WorldWideScience

Sample records for dynamic stochastic models

  1. 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

  2. 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.

  3. Stochastic dynamic modeling of regular and slow earthquakes

    Science.gov (United States)

    Aso, N.; Ando, R.; Ide, S.

    2017-12-01

    Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal

  4. Dynamic optimization deterministic and stochastic models

    CERN Document Server

    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.

  5. Dynamics of a Stochastic Intraguild Predation Model

    Directory of Open Access Journals (Sweden)

    Zejing Xing

    2016-04-01

    Full Text Available Intraguild predation (IGP is a widespread ecological phenomenon which occurs when one predator species attacks another predator species with which it competes for a shared prey species. The objective of this paper is to study the dynamical properties of a stochastic intraguild predation model. We analyze stochastic persistence and extinction of the stochastic IGP model containing five cases and establish the sufficient criteria for global asymptotic stability of the positive solutions. This study shows that it is possible for the coexistence of three species under the influence of environmental noise, and that the noise may have a positive effect for IGP species. A stationary distribution of the stochastic IGP model is established and it has the ergodic property, suggesting that the time average of population size with the development of time is equal to the stationary distribution in space. Finally, we show that our results may be extended to two well-known biological systems: food chains and exploitative competition.

  6. 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.

  7. Stochastic dynamics and irreversibility

    CERN Document Server

    Tomé, Tânia

    2015-01-01

    This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...

  8. Introduction to stochastic dynamic programming

    CERN Document Server

    Ross, Sheldon M; Lukacs, E

    1983-01-01

    Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist-providing counterexamples where appropriate-and the

  9. Stochastic Switching Dynamics

    DEFF Research Database (Denmark)

    Simonsen, Maria

    This thesis treats stochastic systems with switching dynamics. Models with these characteristics are studied from several perspectives. Initially in a simple framework given in the form of stochastic differential equations and, later, in an extended form which fits into the framework of sliding...... mode control. It is investigated how to understand and interpret solutions to models of switched systems, which are exposed to discontinuous dynamics and uncertainties (primarily) in the form of white noise. The goal is to gain knowledge about the performance of the system by interpreting the solution...

  10. A stochastic phase-field model determined from molecular dynamics

    KAUST Repository

    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.

  11. A stochastic phase-field model determined from molecular dynamics

    KAUST Repository

    von Schwerin, Erik; Szepessy, Anders

    2010-01-01

    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.

  12. A Simulation-Based Dynamic Stochastic Route Choice Model for Evacuation

    Directory of Open Access Journals (Sweden)

    Xing Zhao

    2012-01-01

    Full Text Available This paper establishes a dynamic stochastic route choice model for evacuation to simulate the propagation process of traffic flow and estimate the stochastic route choice under evacuation situations. The model contains a lane-group-based cell transmission model (CTM which sets different traffic capacities for links with different turning movements to flow out in an evacuation situation, an actual impedance model which is to obtain the impedance of each route in time units at each time interval and a stochastic route choice model according to the probit-based stochastic user equilibrium. In this model, vehicles loading at each origin at each time interval are assumed to choose an evacuation route under determinate road network, signal design, and OD demand. As a case study, the proposed model is validated on the network nearby Nanjing Olympic Center after the opening ceremony of the 10th National Games of the People's Republic of China. The traffic volumes and clearing time at five exit points of the evacuation zone are calculated by the model to compare with survey data. The results show that this model can appropriately simulate the dynamic route choice and evolution process of the traffic flow on the network in an evacuation situation.

  13. Dynamic stochastic accumulation model with application to pension savings management

    Directory of Open Access Journals (Sweden)

    Melicherčik Igor

    2010-01-01

    Full Text Available We propose a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. Stock prices are assumed to be driven by the geometric Brownian motion. Interest rates are modeled by means of the Cox-Ingersoll-Ross model. The optimal decision as a solution to the corresponding dynamic stochastic program is a function of the duration of saving, the level of savings and the short rate. Qualitative and quantitative properties of the optimal solution are analyzed. The model is tested on the funded pillar of the Slovak pension system. The results are calculated for various risk preferences of a saver.

  14. Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process

    Science.gov (United States)

    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.

  15. Optically levitated nanoparticle as a model system for stochastic bistable dynamics.

    Science.gov (United States)

    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.

  16. A data driven nonlinear stochastic model for blood glucose dynamics.

    Science.gov (United States)

    Zhang, Yan; Holt, Tim A; Khovanova, Natalia

    2016-03-01

    The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

  17. Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters

    Directory of Open Access Journals (Sweden)

    Wen Xu

    2016-10-01

    Full Text Available Time-varying volatility is common in macroeconomic data and has been incorporated into macroeconomic models in recent work. Dynamic panel data models have become increasingly popular in macroeconomics to study common relationships across countries or regions. This paper estimates dynamic panel data models with stochastic volatility by maximizing an approximate likelihood obtained via Rao-Blackwellized particle filters. Monte Carlo studies reveal the good and stable performance of our particle filter-based estimator. When the volatility of volatility is high, or when regressors are absent but stochastic volatility exists, our approach can be better than the maximum likelihood estimator which neglects stochastic volatility and generalized method of moments (GMM estimators.

