. We consider a binomial failure rate (BFR) model as an application of the marked point processes for modelling common cause failure in a system. The parameters of the binomial failure rate model are estimated with the maximum likelihood method
Epigenetics and Evolution: Transposons and the Stochastic Epigenetic Modification Model
Directory of Open Access Journals (Sweden)
Sergio Branciamore
2015-04-01
Full Text Available In addition to genetic variation, epigenetic variation and transposons can greatly affect the evolutionary fitnesses landscape and gene expression. Previously we proposed a mathematical treatment of a general epigenetic variation model that we called Stochastic Epigenetic Modification (SEM model. In this study we follow up with a special case, the Transposon Silencing Model (TSM, with, once again, emphasis on quantitative treatment. We have investigated the evolutionary effects of epigenetic changes due to transposon (T insertions; in particular, we have considered a typical gene locus A and postulated that (i the expression level of gene A depends on the epigenetic state (active or inactive of a cis- located transposon element T, (ii stochastic variability in the epigenetic silencing of T occurs only in a short window of opportunity during development, (iii the epigenetic state is then stable during further development, and (iv the epigenetic memory is fully reset at each generation. We develop the model using two complementary approaches: a standard analytical population genetics framework (di usion equations and Monte-Carlo simulations. Both approaches led to similar estimates for the probability of fixation and time of fixation of locus TA with initial frequency P in a randomly mating diploid population of effective size Ne. We have ascertained the e ect that ρ, the probability of transposon Modification during the developmental window, has on the population (species. One of our principal conclusions is that as ρ increases, the pattern of fixation of the combined TA locus goes from "neutral" to "dominant" to "over-dominant". We observe that, under realistic values of ρ, epigenetic Modifications can provide an e cient mechanism for more rapid fixation of transposons and cis-located gene alleles. The results obtained suggest that epigenetic silencing, even if strictly transient (being reset at each generation, can still have signi cant
Stochastic models for spike trains of single neurons
Sampath, G
1977-01-01
1 Some basic neurophysiology 4 The neuron 1. 1 4 1. 1. 1 The axon 7 1. 1. 2 The synapse 9 12 1. 1. 3 The soma 1. 1. 4 The dendrites 13 13 1. 2 Types of neurons 2 Signals in the nervous system 14 2. 1 Action potentials as point events - point processes in the nervous system 15 18 2. 2 Spontaneous activi~ in neurons 3 Stochastic modelling of single neuron spike trains 19 3. 1 Characteristics of a neuron spike train 19 3. 2 The mathematical neuron 23 4 Superposition models 26 4. 1 superposition of renewal processes 26 4. 2 Superposition of stationary point processe- limiting behaviour 34 4. 2. 1 Palm functions 35 4. 2. 2 Asymptotic behaviour of n stationary point processes superposed 36 4. 3 Superposition models of neuron spike trains 37 4. 3. 1 Model 4. 1 39 4. 3. 2 Model 4. 2 - A superposition model with 40 two input channels 40 4. 3. 3 Model 4. 3 4. 4 Discussion 41 43 5 Deletion models 5. 1 Deletion models with 1nd~endent interaction of excitatory and inhibitory sequences 44 VI 5. 1. 1 Model 5. 1 The basic de...
Setting development goals using stochastic dynamical system models.
Ranganathan, Shyam; Nicolis, Stamatios C; Bali Swain, Ranjula; Sumpter, David J T
2017-01-01
The Millennium Development Goals (MDG) programme was an ambitious attempt to encourage a globalised solution to important but often-overlooked development problems. The programme led to wide-ranging development but it has also been criticised for unrealistic and arbitrary targets. In this paper, we show how country-specific development targets can be set using stochastic, dynamical system models built from historical data. In particular, we show that the MDG target of two-thirds reduction of child mortality from 1990 levels was infeasible for most countries, especially in sub-Saharan Africa. At the same time, the MDG targets were not ambitious enough for fast-developing countries such as Brazil and China. We suggest that model-based setting of country-specific targets is essential for the success of global development programmes such as the Sustainable Development Goals (SDG). This approach should provide clear, quantifiable targets for policymakers.
Stochastic modeling of mode interactions via linear parabolized stability equations
Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo
2017-11-01
Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.
Modeling collective emotions: a stochastic approach based on Brownian agents
International Nuclear Information System (INIS)
Schweitzer, F.
2010-01-01
We develop a agent-based framework to model the emergence of collective emotions, which is applied to online communities. Agents individual emotions are described by their valence and arousal. Using the concept of Brownian agents, these variables change according to a stochastic dynamics, which also considers the feedback from online communication. Agents generate emotional information, which is stored and distributed in a field modeling the online medium. This field affects the emotional states of agents in a non-linear manner. We derive conditions for the emergence of collective emotions, observable in a bimodal valence distribution. Dependent on a saturated or a super linear feedback between the information field and the agent's arousal, we further identify scenarios where collective emotions only appear once or in a repeated manner. The analytical results are illustrated by agent-based computer simulations. Our framework provides testable hypotheses about the emergence of collective emotions, which can be verified by data from online communities. (author)
Modeling the euglycemic hyperinsulinemic clamp by stochastic differential equations.
Picchini, Umberto; Ditlevsen, Susanne; De Gaetano, Andrea
2006-11-01
The Euglycemic Hyperinsulinemic Clamp (EHC) is the most widely used experimental procedure for the determination of insulin sensitivity. In the present study, 16 subjects with BMI between 18.5 and 63.6 kg/m(2) have been studied with a long-duration (5 hours) EHC. In order to explain the oscillations of glycemia occurring in response to the hyperinsulinization and to the continuous glucose infusion at varying speeds, we first hypothesized a system of ordinary differential equations (ODEs), with limited success. We then extended the model and represented the experiment using a system of stochastic differential equations (SDEs). The latter allow for distinction between (i) random variation imputable to observation error and (ii) system noise (intrinsic variability of the metabolic system), due to a variety of influences which change over time. The stochastic model of the EHC was fitted to data and the system noise was estimated by means of a (simulated) maximum likelihood procedure, for a series of different hypothetical measurement error values. We showed that, for the whole range of reasonable measurement error values: (i) the system noise estimates are non-negligible; and (ii) these estimates are robust to changes in the likely value of the measurement error. Explicit expression of system noise is physiologically relevant in this case, since glucose uptake rate is known to be affected by a host of additive influences, usually neglected when modeling metabolism. While in some of the studied subjects system noise appeared to only marginally affect the dynamics, in others the system appeared to be driven more by the erratic oscillations in tissue glucose transport rather than by the overall glucose-insulin control system. It is possible that the quantitative relevance of the unexpressed effects (system noise) should be considered in other physiological situations, represented so far only with deterministic models.
Learning-based stochastic object models for characterizing anatomical variations
Dolly, Steven R.; Lou, Yang; Anastasio, Mark A.; Li, Hua
2018-03-01
It is widely known that the optimization of imaging systems based on objective, task-based measures of image quality via computer-simulation requires the use of a stochastic object model (SOM). However, the development of computationally tractable SOMs that can accurately model the statistical variations in human anatomy within a specified ensemble of patients remains a challenging task. Previously reported numerical anatomic models lack the ability to accurately model inter-patient and inter-organ variations in human anatomy among a broad patient population, mainly because they are established on image data corresponding to a few of patients and individual anatomic organs. This may introduce phantom-specific bias into computer-simulation studies, where the study result is heavily dependent on which phantom is used. In certain applications, however, databases of high-quality volumetric images and organ contours are available that can facilitate this SOM development. In this work, a novel and tractable methodology for learning a SOM and generating numerical phantoms from a set of volumetric training images is developed. The proposed methodology learns geometric attribute distributions (GAD) of human anatomic organs from a broad patient population, which characterize both centroid relationships between neighboring organs and anatomic shape similarity of individual organs among patients. By randomly sampling the learned centroid and shape GADs with the constraints of the respective principal attribute variations learned from the training data, an ensemble of stochastic objects can be created. The randomness in organ shape and position reflects the learned variability of human anatomy. To demonstrate the methodology, a SOM of an adult male pelvis is computed and examples of corresponding numerical phantoms are created.
Stochastic process corrosion growth models for pipeline reliability
International Nuclear Information System (INIS)
Bazán, Felipe Alexander Vargas; Beck, André Teófilo
2013-01-01
Highlights: •Novel non-linear stochastic process corrosion growth model is proposed. •Corrosion rate modeled as random Poisson pulses. •Time to corrosion initiation and inherent time-variability properly represented. •Continuous corrosion growth histories obtained. •Model is shown to precisely fit actual corrosion data at two time points. -- Abstract: Linear random variable corrosion models are extensively employed in reliability analysis of pipelines. However, linear models grossly neglect well-known characteristics of the corrosion process. Herein, a non-linear model is proposed, where corrosion rate is represented as a Poisson square wave process. The resulting model represents inherent time-variability of corrosion growth, produces continuous growth and leads to mean growth at less-than-one power of time. Different corrosion models are adjusted to the same set of actual corrosion data for two inspections. The proposed non-linear random process corrosion growth model leads to the best fit to the data, while better representing problem physics
Stochastic linear hybrid systems: Modeling, estimation, and application
Seah, Chze Eng
Hybrid systems are dynamical systems which have interacting continuous state and discrete state (or mode). Accurate modeling and state estimation of hybrid systems are important in many applications. We propose a hybrid system model, known as the Stochastic Linear Hybrid System (SLHS), to describe hybrid systems with stochastic linear system dynamics in each mode and stochastic continuous-state-dependent mode transitions. We then develop a hybrid estimation algorithm, called the State-Dependent-Transition Hybrid Estimation (SDTHE) algorithm, to estimate the continuous state and discrete state of the SLHS from noisy measurements. It is shown that the SDTHE algorithm is more accurate or more computationally efficient than existing hybrid estimation algorithms. Next, we develop a performance analysis algorithm to evaluate the performance of the SDTHE algorithm in a given operating scenario. We also investigate sufficient conditions for the stability of the SDTHE algorithm. The proposed SLHS model and SDTHE algorithm are illustrated to be useful in several applications. In Air Traffic Control (ATC), to facilitate implementations of new efficient operational concepts, accurate modeling and estimation of aircraft trajectories are needed. In ATC, an aircraft's trajectory can be divided into a number of flight modes. Furthermore, as the aircraft is required to follow a given flight plan or clearance, its flight mode transitions are dependent of its continuous state. However, the flight mode transitions are also stochastic due to navigation uncertainties or unknown pilot intents. Thus, we develop an aircraft dynamics model in ATC based on the SLHS. The SDTHE algorithm is then used in aircraft tracking applications to estimate the positions/velocities of aircraft and their flight modes accurately. Next, we develop an aircraft conformance monitoring algorithm to detect any deviations of aircraft trajectories in ATC that might compromise safety. In this application, the SLHS
Energy Technology Data Exchange (ETDEWEB)
Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 Havana (Cuba); Caleyo, F. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)]. E-mail: fcaleyo@gmail.com; Alfonso, L. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico); Rivas, D. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico); Hallen, J.M. [Departamento de Ingenieria, Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)
2007-02-15
In this work, a new stochastic model capable of simulating pitting corrosion is developed and validated. Pitting corrosion is modeled as the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time for pit initiation is simulated as the realization of a Weibull process. In this way, the exponential and Weibull distributions can be considered as the possible distributions for pit initiation time. Pit growth is simulated using a nonhomogeneous Markov process. Extreme value statistics is used to find the distribution of maximum pit depths resulting from the combination of the initiation and growth processes for multiple pits. The proposed model is validated using several published experiments on pitting corrosion. It is capable of reproducing the experimental observations with higher quality than the stochastic models available in the literature for pitting corrosion.
Lv, Qiming; Schneider, Manuel K; Pitchford, Jonathan W
2008-08-01
We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.
A nested multisite daily rainfall stochastic generation model
Srikanthan, Ratnasingham; Pegram, Geoffrey G. S.
2009-06-01
SummaryThis paper describes a nested multisite daily rainfall generation model which preserves the statistics at daily, monthly and annual levels of aggregation. A multisite two-part daily model is nested in multisite monthly, then annual models. A multivariate set of fourth order Markov chains is used to model the daily occurrence of rainfall; the daily spatial correlation in the occurrence process is handled by using suitably correlated uniformly distributed variates via a Normal Scores Transform (NST) obtained from a set of matched multinormal pseudo-random variates, following Wilks [Wilks, D.S., 1998. Multisite generalisation of a daily stochastic precipitation generation model. Journal of Hydrology 210, 178-191]; we call it a hidden covariance model. A spatially correlated two parameter gamma distribution is used to obtain the rainfall depths; these values are also correlated via a specially matched hidden multinormal process. For nesting, the generated daily rainfall sequences at all the sites are aggregated to monthly rainfall values and these values are modified by a set of lag-1 autoregressive multisite monthly rainfall models. The modified monthly rainfall values are aggregated to annual rainfall and these are then modified by a lag-1 autoregressive multisite annual model. This nesting process ensures that the daily, monthly and annual means and covariances are preserved. The model was applied to a region with 30 rainfall sites, one of the five sets reported by Srikanthan [Srikanthan, R., 2005. Stochastic Generation of Daily Rainfall Data at a Number of Sites. Technical Report 05/7, CRC for Catchment Hydrology. Monash University, 66p]. A comparison of the historical and generated statistics shows that the model preserves all the important characteristics of rainfall at the daily, monthly and annual time scales, including the spatial structure. There are some outstanding features that need to be improved: depths of rainfall on isolated wet days and
Dynamics of a stochastic HIV-1 infection model with logistic growth
Jiang, Daqing; Liu, Qun; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed; Xia, Peiyan
2017-03-01
This paper is concerned with a stochastic HIV-1 infection model with logistic growth. Firstly, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HIV-1 infection model. Then we obtain sufficient conditions for extinction of the infection. The stationary distribution shows that the infection can become persistent in vivo.
Filtering and identification of stochastic volatility for parabolic type factor models
Aihara, ShinIchi; Bagchi, Arunabha
2006-01-01
We consider the dynamics of forward rate process which is modeled by a parabolic type infinite-dimensional factor model with stochastic volatility. The parameters included in the stochastic volatility dynamics are estimated from the factor process as the observation data. Based on the maximum
On cross-currency models with stochastic volatility and correlated interest rates
Grzelak, L.A.; Oosterlee, C.W.
2010-01-01
We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of
An equity-interest rate hybrid model with stochastic volatility and the interest rate smile
Grzelak, L.A.; Oosterlee, C.W.
2010-01-01
We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main
Stochastic regime switching SIR model driven by Lévy noise
Guo, Yingjia
2017-08-01
We propose a new stochastic regime switching SIR model driven by Lévy noise. A unique global positive solution is obtained under some appropriate conditions. Moreover, we investigate the asymptotic behavior of the stochastic SIR model with jumps under regime switching.
Characterization of positive solution to stochastic competitor-competitor-cooperative model
Directory of Open Access Journals (Sweden)
Partha Sarathi Mandal
2013-04-01
Full Text Available In this article we study a randomized three-dimensional Lotka-Volterra model with competitor-competitor-mutualist interaction. We show the existence, uniqueness, moment boundedness, stochastic boundedness and global asymptotic stability of positive global solutions for this stochastic model. Analytical results are validated by numerical examples.
A low-bias simulation scheme for the SABR stochastic volatility model
B. Chen (Bin); C.W. Oosterlee (Cornelis); J.A.M. van der Weide
2012-01-01
htmlabstractThe Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop an lowbias simulation scheme for the SABR-SV model, which deals efficiently with (undesired)
Optimal Stochastic Modeling and Control of Flexible Structures
1988-09-01
2.17. H. Kwakernaak & R. Sivan, Linear Optimal Control Systems, Wiley-Interscicncc, N.Y., 1972. 2.18. Karl J. Astrom , Introduction to Stochastic...Systems with Multiplicative and Additive Noise," UCLA, Ph.D. Dissertation, 1981. 4.7. K.J. Astrom , Introduction to Stochastic Control Theory, Academic...Unified Approach," to appear. 7.29 Astrom , K. J., Introduction to Stochastic Control Theory, Academic Press, N.Y., 1970. 310 CONCLUSIVE REMARKS A
Oriented stochastic data envelopment models: ranking comparison to stochastic frontier approach
Czech Academy of Sciences Publication Activity Database
Brázdik, František
-, č. 271 (2005), s. 1-46 ISSN 1211-3298 Institutional research plan: CEZ:AV0Z70850503 Keywords : stochastic data envelopment analysis * linear programming * rice farm Subject RIV: AH - Economics http://www.cerge-ei.cz/pdf/wp/Wp271.pdf
Modeling Stochastic Route Choice Behaviors with Equivalent Impedance
Directory of Open Access Journals (Sweden)
Jun Li
2015-01-01
Full Text Available A Logit-based route choice model is proposed to address the overlapping and scaling problems in the traditional multinomial Logit model. The nonoverlapping links are defined as a subnetwork, and its equivalent impedance is explicitly calculated in order to simply network analyzing. The overlapping links are repeatedly merged into subnetworks with Logit-based equivalent travel costs. The choice set at each intersection comprises only the virtual equivalent route without overlapping. In order to capture heterogeneity in perception errors of different sizes of networks, different scale parameters are assigned to subnetworks and they are linked to the topological relationships to avoid estimation burden. The proposed model provides an alternative method to model the stochastic route choice behaviors without the overlapping and scaling problems, and it still maintains the simple and closed-form expression from the MNL model. A link-based loading algorithm based on Dial’s algorithm is proposed to obviate route enumeration and it is suitable to be applied on large-scale networks. Finally a comparison between the proposed model and other route choice models is given by numerical examples.
A stochastic differential equation model of diurnal cortisol patterns
Brown, E. N.; Meehan, P. M.; Dempster, A. P.
2001-01-01
Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.
Neural network connectivity and response latency modelled by stochastic processes
DEFF Research Database (Denmark)
Tamborrino, Massimiliano
is connected to thousands of other neurons. The rst question is: how to model neural networks through stochastic processes? A multivariate Ornstein-Uhlenbeck process, obtained as a diffusion approximation of a jump process, is the proposed answer. Obviously, dependencies between neurons imply dependencies...... between their spike times. Therefore, the second question is: how to detect neural network connectivity from simultaneously recorded spike trains? Answering this question corresponds to investigate the joint distribution of sequences of rst passage times. A non-parametric method based on copulas...... generation of pikes. When a stimulus is applied to the network, the spontaneous rings may prevail and hamper detection of the effects of the stimulus. Therefore, the spontaneous rings cannot be ignored and the response latency has to be detected on top of a background signal. Everything becomes more dicult...
A Stochastic Memory Model for ADL Detection in Human Households
Directory of Open Access Journals (Sweden)
Jana Clement
2017-11-01
Full Text Available Many Human Activity Recognition (HAR systems are able to detect sequential executed Activity of Daily Living (ADL. However, a person is capable of doing two things in parallel or pausing one ADL and finishing it later. Thus, a HAR system must be capable of remembering and deciding which ADL is completed and which might be continued after the current ADL. We address this case by combining a stochastic Markov model and a psychological memory function to detect parallel ADL. For the evaluation, we use an input dataset and a publicly available benchmark. Our approach outperforms the leading HAR systems for the used benchmark by 5%, while using a more cost-effective installation environment. Furthermore, we address an unsupervised learning method to train the HAR system and explain the algorithm of parallel ADL detection in detail.
Stochastic modeling of interannual variation of hydrologic variables
Dralle, David; Karst, Nathaniel; Müller, Marc; Vico, Giulia; Thompson, Sally E.
2017-07-01
Quantifying the interannual variability of hydrologic variables (such as annual flow volumes, and solute or sediment loads) is a central challenge in hydrologic modeling. Annual or seasonal hydrologic variables are themselves the integral of instantaneous variations and can be well approximated as an aggregate sum of the daily variable. Process-based, probabilistic techniques are available to describe the stochastic structure of daily flow, yet estimating interannual variations in the corresponding aggregated variable requires consideration of the autocorrelation structure of the flow time series. Here we present a method based on a probabilistic streamflow description to obtain the interannual variability of flow-derived variables. The results provide insight into the mechanistic genesis of interannual variability of hydrologic processes. Such clarification can assist in the characterization of ecosystem risk and uncertainty in water resources management. We demonstrate two applications, one quantifying seasonal flow variability and the other quantifying net suspended sediment export.
Stochastic Energy Deployment System (SEDS) World Oil Model (WOM)
Energy Technology Data Exchange (ETDEWEB)
2009-08-07
The function of the World Oil Market Model (WOMM) is to calculate a world oil price. SEDS will set start and end dates for the forecast period, and a time increment (assumed to be 1 year in the initial version). The WOMM will then randomly select an Annual Energy Outlook (AEO) oil price case and calibrate itself to that case. As it steps through each year, the WOMM will generate a stochastic supply shock to OPEC output and accept a new estimate of U.S. petroleum demand from SEDS. The WOMM will then calculate a new oil market equilibrium for the current year. The world oil price at the new equilibrium will be sent back to SEDS. When the end year is reached, the process will begin again with the selection of a new AEO forecast. Iterations over forecasts will continue until SEDS has completed all its simulation runs.
On the stochastic SIS epidemic model in a periodic environment.
Bacaër, Nicolas
2015-08-01
In the stochastic SIS epidemic model with a contact rate a, a recovery rate b < a, and a population size N, the mean extinction time τ is such that (log τ)/N converges to c = b/a - 1 - log(b/a) as N grows to infinity. This article considers the more realistic case where the contact rate a(t) is a periodic function whose average is bigger than b. Then log τ/N converges to a new limit C, which is linked to a time-periodic Hamilton-Jacobi equation. When a(t) is a cosine function with small amplitude or high (resp. low) frequency, approximate formulas for C can be obtained analytically following the method used in Assaf et al. (Phys Rev E 78:041123, 2008). These results are illustrated by numerical simulations.
Maximum caliber inference and the stochastic Ising model
Cafaro, Carlo; Ali, Sean Alan
2016-11-01
We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we maximize the path entropy over discrete time step trajectories subject to normalization, stationarity, and detailed balance constraints together with a path-dependent dynamical information constraint reflecting a given average global behavior of the complex system. A general expression for the transition probability values associated with the stationary random Markov processes describing the nonequilibrium stationary system is computed. By virtue of our analysis, we uncover that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier of the general expression for the transition probability leads to a formal overlap with the well-known Glauber hyperbolic tangent rule for the transition probability for the stochastic Ising model in the limit of very high temperatures of the heat reservoir.
Porters versus rowers: a unified stochastic model of motor proteins.
Leibler, S; Huse, D A
1993-06-01
We present a general phenomenological theory for chemical to mechanical energy transduction by motor enzymes which is based on the classical "tight-coupling" mechanism. The associated minimal stochastic model takes explicitly into account both ATP hydrolysis and thermal noise effects. It provides expressions for the hydrolysis rate and the sliding velocity, as functions of the ATP concentration and the number of motor enzymes. It explains in a unified way many results of recent in vitro motility assays. More importantly, the theory provides a natural classification scheme for the motors: it correlates the biochemical and mechanical differences between "porters" such as cellular kinesins or dyneins, and "rowers" such as muscular myosins or flagellar dyneins.
Stochastic Modeling Approach to the Incubation Time of Prionic Diseases
Ferreira, A. S.; da Silva, M. A.; Cressoni, J. C.
2003-05-01
Transmissible spongiform encephalopathies are neurodegenerative diseases for which prions are the attributed pathogenic agents. A widely accepted theory assumes that prion replication is due to a direct interaction between the pathologic (PrPSc) form and the host-encoded (PrPC) conformation, in a kind of autocatalytic process. Here we show that the overall features of the incubation time of prion diseases are readily obtained if the prion reaction is described by a simple mean-field model. An analytical expression for the incubation time distribution then follows by associating the rate constant to a stochastic variable log normally distributed. The incubation time distribution is then also shown to be log normal and fits the observed BSE (bovine spongiform encephalopathy) data very well. Computer simulation results also yield the correct BSE incubation time distribution at low PrPC densities.
Handbook of EOQ inventory problems stochastic and deterministic models and applications
Choi, Tsan-Ming
2013-01-01
This book explores deterministic and stochastic EOQ-model based problems and applications, presenting technical analyses of single-echelon EOQ model based inventory problems, and applications of the EOQ model for multi-echelon supply chain inventory analysis.
A Stochastic Programming Model for Fuel Treatment Management
Directory of Open Access Journals (Sweden)
Mohannad Kabli
2015-06-01
Full Text Available This work considers a two-stage stochastic integer programming (SIP approach for optimizing fuel treatment planning under uncertainty in weather and fire occurrence for rural forests. Given a set of areas for potentially performing fuel treatment, the problem is to decide the best treatment option for each area under uncertainty in future weather and fire occurrence. A two-stage SIP model is devised whose objective is to minimize the here-and-now cost of fuel treatment in the first-stage, plus the expected future costs due to uncertain impact from potential fires in the second-stage calculated as ecosystem services losses. The model considers four fuel treatment options: no treatment, mechanical thinning, prescribed fire, and grazing. Several constraints such as budgetary and labor constraints are included in the model and a standard fire behavior model is used to estimate some of the parameters of the model such as fuel levels at the beginning of the fire season. The SIP model was applied to data for a study area in East Texas with 15 treatment areas under different weather scenarios. The results of the study show, for example, that unless the expected ecosystem services values for an area outweigh fuel treatment costs, no treatment is the best choice for the area. Thus the valuation of the area together with the probability of fire occurrence and behavior strongly drive fuel treatment choices.
Stochastic modeling of the cover effect and bedrock erosion
Turowski, Jens M.
2009-03-01
Several important fluvial bedrock erosion processes are driven by the impact of bed load particles. Bed load transport rates fluctuate strongly in both nature and experiment, and stochastic models of the transport processes have been put forward to describe this behavior. In this paper I adapt a model based on a Markov chain formulation to derive probability distributions for bed load transport rate over a rock bed only partly covered by sediment. I propose a way to calculate the probability distribution of bed cover for given sediment supply using a combinatoric model and combine the two curves to calculate probability distributions for bed cover and erosion rate at constant hydraulics. In the proposed model, mean bed cover is an exponentially declining function of the number of particles in the control volume. The model describes recently published experimental data well, but at the moment it is not possible to finally discriminate between the exponential and the previously proposed linear model formulation. Distributions of erosion rate are fairly broad functions slightly skewed toward high erosion rates.
Volkova, Victoriya V; Lu, Zhao; Lanzas, Cristina; Scott, H Morgan; Gröhn, Yrjö T
2013-01-01
The ubiquitous commensal bacteria harbour genes of antimicrobial resistance (AMR), often on conjugative plasmids. Antimicrobial use in food animals subjects their enteric commensals to antimicrobial pressure. A fraction of enteric Escherichia coli in cattle exhibit plasmid-gene mediated AMR to a third-generation cephalosporin ceftiofur. We adapted stochastic differential equations with diffusion approximation (a compartmental stochastic mathematical model) to research the sources and roles of stochasticity in the resistance dynamics, both during parenteral antimicrobial therapy and in its absence. The results demonstrated that demographic stochasticity among enteric E. coli in the occurrence of relevant events was important for the AMR dynamics only when bacterial numbers were depressed during therapy. However, stochasticity in the parameters of enteric E. coli ecology, whether externally or intrinsically driven, contributed to a wider distribution of the resistant E. coli fraction, both during therapy and in its absence, with stochasticities in individual parameters interacting in their contribution.
Transport in two-dimensional scattering stochastic media: Simulations and models
International Nuclear Information System (INIS)
Haran, O.; Shvarts, D.; Thieberger, R.
1999-01-01
Classical monoenergetic transport of neutral particles in a binary, scattering, two-dimensional stochastic media is discussed. The work focuses on the effective representation of the stochastic media, as obtained by averaging over an ensemble of random realizations of the media. Results of transport simulations in two-dimensional stochastic media are presented and compared against results from several models. Problems for which this work is relevant range from transport through cracked or porous concrete shields and transport through boiling coolant of a nuclear reactor, to transport through stochastic stellar atmospheres
Crisan, Dan
2011-01-01
"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa
Stochastic Model for the Vocabulary Growth in Natural Languages
Gerlach, Martin; Altmann, Eduardo G.
2013-04-01
We propose a stochastic model for the number of different words in a given database which incorporates the dependence on the database size and historical changes. The main feature of our model is the existence of two different classes of words: (i) a finite number of core words, which have higher frequency and do not affect the probability of a new word to be used, and (ii) the remaining virtually infinite number of noncore words, which have lower frequency and, once used, reduce the probability of a new word to be used in the future. Our model relies on a careful analysis of the Google Ngram database of books published in the last centuries, and its main consequence is the generalization of Zipf’s and Heaps’ law to two-scaling regimes. We confirm that these generalizations yield the best simple description of the data among generic descriptive models and that the two free parameters depend only on the language but not on the database. From the point of view of our model, the main change on historical time scales is the composition of the specific words included in the finite list of core words, which we observe to decay exponentially in time with a rate of approximately 30 words per year for English.
Stochastic Dynamics on Hypergraphs and the Spatial Majority Rule Model
Lanchier, N.; Neufer, J.
2013-04-01
This article starts by introducing a new theoretical framework to model spatial systems which is obtained from the framework of interacting particle systems by replacing the traditional graphical structure that defines the network of interactions with a structure of hypergraph. This new perspective is more appropriate to define stochastic spatial processes in which large blocks of vertices may flip simultaneously, which is then applied to define a spatial version of the Galam's majority rule model. In our spatial model, each vertex of the lattice has one of two possible competing opinions, say opinion 0 and opinion 1, as in the popular voter model. Hyperedges are updated at rate one, which results in all the vertices in the hyperedge changing simultaneously their opinion to the majority opinion of the hyperedge. In the case of a tie in hyperedges with even size, a bias is introduced in favor of type 1, which is motivated by the principle of social inertia. Our analytical results along with simulations and heuristic arguments suggest that, in any spatial dimensions and when the set of hyperedges consists of the collection of all n×⋯× n blocks of the lattice, opinion 1 wins when n is even while the system clusters when n is odd, which contrasts with results about the voter model in high dimensions for which opinions coexist. This is fully proved in one dimension while the rest of our analysis focuses on the cases when n=2 and n=3 in two dimensions.
Matrix models and stochastic growth in Donaldson-Thomas theory
International Nuclear Information System (INIS)
Szabo, Richard J.; Tierz, Miguel
2012-01-01
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Llopis-Albert, C.; Capilla, J. E.
2010-09-01
SummaryMajor factors affecting groundwater flow through fractured rocks include the geometry of each fracture, its properties and the fracture-network connectivity together with the porosity and conductivity of the rock matrix. When modelling fractured rocks this is translated into attaining a characterization of the hydraulic conductivity ( K) as adequately as possible, despite its high heterogeneity. This links with the main goal of this paper, which is to present an improvement of a stochastic inverse model, named as Gradual Conditioning (GC) method, to better characterise K in a fractured rock medium by considering different K stochastic structures, belonging to independent K statistical populations (SP) of fracture families and the rock matrix, each one with its own statistical properties. The new methodology is carried out by applying independent deformations to each SP during the conditioning process for constraining stochastic simulations to data. This allows that the statistical properties of each SPs tend to be preserved during the iterative optimization process. It is worthwhile mentioning that so far, no other stochastic inverse modelling technique, with the whole capabilities implemented in the GC method, is able to work with a domain covered by several different stochastic structures taking into account the independence of different populations. The GC method is based on a procedure that gradually changes an initial K field, which is conditioned only to K data, to approximate the reproduction of other types of information, i.e., piezometric head and solute concentration data. The approach is applied to the Äspö Hard Rock Laboratory (HRL) in Sweden, where, since the middle nineties, many experiments have been carried out to increase confidence in alternative radionuclide transport modelling approaches. Because the description of fracture locations and the distribution of hydrodynamic parameters within them are not accurate enough, we address the
Geel, C.R.; Donselaar, M.E.
2007-01-01
Object-based stochastic modelling techniques are routinely employed to generate multiple realisations of the spatial distribution of sediment properties in settings where data density is insufficient to construct a unique deterministic facies architecture model. Challenge is to limit the wide range
DEFF Research Database (Denmark)
Duun-Henriksen, Anne Katrine; Schmidt, S.; Nørgaard, K.
2013-01-01
extension incorporating exercise effects on insulin and glucose dynamics. Our model is constructed as a stochastic state space model consisting of a set of stochastic differential equations (SDEs). In a stochastic state space model, the residual error is split into random measurement error...... physical activity. Exercise constitutes a substantial challenge to closed-loop control of T1D. The effects are many and depend on intensity and duration and may be delayed by several hours. In this study, we use a model for the glucoregulatory system based on the minimal model and a previously published...
A stochastic discrete optimization model for designing container terminal facilities
Zukhruf, Febri; Frazila, Russ Bona; Burhani, Jzolanda Tsavalista
2017-11-01
As uncertainty essentially affect the total transportation cost, it remains important in the container terminal that incorporates several modes and transshipments process. This paper then presents a stochastic discrete optimization model for designing the container terminal, which involves the decision of facilities improvement action. The container terminal operation model is constructed by accounting the variation of demand and facilities performance. In addition, for illustrating the conflicting issue that practically raises in the terminal operation, the model also takes into account the possible increment delay of facilities due to the increasing number of equipment, especially the container truck. Those variations expectantly reflect the uncertainty issue in the container terminal operation. A Monte Carlo simulation is invoked to propagate the variations by following the observed distribution. The problem is constructed within the framework of the combinatorial optimization problem for investigating the optimal decision of facilities improvement. A new variant of glow-worm swarm optimization (GSO) is thus proposed for solving the optimization, which is rarely explored in the transportation field. The model applicability is tested by considering the actual characteristics of the container terminal.
Stochastic many-particle model for LFP electrodes
Guhlke, Clemens; Gajewski, Paul; Maurelli, Mario; Friz, Peter K.; Dreyer, Wolfgang
2018-02-01
In the framework of non-equilibrium thermodynamics, we derive a new model for many-particle electrodes. The model is applied to LiFePO4 (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by both different particle sizes and surface fluctuations leading to a system of stochastic differential equations. An explicit relation between battery voltage and current controlled by the thermodynamic state variables is derived. This voltage-current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate-limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate-limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltage-charge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.
A continuous stochastic model for non-equilibrium dense gases
Sadr, M.; Gorji, M. H.
2017-12-01
While accurate simulations of dense gas flows far from the equilibrium can be achieved by direct simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order to cope with that, an efficient yet accurate solution algorithm based on the Fokker-Planck approximation of the Enskog equation is devised in this paper; the approximation is very much associated with the Fokker-Planck model derived from the Boltzmann equation by Jenny et al. ["A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion," J. Comput. Phys. 229, 1077-1098 (2010)] and Gorji et al. ["Fokker-Planck model for computational studies of monatomic rarefied gas flows," J. Fluid Mech. 680, 574-601 (2011)]. The idea behind these Fokker-Planck descriptions is to project the dynamics of discrete collisions implied by the molecular encounters into a set of continuous Markovian processes subject to the drift and diffusion. Thereby, the evolution of particles representing the governing stochastic process becomes independent from each other and thus very efficient numerical schemes can be constructed. By close inspection of the Enskog operator, it is observed that the dense gas effects contribute further to the advection of molecular quantities. That motivates a modelling approach where the dense gas corrections can be cast in the extra advection of particles. Therefore, the corresponding Fokker-Planck approximation is derived such that the evolution in the physical space accounts for the dense effects present in the pressure, stress tensor, and heat fluxes. Hence the consistency between the devised Fokker-Planck approximation and the Enskog operator is shown for the velocity moments up to the heat fluxes. For validation studies, a homogeneous gas inside a box besides Fourier, Couette, and lid-driven cavity flow setups is considered. The results based on the Fokker-Planck model are
ARIMA-Based Time Series Model of Stochastic Wind Power Generation
DEFF Research Database (Denmark)
Chen, Peiyuan; Pedersen, Troels; Bak-Jensen, Birgitte
2010-01-01
This paper proposes a stochastic wind power model based on an autoregressive integrated moving average (ARIMA) process. The model takes into account the nonstationarity and physical limits of stochastic wind power generation. The model is constructed based on wind power measurement of one year from...... the Nysted offshore wind farm in Denmark. The proposed limited-ARIMA (LARIMA) model introduces a limiter and characterizes the stochastic wind power generation by mean level, temporal correlation and driving noise. The model is validated against the measurement in terms of temporal correlation...... and probability distribution. The LARIMA model outperforms a first-order transition matrix based discrete Markov model in terms of temporal correlation, probability distribution and model parameter number. The proposed LARIMA model is further extended to include the monthly variation of the stochastic wind power...
DEFF Research Database (Denmark)
Sommer, Stefan Horst; Svane, Anne Marie
2017-01-01
We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed in...
On the modelling of nested risk-neutral stochastic processes with applications in insurance
S.N. Singor (Stefan); A. Boer; J.S.C. Alberts; C.W. Oosterlee (Cornelis)
2017-01-01
textabstractWe propose a modelling framework for risk-neutral stochastic processes nested in a real-world stochastic process. The framework is important for insurers that deal with the valuation of embedded options and in particular at future points in time. We make use of the class of State Space
Periodic solution of a stochastic SIRS epidemic model with seasonal variation.
Jin, Manli; Lin, Yuguo
2018-12-01
In this paper, we consider a stochastic SIRS epidemic model with seasonal variation and saturated incidence. Firstly, we obtain the threshold of stochastic system which determines whether the epidemic occurs or not. Secondly, we prove that there is a non-trivial positive periodic solution if [Formula: see text].
van der Linden, Willem J.
1995-01-01
Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributiom. The focus is on the conditions under which stochastic order in families of conditional
Hybrid approaches for multiple-species stochastic reaction–diffusion models
Energy Technology Data Exchange (ETDEWEB)
Spill, Fabian, E-mail: fspill@bu.edu [Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215 (United States); Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Guerrero, Pilar [Department of Mathematics, University College London, Gower Street, London WC1E 6BT (United Kingdom); Alarcon, Tomas [Centre de Recerca Matematica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona) (Spain); Departament de Matemàtiques, Universitat Atonòma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Maini, Philip K. [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Byrne, Helen [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Computational Biology Group, Department of Computer Science, University of Oxford, Oxford OX1 3QD (United Kingdom)
2015-10-15
Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.
Stochastic Coloured Petrinet Based Healthcare Infrastructure Interdependency Model
Nukavarapu, Nivedita; Durbha, Surya
2016-06-01
The Healthcare Critical Infrastructure (HCI) protects all sectors of the society from hazards such as terrorism, infectious disease outbreaks, and natural disasters. HCI plays a significant role in response and recovery across all other sectors in the event of a natural or manmade disaster. However, for its continuity of operations and service delivery HCI is dependent on other interdependent Critical Infrastructures (CI) such as Communications, Electric Supply, Emergency Services, Transportation Systems, and Water Supply System. During a mass casualty due to disasters such as floods, a major challenge that arises for the HCI is to respond to the crisis in a timely manner in an uncertain and variable environment. To address this issue the HCI should be disaster prepared, by fully understanding the complexities and interdependencies that exist in a hospital, emergency department or emergency response event. Modelling and simulation of a disaster scenario with these complexities would help in training and providing an opportunity for all the stakeholders to work together in a coordinated response to a disaster. The paper would present interdependencies related to HCI based on Stochastic Coloured Petri Nets (SCPN) modelling and simulation approach, given a flood scenario as the disaster which would disrupt the infrastructure nodes. The entire model would be integrated with Geographic information based decision support system to visualize the dynamic behaviour of the interdependency of the Healthcare and related CI network in a geographically based environment.
Unified Stochastic Geometry Model for MIMO Cellular Networks with Retransmissions
Afify, Laila H.
2016-10-11
This paper presents a unified mathematical paradigm, based on stochastic geometry, for downlink cellular networks with multiple-input-multiple-output (MIMO) base stations (BSs). The developed paradigm accounts for signal retransmission upon decoding errors, in which the temporal correlation among the signal-to-interference-plus-noise-ratio (SINR) of the original and retransmitted signals is captured. In addition to modeling the effect of retransmission on the network performance, the developed mathematical model presents twofold analysis unification for MIMO cellular networks literature. First, it integrates the tangible decoding error probability and the abstracted (i.e., modulation scheme and receiver type agnostic) outage probability analysis, which are largely disjoint in the literature. Second, it unifies the analysis for different MIMO configurations. The unified MIMO analysis is achieved by abstracting unnecessary information conveyed within the interfering signals by Gaussian signaling approximation along with an equivalent SISO representation for the per-data stream SINR in MIMO cellular networks. We show that the proposed unification simplifies the analysis without sacrificing the model accuracy. To this end, we discuss the diversity-multiplexing tradeoff imposed by different MIMO schemes and shed light on the diversity loss due to the temporal correlation among the SINRs of the original and retransmitted signals. Finally, several design insights are highlighted.
Stochastic resonance in noisy spiking retinal and sensory neuron models.
Patel, Ashok; Kosko, Bart
2005-01-01
Two new theorems show that small amounts of additive white noise can improve the bit count or mutual information of several popular models of spiking retinal neurons and spiking sensory neurons. The first theorem gives necessary and sufficient conditions for this noise benefit or stochastic resonance (SR) effect for subthreshold signals in a standard family of Poisson spiking models of retinal neurons. The result holds for all types of finite-variance noise and for all types of infinite-variance stable noise: SR occurs if and only if a sum of noise means or location parameters falls outside a 'forbidden interval' of values. The second theorem gives a similar forbidden-interval sufficient condition for the SR effect for several types of spiking sensory neurons that include the Fitzhugh-Nagumo neuron, the leaky integrate-and-fire neuron, and the reduced Type I neuron model if the additive noise is Gaussian white noise. Simulations show that neither the forbidden-interval condition nor Gaussianity is necessary for the SR effect.
Stochastic model for gene transcription on Drosophila melanogaster embryos
Prata, Guilherme N.; Hornos, José Eduardo M.; Ramos, Alexandre F.
2016-02-01
We examine immunostaining experimental data for the formation of stripe 2 of even-skipped (eve) transcripts on D. melanogaster embryos. An estimate of the factor converting immunofluorescence intensity units into molecular numbers is given. The analysis of the eve dynamics at the region of stripe 2 suggests that the promoter site of the gene has two distinct regimes: an earlier phase when it is predominantly activated until a critical time when it becomes mainly repressed. That suggests proposing a stochastic binary model for gene transcription on D. melanogaster embryos. Our model has two random variables: the transcripts number and the state of the source of mRNAs given as active or repressed. We are able to reproduce available experimental data for the average number of transcripts. An analysis of the random fluctuations on the number of eves and their consequences on the spatial precision of stripe 2 is presented. We show that the position of the anterior or posterior borders fluctuate around their average position by ˜1 % of the embryo length, which is similar to what is found experimentally. The fitting of data by such a simple model suggests that it can be useful to understand the functions of randomness during developmental processes.
Bayesian parameter estimation for stochastic models of biological cell migration
Dieterich, Peter; Preuss, Roland
2013-08-01
Cell migration plays an essential role under many physiological and patho-physiological conditions. It is of major importance during embryonic development and wound healing. In contrast, it also generates negative effects during inflammation processes, the transmigration of tumors or the formation of metastases. Thus, a reliable quantification and characterization of cell paths could give insight into the dynamics of these processes. Typically stochastic models are applied where parameters are extracted by fitting models to the so-called mean square displacement of the observed cell group. We show that this approach has several disadvantages and problems. Therefore, we propose a simple procedure directly relying on the positions of the cell's trajectory and the covariance matrix of the positions. It is shown that the covariance is identical with the spatial aging correlation function for the supposed linear Gaussian models of Brownian motion with drift and fractional Brownian motion. The technique is applied and illustrated with simulated data showing a reliable parameter estimation from single cell paths.
A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis
Directory of Open Access Journals (Sweden)
Linda J.S. Allen
2017-05-01
Full Text Available Some mathematical methods for formulation and numerical simulation of stochastic epidemic models are presented. Specifically, models are formulated for continuous-time Markov chains and stochastic differential equations. Some well-known examples are used for illustration such as an SIR epidemic model and a host-vector malaria model. Analytical methods for approximating the probability of a disease outbreak are also discussed. Keywords: Branching process, Continuous-time Markov chain, Minor outbreak, Stochastic differential equation, 2000 MSC: 60H10, 60J28, 92D30
Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps
Directory of Open Access Journals (Sweden)
Xinhong Zhang
2013-07-01
Full Text Available This article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for the existence of global positive solutions, stochastically ultimate boundedness and stochastic permanence are established for the n-dimensional model. Asymptotic pathwise behavior of n-dimensional Gilpin-Ayala mutualism model with jumps is also discussed. Finally numerical examples are introduced to illustrate the results developed.
Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory.
Constable, George W A; McKane, Alan J
2017-08-01
The relationship between the M-species stochastic Lotka-Volterra competition (SLVC) model and the M-allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the population size is large but finite, precise conditions are determined for the stochastic dynamics of the SLVC model to be mappable to the neutral Moran model, the Moran model with frequency-independent selection, and the Moran model with frequency-dependent selection (equivalently a game-theoretic formulation of the Moran model). We demonstrate how these mappings can be used to calculate extinction probabilities and the times until a species' extinction in the SLVC model.
SMART (Stochastic Model Acquisition with ReinforcemenT) learning agents: A preliminary report
Child, C. H. T.; Stathis, K.
2005-01-01
We present a framework for building agents that learn using SMART, a system that combines stochastic model acquisition with reinforcement learning to enable an agent to model its environment through experience and subsequently form action selection policies using the acquired model. We extend an existing algorithm for automatic creation of stochastic strips operators [9] as a preliminary method of environment modelling. We then define the process of generation of future states using these ope...
A stochastic model for EEG microstate sequence analysis.
Gärtner, Matthias; Brodbeck, Verena; Laufs, Helmut; Schneider, Gaby
2015-01-01
The analysis of spontaneous resting state neuronal activity is assumed to give insight into the brain function. One noninvasive technique to study resting state activity is electroencephalography (EEG) with a subsequent microstate analysis. This technique reduces the recorded EEG signal to a sequence of prototypical topographical maps, which is hypothesized to capture important spatio-temporal properties of the signal. In a statistical EEG microstate analysis of healthy subjects in wakefulness and three stages of sleep, we observed a simple structure in the microstate transition matrix. It can be described with a first order Markov chain in which the transition probability from the current state (i.e., map) to a different map does not depend on the current map. The resulting transition matrix shows a high agreement with the observed transition matrix, requiring only about 2% of mass transport (1/2 L1-distance). In the second part, we introduce an extended framework in which the simple Markov chain is used to make inferences on a potential underlying time continuous process. This process cannot be directly observed and is therefore usually estimated from discrete sampling points of the EEG signal given by the local maxima of the global field power. Therefore, we propose a simple stochastic model called sampled marked intervals (SMI) model that relates the observed sequence of microstates to an assumed underlying process of background intervals and thus, complements approaches that focus on the analysis of observable microstate sequences. Copyright © 2014 Elsevier Inc. All rights reserved.
A Stochastic Approach to Noise Modeling for Barometric Altimeters
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Angelo Maria Sabatini
2013-11-01
Full Text Available The question whether barometric altimeters can be applied to accurately track human motions is still debated, since their measurement performance are rather poor due to either coarse resolution or drifting behavior problems. As a step toward accurate short-time tracking of changes in height (up to few minutes, we develop a stochastic model that attempts to capture some statistical properties of the barometric altimeter noise. The barometric altimeter noise is decomposed in three components with different physical origin and properties: a deterministic time-varying mean, mainly correlated with global environment changes, and a first-order Gauss-Markov (GM random process, mainly accounting for short-term, local environment changes, the effects of which are prominent, respectively, for long-time and short-time motion tracking; an uncorrelated random process, mainly due to wideband electronic noise, including quantization noise. Autoregressive-moving average (ARMA system identification techniques are used to capture the correlation structure of the piecewise stationary GM component, and to estimate its standard deviation, together with the standard deviation of the uncorrelated component. M-point moving average filters used alone or in combination with whitening filters learnt from ARMA model parameters are further tested in few dynamic motion experiments and discussed for their capability of short-time tracking small-amplitude, low-frequency motions.
Stochastic modeling for magnetic resonance quantification of myocardial blood flow
Seethamraju, Ravi T.; Muehling, Olaf; Panse, Prasad M.; Wilke, Norbert M.; Jerosch-Herold, Michael
2000-10-01
Quantification of myocardial blood flow is useful for determining the functional severity of coronary artery lesions. With advances in MR imaging it has become possible to assess myocardial perfusion and blood flow in a non-invasive manner by rapid serial imaging following injection of contrast agent. To date most approaches reported in the literature relied mostly on deriving relative indices of myocardial perfusion directly from the measured signal intensity curves. The central volume principle on the other hand states that it is possible to derive absolute myocardial blood flow from the tissue impulse response. Because of the sensitivity involved in deconvolution due to noise in measured data, conventional methods are sub-optimal, hence, we propose to use stochastic time series modeling techniques like ARMA to obtain a robust impulse response estimate. It is shown that these methods when applied for the optical estimation of the transfer function give accurate estimates of myocardial blood flow. The most significant advantage of this approach, compared with compartmental tracer kinetic models, is the use of a minimum set of prior assumptions on data. The bottleneck in assessing myocardial blood flow, does not lie in the MRI acquisition, but rather in the effort or time for post processing. It is anticipated that the very limited requirements for user input and interaction will be of significant advantage for the clinical application of these methods. The proposed methods are validated by comparison with mean blood flow measurements obtained from radio-isotope labeled microspheres.
Fish Processed Production Planning Using Integer Stochastic Programming Model
Firmansyah, Mawengkang, Herman
2011-06-01
Fish and its processed products are the most affordable source of animal protein in the diet of most people in Indonesia. The goal in production planning is to meet customer demand over a fixed time horizon divided into planning periods by optimizing the trade-off between economic objectives such as production cost and customer satisfaction level. The major decisions are production and inventory levels for each product and the number of workforce in each planning period. In this paper we consider the management of small scale traditional business at North Sumatera Province which performs processing fish into several local seafood products. The inherent uncertainty of data (e.g. demand, fish availability), together with the sequential evolution of data over time leads the production planning problem to a nonlinear mixed-integer stochastic programming model. We use scenario generation based approach and feasible neighborhood search for solving the model. The results which show the amount of each fish processed product and the number of workforce needed in each horizon planning are presented.
Learning Deep Generative Models With Doubly Stochastic Gradient MCMC.
Du, Chao; Zhu, Jun; Zhang, Bo
2017-06-28
Deep generative models (DGMs), which are often organized in a hierarchical manner, provide a principled framework of capturing the underlying causal factors of data. Recent work on DGMs focussed on the development of efficient and scalable variational inference methods that learn a single model under some mean-field or parameterization assumptions. However, little work has been done on extending Markov chain Monte Carlo (MCMC) methods to Bayesian DGMs, which enjoy many advantages compared with variational methods. We present doubly stochastic gradient MCMC, a simple and generic method for (approximate) Bayesian inference of DGMs in a collapsed continuous parameter space. At each MCMC sampling step, the algorithm randomly draws a mini-batch of data samples to estimate the gradient of log-posterior and further estimates the intractable expectation over hidden variables via a neural adaptive importance sampler, where the proposal distribution is parameterized by a deep neural network and learnt jointly along with the sampling process. We demonstrate the effectiveness of learning various DGMs on a wide range of tasks, including density estimation, data generation, and missing data imputation. Our method outperforms many state-of-the-art competitors.
Hierarchic stochastic modelling applied to intracellular Ca(2+ signals.
Directory of Open Access Journals (Sweden)
Gregor Moenke
Full Text Available Important biological processes like cell signalling and gene expression have noisy components and are very complex at the same time. Mathematical analysis of such systems has often been limited to the study of isolated subsystems, or approximations are used that are difficult to justify. Here we extend a recently published method (Thurley and Falcke, PNAS 2011 which is formulated in observable system configurations instead of molecular transitions. This reduces the number of system states by several orders of magnitude and avoids fitting of kinetic parameters. The method is applied to Ca(2+ signalling. Ca(2+ is a ubiquitous second messenger transmitting information by stochastic sequences of concentration spikes, which arise by coupling of subcellular Ca(2+ release events (puffs. We derive analytical expressions for a mechanistic Ca(2+ model, based on recent data from live cell imaging, and calculate Ca(2+ spike statistics in dependence on cellular parameters like stimulus strength or number of Ca(2+ channels. The new approach substantiates a generic Ca(2+ model, which is a very convenient way to simulate Ca(2+ spike sequences with correct spiking statistics.
A stochastic optimization model for shift scheduling in emergency departments.
El-Rifai, Omar; Garaix, Thierry; Augusto, Vincent; Xie, Xiaolan
2015-09-01
Excessive waiting time in Emergency Departments (ED) can be both a cause of frustration and more importantly, a health concern for patients. Waiting time arises when the demand for work goes beyond the facility's service capacity. ED service capacity mainly depends on human resources and on beds available for patients. In this paper, we focus on human resources organization in an ED and seek to best balance between service quality and working conditions. More specifically, we address the personnel scheduling problem in order to optimize the shift distribution among employees and minimize the total expected patients' waiting time. The problem is also characterized by a multi-stage re-entrant service process. With an appropriate approximation of patients' waiting times, we first propose a stochastic mixed-integer programming model that is solved by a sample average approximation (SAA) approach. The resulting personnel schedules are then evaluated using a discrete-event simulation model. Numerical experiments are then performed with data from a French hospital to compare different personnel scheduling strategies.
Using an atmospheric turbulence model for the stochastic model of geodetic VLBI data analysis
Halsig, Sebastian; Artz, Thomas; Iddink, Andreas; Nothnagel, Axel
2016-06-01
Space-geodetic techniques at radio wavelength, such as global navigation satellite systems and very long baseline interferometry (VLBI), suffer from refractivity of the Earth's atmosphere. These highly dynamic processes, particularly refractivity variations in the neutral atmosphere, contribute considerably to the error budget of these space-geodetic techniques. Here, microscale fluctuations in refractivity lead to elevation-dependent uncertainties and induce physical correlations between the observations. However, up to now such correlations are not considered routinely in the stochastic model of space-geodetic observations, which leads to very optimistic standard deviations of the derived target parameters, such as Earth orientation parameters and station positions. In this study, the standard stochastic model of VLBI observations, which only includes, almost exclusively, the uncertainties from the VLBI correlation process, is now augmented by a variance-covariance matrix derived from an atmospheric turbulence model. Thus, atmospheric refractivity fluctuations in space and time can be quantified. One of the main objectives is to realize a suitable stochastic model of VLBI observations in an operational way. In order to validate the new approach, the turbulence model is applied to several VLBI observation campaigns consisting of different network geometries leading the path for the next-generation VLBI campaigns. It is shown that the stochastic model of VLBI observations can be improved by using high-frequency atmospheric variations and, thus, refining the stochastic model leads to far more realistic standard deviations of the target parameters. The baseline length repeatabilities as a general measure of accuracy of baseline length determinations improve for the turbulence-based solution. Further, this method is well suited for routine VLBI data analysis with limited computational costs.
ARMA modeling of stochastic processes in nuclear reactor with significant detection noise
International Nuclear Information System (INIS)
Zavaljevski, N.
1992-01-01
The theoretical basis of ARMA modelling of stochastic processes in nuclear reactor was presented in a previous paper, neglecting observational noise. The identification of real reactor data indicated that in some experiments the detection noise is significant. Thus a more rigorous theoretical modelling of stochastic processes in nuclear reactor is performed. Starting from the fundamental stochastic differential equations of the Langevin type for the interaction of the detector with neutron field, a new theoretical ARMA model is developed. preliminary identification results confirm the theoretical expectations. (author)
The threshold of a stochastic avian-human influenza epidemic model with psychological effect
Zhang, Fengrong; Zhang, Xinhong
2018-02-01
In this paper, a stochastic avian-human influenza epidemic model with psychological effect in human population and saturation effect within avian population is investigated. This model describes the transmission of avian influenza among avian population and human population in random environments. For stochastic avian-only system, persistence in the mean and extinction of the infected avian population are studied. For the avian-human influenza epidemic system, sufficient conditions for the existence of an ergodic stationary distribution are obtained. Furthermore, a threshold of this stochastic model which determines the outcome of the disease is obtained. Finally, numerical simulations are given to support the theoretical results.
Analyzing Properties of Stochastic Business Processes By Model Checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2013-01-01
This chapter presents an approach to precise formal analysis of business processes with stochastic properties. The method presented here allows for both qualitative and quantitative properties to be individually analyzed at design time without requiring a full specification. This provides...
Complex accident scenarios modelled and analysed by Stochastic Petri Nets
International Nuclear Information System (INIS)
Nývlt, Ondřej; Haugen, Stein; Ferkl, Lukáš
2015-01-01
This paper is focused on the usage of Petri nets for an effective modelling and simulation of complicated accident scenarios, where an order of events can vary and some events may occur anywhere in an event chain. These cases are hardly manageable by traditional methods as event trees – e.g. one pivotal event must be often inserted several times into one branch of the tree. Our approach is based on Stochastic Petri Nets with Predicates and Assertions and on an idea, which comes from the area of Programmable Logic Controllers: an accidental scenario is described as a net of interconnected blocks, which represent parts of the scenario. So the scenario is firstly divided into parts, which are then modelled by Petri nets. Every block can be easily interconnected with other blocks by input/output variables to create complex ones. In the presented approach, every event or a part of a scenario is modelled only once, independently on a number of its occurrences in the scenario. The final model is much more transparent then the corresponding event tree. The method is shown in two case studies, where the advanced one contains a dynamic behavior. - Highlights: • Event & Fault trees have problems with scenarios where an order of events can vary. • Paper presents a method for modelling and analysis of dynamic accident scenarios. • The presented method is based on Petri nets. • The proposed method solves mentioned problems of traditional approaches. • The method is shown in two case studies: simple and advanced (with dynamic behavior)
Model Checking for a Class of Performance Properties of Fluid Stochastic Models
Bujorianu, L.M.; Bujorianu, M.C.; Horváth, A.; Telek, M.
2006-01-01
Recently, there is an explosive development of fluid approa- ches to computer and distributed systems. These approaches are inherently stochastic and generate continuous state space models. Usually, the performance measures for these systems are defined using probabilities of reaching certain sets
Earthquake occurrence as stochastic event: (1) theoretical models
Energy Technology Data Exchange (ETDEWEB)
Basili, A.; Basili, M.; Cagnetti, V.; Colombino, A.; Jorio, V.M.; Mosiello, R.; Norelli, F.; Pacilio, N.; Polinari, D.
1977-01-01
The present article intends liaisoning the stochastic approach in the description of earthquake processes suggested by Lomnitz with the experimental evidence reached by Schenkova that the time distribution of some earthquake occurrence is better described by a Negative Bionomial distribution than by a Poisson distribution. The final purpose of the stochastic approach might be a kind of new way for labeling a given area in terms of seismic risk.
Model Identification Using Stochastic Differential Equation Grey-Box Models in Diabetes
DEFF Research Database (Denmark)
Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard
2013-01-01
BACKGROUND: The acceptance of virtual preclinical testing of control algorithms is growing and thus also the need for robust and reliable models. Models based on ordinary differential equations (ODEs) can rarely be validated with standard statistical tools. Stochastic differential equations (SDEs...... are uncorrelated and provides the possibility to pinpoint model deficiencies. METHODS: An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters...... are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the "time to peak of meal response" parameter. RESULTS: We found that the transformation of the ODE model into an SDE-GB resulted...
Directory of Open Access Journals (Sweden)
Chubing Zhang
2013-01-01
Full Text Available We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.
The Dynamical Behaviors in a Stochastic SIS Epidemic Model with Nonlinear Incidence.
Rifhat, Ramziya; Ge, Qing; Teng, Zhidong
2016-01-01
A stochastic SIS-type epidemic model with general nonlinear incidence and disease-induced mortality is investigated. It is proved that the dynamical behaviors of the model are determined by a certain threshold value [Formula: see text]. That is, when [Formula: see text] and together with an additional condition, the disease is extinct with probability one, and when [Formula: see text], the disease is permanent in the mean in probability, and when there is not disease-related death, the disease oscillates stochastically about a positive number. Furthermore, when [Formula: see text], the model admits positive recurrence and a unique stationary distribution. Particularly, the effects of the intensities of stochastic perturbation for the dynamical behaviors of the model are discussed in detail, and the dynamical behaviors for the stochastic SIS epidemic model with standard incidence are established. Finally, the numerical simulations are presented to illustrate the proposed open problems.
Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control
Gao, Shujing; Zhong, Deming; Zhang, Yan
2018-04-01
In this paper, we establish two new stochastic switched epidemic models with continuous and impulsive control. The stochastic perturbations are considered for the natural death rate in each equation of the models. Firstly, a stochastic switched SILI model with continuous control schemes is investigated. By using Lyapunov-Razumikhin method, the sufficient conditions for extinction in mean are established. Our result shows that the disease could be die out theoretically if threshold value R is less than one, regardless of whether the disease-free solutions of the corresponding subsystems are stable or unstable. Then, a stochastic switched SILI model with continuous control schemes and pulse vaccination is studied. The threshold value R is derived. The global attractivity of the model is also obtained. At last, numerical simulations are carried out to support our results.
Stochastic model of microcredit interest rate in Morocco
Directory of Open Access Journals (Sweden)
Ghita Bennouna
2016-11-01
Full Text Available Access to microcredit can have a beneficial effect on the well-being of low-income households excluded from the traditional banking system. It allows this population to receive affordable financial services to help them to meet their needs and to improve their living conditions. However to provide access to credit, microfinance institutions should ensure not only their social mission but also commercial and financial mission to enable the institution to perpetuate and become self-sufficient. To this end, MFIs (microfinance institutions must apply an interest rate that covers their costs and risk, while generating profits, Also microentrepreneurs need, to this end, to ensure the profitability of their activities. This paper presents the microfinance sector in Morocco. It focuses then on the interest rate applied by the Moroccan microfinance institutions; it provides also a comparative study between Morocco and other comparable countries in terms of interest rates charged to borrowers. Finally, this article presents a stochastic model of the interest rate in microcredit built in random loan repayment periods and on a real example of the program of loans of microfinance institution in Morocco
A model for energy pricing with stochastic emission costs
International Nuclear Information System (INIS)
Elliott, Robert J.; Lyle, Matthew R.; Miao Hong
2010-01-01
We use a supply-demand approach to value energy products exposed to emission cost uncertainty. We find closed form solutions for a number of popularly traded energy derivatives such as: forwards, European call options written on spot prices and European Call options written on forward contracts. Our modeling approach is to first construct noisy supply and demand processes and then equate them to find an equilibrium price. This approach is very general while still allowing for sensitivity analysis within a valuation setting. Our assumption is that, in the presence of emission costs, traditional supply growth will slow down causing output prices of energy products to become more costly over time. However, emission costs do not immediately cause output price appreciation, but instead expose individual projects, particularly those with high emission outputs, to much more extreme risks through the cost side of their profit stream. Our results have implications for hedging and pricing for producers operating in areas facing a stochastic emission cost environment.
OPTIMAL TRAINING POLICY FOR PROMOTION - STOCHASTIC MODELS OF MANPOWER SYSTEMS
Directory of Open Access Journals (Sweden)
V.S.S. Yadavalli
2012-01-01
Full Text Available In this paper, the optimal planning of manpower training programmes in a manpower system with two grades is discussed. The planning of manpower training within a given organization involves a trade-off between training costs and expected return. These planning problems are examined through models that reflect the random nature of manpower movement in two grades. To be specific, the system consists of two grades, grade 1 and grade 2. Any number of persons in grade 2 can be sent for training and after the completion of training, they will stay in grade 2 and will be given promotion as and when vacancies arise in grade 1. Vacancies arise in grade 1 only by wastage. A person in grade 1 can leave the system with probability p. Vacancies are filled with persons in grade 2 who have completed the training. It is assumed that there is a perfect passing rate and that the sizes of both grades are fixed. Assuming that the planning horizon is finite and is T, the underlying stochastic process is identified as a finite state Markov chain and using dynamic programming, a policy is evolved to determine how many persons should be sent for training at any time k so as to minimize the total expected cost for the entire planning period T.
Stochastic Modelling of the Hydraulic Anisotropy of Ash Impoundment Sediment
Slávik, Ivan
2017-12-01
In the case reported here the impoundments of a 400 MW coal heated power plant with an annual production of about 1.5 million tons of fuel ash are of the cross-valley type, operated by the simple and cheap „upstream method”. The aim of the research was to determine overall and local values of the permeability in horizontal as well as in vertical direction and the anisotropy of the thin-layered sedimented ash. The coal ashes are hydraulically transported through pipelines in form of a slurry and periodically floated on the beach of the impoundment. The ashes are deposited in the form of a thin-layered sediment, with random alternation of layers with a coarser or finer granularity. The ash impoundment sediment is anthropogenic sediment with horizontally laminated texture. Therefore, the sediment is anisotropic from the viewpoint of water seepage. The knowledge of the permeability and the seepage anisotropy of the sediment is a basic requirement for the design of an appropriate dewatering system. The seepage anisotropy of the ash sediment has been checked by means of stochastic modelling, based on the correlation between the effective grain diameter and the coefficient of permeability of the ash: the effective grain diameter and the thickness of individual layers have been proposed to be random events.
Longitudinal functional principal component modelling via Stochastic Approximation Monte Carlo
Martinez, Josue G.
2010-06-01
The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented.
The Stochastic stability of a Logistic model with Poisson white noise
International Nuclear Information System (INIS)
Duan Dong-Hai; Xu Wei; Zhou Bing-Chang; Su Jun
2011-01-01
The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised Itô differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species. (general)
The Stochastic stability of a Logistic model with Poisson white noise
Duan, Dong-Hai; Xu, Wei; Su, Jun; Zhou, Bing-Chang
2011-03-01
The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised Itô differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species. Project supported by the National Natural Science Foundation of China (Grant Nos. 10872165 and 10932009).
2017-07-04
This paper presents a stochastic multi-agent optimization model that supports energy infrastruc- : ture planning under uncertainty. The interdependence between dierent decision entities in the : system is captured in an energy supply chain network, w...
Rules of thumb for conservation of metapopulations based on a stochastic winking-patch model
Etienne, R.S.; Heesterbeek, J.A.P.
2001-01-01
From a theoretical viewpoint, nature management basically has two options to prolong metapopulation persistence: decreasing local extinction probabilities and increasing colonization probabilities. This article focuses on those options with a stochastic, single-species metapopulation model. We found
A scalable community detection algorithm for large graphs using stochastic block models
Peng, Chengbin
2017-11-24
Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of
Large Deviations for Stochastic Models of Two-Dimensional Second Grade Fluids
Energy Technology Data Exchange (ETDEWEB)
Zhai, Jianliang, E-mail: zhaijl@ustc.edu.cn [University of Science and Technology of China, School of Mathematical Sciences (China); Zhang, Tusheng, E-mail: Tusheng.Zhang@manchester.ac.uk [University of Manchester, School of Mathematics (United Kingdom)
2017-06-15
In this paper, we establish a large deviation principle for stochastic models of incompressible second grade fluids. The weak convergence method introduced by Budhiraja and Dupuis (Probab Math Statist 20:39–61, 2000) plays an important role.
National Research Council Canada - National Science Library
Shao, Y
2004-01-01
Lagrangian Stochastic (LS) particle models have proven to be a useful computational tool for the description and prediction of dispersion of pollutant releases in complex meteorological situations (e.g...
Rejection-free stochastic simulation of BNGL-encoded models
Energy Technology Data Exchange (ETDEWEB)
Hlavacek, William S [Los Alamos National Laboratory; Monine, Michael I [Los Alamos National Laboratory; Colvin, Joshua [TRANSLATIONAL GENOM; Posner, Richard G [NORTHERN ARIZONA UNIV.; Von Hoff, Daniel D [TRANSLATIONAL GENOMICS RESEARCH INSTIT.
2009-01-01
Formal rules encoded using the BioNetGen language (BNGL) can be used to represent the system-level dynamics of molecular interactions. Rules allow one to compactly and implicitly specify the reaction network implied by a set of molecules and their interactions. Typically, the reaction network implied by a set of rules is large, which makes generation of the underlying rule-defined network expensive. Moreover, the cost of conventional simulation methods typically depends on network size. Together these factors have limited application of the rule-based modeling approach. To overcome this limitation, several methods have recently been developed for determining the reaction dynamics implied by rules while avoiding the expensive step of network generation. The cost of these 'network-free' simulation methods is independent of the number of reactions implied by rules. Software implementing such methods is needed for the analysis of rule-based models of biochemical systems. Here, we present a software tool called RuleMonkey that implements a network-free stochastic simulation method for rule-based models. The method is rejection free, unlike other network-free methods that introduce null events (i.e., steps in the simulation procedure that do not change the state of the reaction system being simulated), and the software is capable of simulating models encoded in BNGL, a general-purpose model-specification language. We verify that RuleMonkey produces correct simulation results, and we compare its performance against DYNSTOC, another BNGL-compliant general-purpose simulator for rule-based models, as well as various problem-specific codes that implement network-free simulation methods. RuleMonkey enables the simulation of models defined by rule sets that imply large-scale reaction networks. It is faster than DYNSTOC for stiff problems, although it requires the use of more computer memory. RuleMonkey is freely available for non-commercial use as a stand
A Stochastic and State Space Model for Tumour Growth and Applications
Directory of Open Access Journals (Sweden)
Wai-Yuan Tan
2009-01-01
Full Text Available We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb (1991, and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables (number of tumour cells. We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.
Rifhat, Ramziya; Wang, Lei; Teng, Zhidong
2017-09-01
In this paper, we investigate the dynamics of a class of periodic stochastic SIS epidemic models with general nonlinear incidence f(S , I) . Some sufficient conditions on the permanence in the mean and extinction of positive solutions with probability one are established. By using the Khasminskii's boundary periodic Markov processes, the existence of stochastic nontrivial periodic solution for the models is also obtained. The numerical simulations are given to illustrate the main theoretical results and some interesting conjectures are presented.
Estimation in continuous-time stochastic| volatility models using nonlinear filters
DEFF Research Database (Denmark)
Nielsen, Jan Nygaard; Vestergaard, M.; Madsen, Henrik
2000-01-01
Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308.......Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308....
Obour Agyekum Kwame O-B; Maxwell Oppong Afriyie; Paul Oswald Kwasi Anane; Affum Emmanuel Ampoma; Matthew Seddoh Akatey
2017-01-01
We explore the dependency of MIMO performance on azimuthal spread (AS) and elevation spread (ES) using correlated-based stochastic models (CBSMs). We represent the transmitter as uniform rectangular array (URA), and derive an analytical function for spatial correlation, in terms of maximum power when phase gradient of the incident wave follows a Student’s t-distribution. We model the correlated-based stochastic MIMO system to investigate the usefulness of the analytical function, under the co...
Microgrid Reliability Modeling and Battery Scheduling Using Stochastic Linear Programming
Energy Technology Data Exchange (ETDEWEB)
Cardoso, Goncalo; Stadler, Michael; Siddiqui, Afzal; Marnay, Chris; DeForest, Nicholas; Barbosa-Povoa, Ana; Ferrao, Paulo
2013-05-23
This paper describes the introduction of stochastic linear programming into Operations DER-CAM, a tool used to obtain optimal operating schedules for a given microgrid under local economic and environmental conditions. This application follows previous work on optimal scheduling of a lithium-iron-phosphate battery given the output uncertainty of a 1 MW molten carbonate fuel cell. Both are in the Santa Rita Jail microgrid, located in Dublin, California. This fuel cell has proven unreliable, partially justifying the consideration of storage options. Several stochastic DER-CAM runs are executed to compare different scenarios to values obtained by a deterministic approach. Results indicate that using a stochastic approach provides a conservative yet more lucrative battery schedule. Lower expected energy bills result, given fuel cell outages, in potential savings exceeding 6percent.
GERMcode: A Stochastic Model for Space Radiation Risk Assessment
Kim, Myung-Hee Y.; Ponomarev, Artem L.; Cucinotta, Francis A.
2012-01-01
A new computer model, the GCR Event-based Risk Model code (GERMcode), was developed to describe biophysical events from high-energy protons and high charge and energy (HZE) particles that have been studied at the NASA Space Radiation Laboratory (NSRL) for the purpose of simulating space radiation biological effects. In the GERMcode, the biophysical description of the passage of HZE particles in tissue and shielding materials is made with a stochastic approach that includes both particle track structure and nuclear interactions. The GERMcode accounts for the major nuclear interaction processes of importance for describing heavy ion beams, including nuclear fragmentation, elastic scattering, and knockout-cascade processes by using the quantum multiple scattering fragmentation (QMSFRG) model. The QMSFRG model has been shown to be in excellent agreement with available experimental data for nuclear fragmentation cross sections. For NSRL applications, the GERMcode evaluates a set of biophysical properties, such as the Poisson distribution of particles or delta-ray hits for a given cellular area and particle dose, the radial dose on tissue, and the frequency distribution of energy deposition in a DNA volume. By utilizing the ProE/Fishbowl ray-tracing analysis, the GERMcode will be used as a bi-directional radiation transport model for future spacecraft shielding analysis in support of Mars mission risk assessments. Recent radiobiological experiments suggest the need for new approaches to risk assessment that include time-dependent biological events due to the signaling times for activation and relaxation of biological processes in cells and tissue. Thus, the tracking of the temporal and spatial distribution of events in tissue is a major goal of the GERMcode in support of the simulation of biological processes important in GCR risk assessments. In order to validate our approach, basic radiobiological responses such as cell survival curves, mutation, chromosomal
Cluster dynamics modelling of materials: A new hybrid deterministic/stochastic coupling approach
Terrier, Pierre; Athènes, Manuel; Jourdan, Thomas; Adjanor, Gilles; Stoltz, Gabriel
2017-12-01
Deterministic simulations of the rate equations governing cluster dynamics in materials are limited by the number of equations to integrate. Stochastic simulations are limited by the high frequency of certain events. We propose a coupling method combining deterministic and stochastic approaches. It allows handling different time scale phenomena for cluster dynamics. This method, based on a splitting of the dynamics, is generic and we highlight two different hybrid deterministic/stochastic methods. These coupling schemes are highly parallelizable and specifically designed to treat large size cluster problems. The proof of concept is made on a simple model of vacancy clustering under thermal ageing.
Optically levitated nanoparticle as a model system for stochastic bistable dynamics.
Ricci, F; Rica, R A; Spasenović, M; Gieseler, J; Rondin, L; Novotny, L; Quidant, R
2017-05-09
Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.
Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence
Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir
2017-11-01
In this paper, a stochastic delayed HIV-1 infection model with nonlinear incidence is proposed and investigated. First of all, we prove that there is a unique global positive solution as desired in any population dynamics. Then by constructing some suitable Lyapunov functions, we show that if the basic reproduction number R0 ≤ 1, then the solution of the stochastic system oscillates around the infection-free equilibrium E0, while if R0 > 1, then the solution of the stochastic system fluctuates around the infective equilibrium E∗. Sufficient conditions of these results are established. Finally, we give some examples and a series of numerical simulations to illustrate the analytical results.
Nonperturbative stochastic method for driven spin-boson model
Orth, Peter P.; Imambekov, Adilet; Le Hur, Karyn
2013-01-01
We introduce and apply a numerically exact method for investigating the real-time dissipative dynamics of quantum impurities embedded in a macroscopic environment beyond the weak-coupling limit. We focus on the spin-boson Hamiltonian that describes a two-level system interacting with a bosonic bath of harmonic oscillators. This model is archetypal for investigating dissipation in quantum systems, and tunable experimental realizations exist in mesoscopic and cold-atom systems. It finds abundant applications in physics ranging from the study of decoherence in quantum computing and quantum optics to extended dynamical mean-field theory. Starting from the real-time Feynman-Vernon path integral, we derive an exact stochastic Schrödinger equation that allows us to compute the full spin density matrix and spin-spin correlation functions beyond weak coupling. We greatly extend our earlier work [P. P. Orth, A. Imambekov, and K. Le Hur, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.032118 82, 032118 (2010)] by fleshing out the core concepts of the method and by presenting a number of interesting applications. Methodologically, we present an analogy between the dissipative dynamics of a quantum spin and that of a classical spin in a random magnetic field. This analogy is used to recover the well-known noninteracting-blip approximation in the weak-coupling limit. We explain in detail how to compute spin-spin autocorrelation functions. As interesting applications of our method, we explore the non-Markovian effects of the initial spin-bath preparation on the dynamics of the coherence σx(t) and of σz(t) under a Landau-Zener sweep of the bias field. We also compute to a high precision the asymptotic long-time dynamics of σz(t) without bias and demonstrate the wide applicability of our approach by calculating the spin dynamics at nonzero bias and different temperatures.
Design starch: stochastic modeling of starch granule biogenesis.
Raguin, Adélaïde; Ebenhöh, Oliver
2017-08-15
Starch is the most widespread and abundant storage carbohydrate in plants and the main source of carbohydrate in the human diet. Owing to its remarkable properties and commercial applications, starch is still of growing interest. Its unique granular structure made of intercalated layers of amylopectin and amylose has been unraveled thanks to recent progress in microscopic imaging, but the origin of such periodicity is still under debate. Both amylose and amylopectin are made of linear chains of α-1,4-bound glucose residues, with branch points formed by α-1,6 linkages. The net difference in the distribution of chain lengths and the branching pattern of amylose (mainly linear), compared with amylopectin (racemose structure), leads to different physico-chemical properties. Amylose is an amorphous and soluble polysaccharide, whereas amylopectin is insoluble and exhibits a highly organized structure of densely packed double helices formed between neighboring linear chains. Contrarily to starch degradation that has been investigated since the early 20th century, starch production is still poorly understood. Most enzymes involved in starch growth (elongation, branching, debranching, and partial hydrolysis) are now identified. However, their specific action, their interplay (cooperative or competitive), and their kinetic properties are still largely unknown. After reviewing recent results on starch structure and starch growth and degradation enzymatic activity, we discuss recent results and current challenges for growing polysaccharides on granular surface. Finally, we highlight the importance of novel stochastic models to support the analysis of recent and complex experimental results, and to address how macroscopic properties emerge from enzymatic activity and structural rearrangements. © 2017 The Author(s).
Design starch: stochastic modeling of starch granule biogenesis
Ebenhöh, Oliver
2017-01-01
Starch is the most widespread and abundant storage carbohydrate in plants and the main source of carbohydrate in the human diet. Owing to its remarkable properties and commercial applications, starch is still of growing interest. Its unique granular structure made of intercalated layers of amylopectin and amylose has been unraveled thanks to recent progress in microscopic imaging, but the origin of such periodicity is still under debate. Both amylose and amylopectin are made of linear chains of α-1,4-bound glucose residues, with branch points formed by α-1,6 linkages. The net difference in the distribution of chain lengths and the branching pattern of amylose (mainly linear), compared with amylopectin (racemose structure), leads to different physico-chemical properties. Amylose is an amorphous and soluble polysaccharide, whereas amylopectin is insoluble and exhibits a highly organized structure of densely packed double helices formed between neighboring linear chains. Contrarily to starch degradation that has been investigated since the early 20th century, starch production is still poorly understood. Most enzymes involved in starch growth (elongation, branching, debranching, and partial hydrolysis) are now identified. However, their specific action, their interplay (cooperative or competitive), and their kinetic properties are still largely unknown. After reviewing recent results on starch structure and starch growth and degradation enzymatic activity, we discuss recent results and current challenges for growing polysaccharides on granular surface. Finally, we highlight the importance of novel stochastic models to support the analysis of recent and complex experimental results, and to address how macroscopic properties emerge from enzymatic activity and structural rearrangements. PMID:28673938
Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem
Directory of Open Access Journals (Sweden)
V. Charles
2011-01-01
Full Text Available In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP problem approach is proposed, which strikes the balance between previous models available in the literature.
Directory of Open Access Journals (Sweden)
Jha Sumit
2012-04-01
Full Text Available Abstract Stochastic Differential Equations (SDE are often used to model the stochastic dynamics of biological systems. Unfortunately, rare but biologically interesting behaviors (e.g., oncogenesis can be difficult to observe in stochastic models. Consequently, the analysis of behaviors of SDE models using numerical simulations can be challenging. We introduce a method for solving the following problem: given a SDE model and a high-level behavioral specification about the dynamics of the model, algorithmically decide whether the model satisfies the specification. While there are a number of techniques for addressing this problem for discrete-state stochastic models, the analysis of SDE and other continuous-state models has received less attention. Our proposed solution uses a combination of Bayesian sequential hypothesis testing, non-identically distributed samples, and Girsanov's theorem for change of measures to examine rare behaviors. We use our algorithm to analyze two SDE models of tumor dynamics. Our use of non-identically distributed samples sampling contributes to the state of the art in statistical verification and model checking of stochastic models by providing an effective means for exposing rare events in SDEs, while retaining the ability to compute bounds on the probability that those events occur.
Jha, Sumit Kumar; Langmead, Christopher James
2012-04-12
Stochastic Differential Equations (SDE) are often used to model the stochastic dynamics of biological systems. Unfortunately, rare but biologically interesting behaviors (e.g., oncogenesis) can be difficult to observe in stochastic models. Consequently, the analysis of behaviors of SDE models using numerical simulations can be challenging. We introduce a method for solving the following problem: given a SDE model and a high-level behavioral specification about the dynamics of the model, algorithmically decide whether the model satisfies the specification. While there are a number of techniques for addressing this problem for discrete-state stochastic models, the analysis of SDE and other continuous-state models has received less attention. Our proposed solution uses a combination of Bayesian sequential hypothesis testing, non-identically distributed samples, and Girsanov's theorem for change of measures to examine rare behaviors. We use our algorithm to analyze two SDE models of tumor dynamics. Our use of non-identically distributed samples sampling contributes to the state of the art in statistical verification and model checking of stochastic models by providing an effective means for exposing rare events in SDEs, while retaining the ability to compute bounds on the probability that those events occur.
Stochastic Greybox Modeling for Control of an Alternating Activated Sludge Process
DEFF Research Database (Denmark)
Halvgaard, Rasmus Fogtmann; Vezzaro, Luca; Grum, M.
We present a stochastic greybox model of a BioDenitro WWTP that can be used for short time horizon Model Predictive Control. The model is based on a simpliﬁed ASM1 model and takes model uncertainty in to account. It estimates unmeasured state variables in the system, e.g. the inlet concentration...
Optimal investment models with stochastic volatility: the time ...
African Journals Online (AJOL)
Therefore, a transform is primordial to express the value function in terms of a semilinear PDE with quadratic growth on the derivative term. Some proofs for the existence of smooth solution to this equation have been provided for this equation by Pham [11]. In that paper they illustrated some common stochastic volatility ...
Stochastic Modeling of the Persistence of HIV: Early Population Dynamics
2013-05-10
move about. Mathematically, this process was described first by Norbert Wiener , after whom the process is named. We abbreviate the Wiener process W...stochastic process is Brownian motion, which is also known as the Wiener process. Originally used to describe the motion of particles suspended within a
Analyzing Properties of Stochastic Business Processes By Model Checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2013-01-01
This chapter presents an approach to precise formal analysis of business processes with stochastic properties. The method presented here allows for both qualitative and quantitative properties to be individually analyzed at design time without requiring a full specification. This provides...... an effective means to explore possible designs for a business process and to debug any flaws....
A contribution to the systematics of stochastic volatility models
Czech Academy of Sciences Publication Activity Database
Slanina, František
2010-01-01
Roč. 389, č. 16 (2010), s. 3230-3239 ISSN 0378-4371 R&D Projects: GA MŠk OC09078 Institutional research plan: CEZ:AV0Z10100520 Keywords : fluctuations * econophysics * stochastic differential equations Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.521, year: 2010
A stochastic dynamic programming model for stream water quality ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Keywords. Fuzzy decision; stochastic optimization; water quality; streamflow. 1. Introduction. River water quality management problems are characterized by various uncertainties at differ- ent stages of decision making to arrive at optimal allocation of the assimilative capacity of the river system. The two types of uncertainties ...
On stochastic modeling of the modernized global positioning system (GPS) L2C signal
International Nuclear Information System (INIS)
Elsobeiey, Mohamed; El-Rabbany, Ahmed
2010-01-01
In order to take full advantage of the modernized GPS L2C signal, it is essential that its stochastic characteristics and code bias be rigorously determined. In this paper, long sessions of GPS measurements are used to study the stochastic characteristics of the modernized GPS L2C signal. As a byproduct, the stochastic characteristics of the legacy GPS signals, namely C/A and P2 codes, are also determined, which are used to verify the developed stochastic model of the modernized signal. The differential code biases between P2 and C2, DCB P2-C2 , are also estimated using the Bernese GPS software. It is shown that the developed models improved the precise point positioning (PPP) solution and convergence time
DEFF Research Database (Denmark)
Chon, K H; Hoyer, D; Armoundas, A A
1999-01-01
In this study, we introduce a new approach for estimating linear and nonlinear stochastic autoregressive moving average (ARMA) model parameters, given a corrupt signal, using artificial recurrent neural networks. This new approach is a two-step approach in which the parameters of the deterministic...... part of the stochastic ARMA model are first estimated via a three-layer artificial neural network (deterministic estimation step) and then reestimated using the prediction error as one of the inputs to the artificial neural networks in an iterative algorithm (stochastic estimation step). The prediction...... of significant amounts of either dynamic or measurement noise in the output signal. The comparison between the deterministic and stochastic recurrent neural network approaches is furthered by applying both approaches to experimentally obtained renal blood pressure and flow signals....
Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds
Czech Academy of Sciences Publication Activity Database
Cressman, R.; Křivan, Vlastimil
2013-01-01
Roč. 67, č. 2 (2013), s. 329-358 ISSN 0303-6812 Grant - others:The University of Tennessee(US) EF-0832858; National Science Foundation(US) DMS 0931642 Institutional support: RVO:60077344 Keywords : competition * dispersal * evolution Subject RIV: EH - Ecology, Behaviour Impact factor: 2.388, year: 2013 http://link.springer.com/content/pdf/10.1007%2Fs00285-012-0548-3.pdf
Ekofisk chalk: core measurements, stochastic reconstruction, network modeling and simulation
Energy Technology Data Exchange (ETDEWEB)
Talukdar, Saifullah
2002-07-01
This dissertation deals with (1) experimental measurements on petrophysical, reservoir engineering and morphological properties of Ekofisk chalk, (2) numerical simulation of core flood experiments to analyze and improve relative permeability data, (3) stochastic reconstruction of chalk samples from limited morphological information, (4) extraction of pore space parameters from the reconstructed samples, development of network model using pore space information, and computation of petrophysical and reservoir engineering properties from network model, and (5) development of 2D and 3D idealized fractured reservoir models and verification of the applicability of several widely used conventional up scaling techniques in fractured reservoir simulation. Experiments have been conducted on eight Ekofisk chalk samples and porosity, absolute permeability, formation factor, and oil-water relative permeability, capillary pressure and resistivity index are measured at laboratory conditions. Mercury porosimetry data and backscatter scanning electron microscope images have also been acquired for the samples. A numerical simulation technique involving history matching of the production profiles is employed to improve the relative permeability curves and to analyze hysteresis of the Ekofisk chalk samples. The technique was found to be a powerful tool to supplement the uncertainties in experimental measurements. Porosity and correlation statistics obtained from backscatter scanning electron microscope images are used to reconstruct microstructures of chalk and particulate media. The reconstruction technique involves a simulated annealing algorithm, which can be constrained by an arbitrary number of morphological parameters. This flexibility of the algorithm is exploited to successfully reconstruct particulate media and chalk samples using more than one correlation functions. A technique based on conditional simulated annealing has been introduced for exact reproduction of vuggy
An Empirical Application of a Two-Factor Model of Stochastic Volatility
Czech Academy of Sciences Publication Activity Database
Kuchyňka, Alexandr
2008-01-01
Roč. 17, č. 3 (2008), s. 243-253 ISSN 1210-0455 R&D Projects: GA ČR GA402/07/1113; GA MŠk(CZ) LC06075 Institutional research plan: CEZ:AV0Z10750506 Keywords : stochastic volatility * Kalman filter Subject RIV: AH - Economics http://library.utia.cas.cz/separaty/2008/E/kuchynka-an empirical application of a two-factor model of stochastic volatility.pdf
Granita, Bahar, A.
2015-03-01
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.
Estimation of stochastic volatility by using Ornstein-Uhlenbeck type models
Mariani, Maria C.; Bhuiyan, Md Al Masum; Tweneboah, Osei K.
2018-02-01
In this study, we develop a technique for estimating the stochastic volatility (SV) of a financial time series by using Ornstein-Uhlenbeck type models. Using the daily closing prices from developed and emergent stock markets, we conclude that the incorporation of stochastic volatility into the time varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. Furthermore, our estimation algorithm is feasible with large data sets and have good convergence properties.
Effects of Risk Aversion on Market Outcomes: A Stochastic Two-Stage Equilibrium Model
DEFF Research Database (Denmark)
Kazempour, Jalal; Pinson, Pierre
2016-01-01
This paper evaluates how different risk preferences of electricity producers alter the market-clearing outcomes. Toward this goal, we propose a stochastic equilibrium model for electricity markets with two settlements, i.e., day-ahead and balancing, in which a number of conventional and stochastic...... by its optimality conditions, resulting in a mixed complementarity problem. Numerical results from a case study based on the IEEE one-area reliability test system are derived and discussed....
Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate
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Chaoqun Xu
2013-01-01
Full Text Available We present a stochastic simple chemostat model in which the dilution rate was influenced by white noise. The long time behavior of the system is studied. Mainly, we show how the solution spirals around the washout equilibrium and the positive equilibrium of deterministic system under different conditions. Furthermore, the sufficient conditions for persistence in the mean of the stochastic system and washout of the microorganism are obtained. Numerical simulations are carried out to support our results.
International Nuclear Information System (INIS)
Granita; Bahar, A.
2015-01-01
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found
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Granita, E-mail: granitafc@gmail.com [Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia); Bahar, A. [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)
2015-03-09
This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.
Chowdhury, A. F. M. K.; Lockart, N.; Willgoose, G. R.; Kuczera, G. A.; Kiem, A.; Nadeeka, P. M.
2016-12-01
One of the key objectives of stochastic rainfall modelling is to capture the full variability of climate system for future drought and flood risk assessment. However, it is not clear how well these models can capture the future climate variability when they are calibrated to Global/Regional Climate Model data (GCM/RCM) as these datasets are usually available for very short future period/s (e.g. 20 years). This study has assessed the ability of two stochastic daily rainfall models to capture climate variability by calibrating them to a dynamically downscaled RCM dataset in an east Australian catchment for 1990-2010, 2020-2040, and 2060-2080 epochs. The two stochastic models are: (1) a hierarchical Markov Chain (MC) model, which we developed in a previous study and (2) a semi-parametric MC model developed by Mehrotra and Sharma (2007). Our hierarchical model uses stochastic parameters of MC and Gamma distribution, while the semi-parametric model uses a modified MC process with memory of past periods and kernel density estimation. This study has generated multiple realizations of rainfall series by using parameters of each model calibrated to the RCM dataset for each epoch. The generated rainfall series are used to generate synthetic streamflow by using a SimHyd hydrology model. Assessing the synthetic rainfall and streamflow series, this study has found that both stochastic models can incorporate a range of variability in rainfall as well as streamflow generation for both current and future periods. However, the hierarchical model tends to overestimate the multiyear variability of wet spell lengths (therefore, is less likely to simulate long periods of drought and flood), while the semi-parametric model tends to overestimate the mean annual rainfall depths and streamflow volumes (hence, simulated droughts are likely to be less severe). Sensitivity of these limitations of both stochastic models in terms of future drought and flood risk assessment will be discussed.
Simulating transmission and control of Taenia solium infections using a reed-frost stochastic model
DEFF Research Database (Denmark)
Kyvsgaard, Niels Chr.; Johansen, Maria Vang; Carabin, Hélène
2007-01-01
The transmission dynamics of the human-pig zoonotic cestode Taenia solium are explored with both deterministic and stochastic versions of a modified Reed-Frost model. This model, originally developed for microparasitic infections (i.e. bacteria, viruses and protozoa), assumes that random contacts...... humans eating under-cooked pork meat harbouring T. solium metacestodes. Deterministic models of each scenario were first run, followed by stochastic versions of the models to assess the likelihood of infection elimination in the small population modelled. The effects of three groups of interventions were...
Hybrid approaches for multiple-species stochastic reaction-diffusion models
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Hybrid approaches for multiple-species stochastic reaction-diffusion models.
Spill, Fabian
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Modeling the lake eutrophication stochastic ecosystem and the research of its stability.
Wang, Bo; Qi, Qianqian
2018-03-20
In the reality, the lake system will be disturbed by stochastic factors including the external and internal factors. By adding the additive noise and the multiplicative noise to the right-hand sides of the model equation, the additive stochastic model and the multiplicative stochastic model are established respectively in order to reduce model errors induced by the absence of some physical processes. For both the two kinds of stochastic ecosystems, the authors studied the bifurcation characteristics with the FPK equation and the Lyapunov exponent method based on the Stratonovich-Khasminiskii stochastic average principle. Results show that, for the additive stochastic model, when control parameter (i.e, nutrient loading rate) falls into the interval [0.388644, 0.66003825], there exists bistability for the ecosystem and the additive noise intensities cannot make the bifurcation point drift. In the region of the bistability, the external stochastic disturbance which is one of the main triggers causing the lake eutrophication, may make the ecosystem unstable and induce a transition. When control parameter (nutrient loading rate) falls into the interval (0, 0.388644) and (0.66003825, 1.0), there only exists a stable equilibrium state and the additive noise intensity couldn't change it. For the multiplicative stochastic model, there exists more complex bifurcation performance and the multiplicative ecosystem will be broken by the multiplicative noise. Also, the multiplicative noise could reduce the extent of the bistable region, ultimately, the bistable region vanishes for sufficiently large noise. What's more, both the nutrient loading rate and the multiplicative noise will make the ecosystem have a regime shift. On the other hand, for the two kinds of stochastic ecosystems, the authors also discussed the evolution of the ecological variable in detail by using the Four-stage Runge-Kutta method of strong order γ=1.5. The numerical method was found to be
Methods of Stochastic Analysis of Complex Regimes in the 3D Hindmarsh-Rose Neuron Model
Bashkirtseva, Irina; Ryashko, Lev; Slepukhina, Evdokia
A problem of the stochastic nonlinear analysis of neuronal activity is studied by the example of the Hindmarsh-Rose (HR) model. For the parametric region of tonic spiking oscillations, it is shown that random noise transforms the spiking dynamic regime into the bursting one. This stochastic phenomenon is specified by qualitative changes in distributions of random trajectories and interspike intervals (ISIs). For a quantitative analysis of the noise-induced bursting, we suggest a constructive semi-analytical approach based on the stochastic sensitivity function (SSF) technique and the method of confidence domains that allows us to describe geometrically a distribution of random states around the deterministic attractors. Using this approach, we develop a new algorithm for estimation of critical values for the noise intensity corresponding to the qualitative changes in stochastic dynamics. We show that the obtained estimations are in good agreement with the numerical results. An interplay between noise-induced bursting and transitions from order to chaos is discussed.
International Nuclear Information System (INIS)
Sabass, Benedikt; Schwarz, Ulrich S
2010-01-01
In migrating cells, retrograde flow of the actin cytoskeleton is related to traction at adhesion sites located at the base of the lamellipodium. The coupling between the moving cytoskeleton and the stationary adhesions is mediated by the continuous association and dissociation of molecular bonds. We introduce a simple model for the competition between the stochastic dynamics of elastic bonds at the moving interface and relaxation within the moving actin cytoskeleton represented by an internal viscous friction coefficient. Using exact stochastic simulations and an analytical mean field theory, we show that the stochastic bond dynamics lead to biphasic friction laws as observed experimentally. At low internal dissipation, stochastic bond dynamics lead to a regime of irregular stick-and-slip motion. High internal dissipation effectively suppresses cooperative effects among bonds and hence stabilizes the adhesion.
Simulation of the stochastic wave loads using a physical modeling approach
DEFF Research Database (Denmark)
Liu, W.F.; Sichani, Mahdi Teimouri; Nielsen, Søren R.K.
2013-01-01
In analyzing stochastic dynamic systems, analysis of the system uncertainty due to randomness in the loads plays a crucial role. Typically time series of the stochastic loads are simulated using traditional random phase method. This approach combined with fast Fourier transform algorithm makes...... an efficient way of simulating realizations of the stochastic load processes. However it requires many random variables, i.e. in the order of magnitude of 1000, to be included in the load model. Unfortunately having too many random variables in the problem makes considerable difficulties in analyzing system...... reliability or its uncertainty. Moreover applicability of the probability density evolution method on engineering problems faces critical difficulties when the system embeds too many random variables. Hence it is useful to devise a method which can make realization of the stochastic load processes with low...