  18. Stochastic inequalities and applications to dynamics analysis of a novel SIVS epidemic model with jumps

    Directory of Open Access Journals (Sweden)

    Xiaona Leng

    2017-06-01

    Full Text Available Abstract This paper proposes a new nonlinear stochastic SIVS epidemic model with double epidemic hypothesis and Lévy jumps. The main purpose of this paper is to investigate the threshold dynamics of the stochastic SIVS epidemic model. By using the technique of a series of stochastic inequalities, we obtain sufficient conditions for the persistence in mean and extinction of the stochastic system and the threshold which governs the extinction and the spread of the epidemic diseases. Finally, this paper describes the results of numerical simulations investigating the dynamical effects of stochastic disturbance. Our results significantly improve and generalize the corresponding results in recent literatures. The developed theoretical methods and stochastic inequalities technique can be used to investigate the high-dimensional nonlinear stochastic differential systems.

  19. Stochastic Online Learning in Dynamic Networks under Unknown Models

    Science.gov (United States)

    2016-08-02

    The key is to develop online learning strategies at each individual node. Specifically, through local information exchange with its neighbors, each...infinitely repeated game with incomplete information and developed a dynamic pricing strategy referred to as Competitive and Cooperative Demand Learning...Stochastic Online Learning in Dynamic Networks under Unknown Models This research aims to develop fundamental theories and practical algorithms for

  20. Stochastic Thermodynamics: A Dynamical Systems Approach

    Directory of Open Access Journals (Sweden)

    Tanmay Rajpurohit

    2017-12-01

    Full Text Available In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic compartmental dynamical system model characterized by energy conservation laws that is consistent with statistical thermodynamic principles. In particular, we show that the difference between the average supplied system energy and the average stored system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration. In addition, we show that the average stored system energy is equal to the mean energy that can be extracted from the system and the mean energy that can be delivered to the system in order to transfer it from a zero energy level to an arbitrary nonempty subset in the state space over a finite stopping time.

  1. Information-theoretic model selection for optimal prediction of stochastic dynamical systems from data

    Science.gov (United States)

    Darmon, David

    2018-03-01

    In the absence of mechanistic or phenomenological models of real-world systems, data-driven models become necessary. The discovery of various embedding theorems in the 1980s and 1990s motivated a powerful set of tools for analyzing deterministic dynamical systems via delay-coordinate embeddings of observations of their component states. However, in many branches of science, the condition of operational determinism is not satisfied, and stochastic models must be brought to bear. For such stochastic models, the tool set developed for delay-coordinate embedding is no longer appropriate, and a new toolkit must be developed. We present an information-theoretic criterion, the negative log-predictive likelihood, for selecting the embedding dimension for a predictively optimal data-driven model of a stochastic dynamical system. We develop a nonparametric estimator for the negative log-predictive likelihood and compare its performance to a recently proposed criterion based on active information storage. Finally, we show how the output of the model selection procedure can be used to compare candidate predictors for a stochastic system to an information-theoretic lower bound.

  2. Stochastic Wilson–Cowan models of neuronal network dynamics with memory and delay

    International Nuclear Information System (INIS)

    Goychuk, Igor; Goychuk, Andriy

    2015-01-01

    We consider a simple Markovian class of the stochastic Wilson–Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory, which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory and inhibitory neurons. Such avalanches emerge due to the network size dependent noise (mesoscopic noise). Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around −1.16. We show that this power law is robust upon a variation of the refractory time over several orders of magnitude. However, the avalanche time distribution is biexponential. It does not reflect any genuine power law dependence. (paper)

  3. Outbreak and Extinction Dynamics in a Stochastic Ebola Model

    Science.gov (United States)

    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.

  4. Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination

    Directory of Open Access Journals (Sweden)

    Lei Wang

    2017-01-01

    Full Text Available In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed.

  5. Advanced models of neural networks nonlinear dynamics and stochasticity in biological neurons

    CERN Document Server

    Rigatos, Gerasimos G

    2015-01-01

    This book provides a complete study on neural structures exhibiting nonlinear and stochastic dynamics, elaborating on neural dynamics by introducing advanced models of neural networks. It overviews the main findings in the modelling of neural dynamics in terms of electrical circuits and examines their stability properties with the use of dynamical systems theory. It is suitable for researchers and postgraduate students engaged with neural networks and dynamical systems theory.

  6. On the stochastic dynamics of disordered spin models

    International Nuclear Information System (INIS)

    Semerjian, G.; Montanari, A.; Cugliandolo, L.F.

    2003-09-01

    In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in equilibrium with a thermal bath. We propose a fluctuation principle that allows us to derive fluctuation-dissipation relations for many-time correlations and linear responses. We also speculate on how these features will be modified in systems evolving slowly out of equilibrium, as finite-dimensional or dilute spin-glasses. Secondly, we present a formalism that allows one to derive a series of approximated equations that determine the dynamics of disordered spin models on random (hyper) graphs. (author)

  7. Dynamic-stochastic modeling of snow cover formation on the European territory of Russia

    OpenAIRE

    A. N. Gelfan; V. M. Moreido

    2014-01-01

    A dynamic-stochastic model, which combines a deterministic model of snow cover formation with a stochastic weather generator, has been developed. The deterministic snow model describes temporal change of the snow depth, content of ice and liquid water, snow density, snowmelt, sublimation, re-freezing of melt water, and snow metamorphism. The model has been calibrated and validated against the long-term data of snow measurements over the territory of the European Russia. The model showed good ...

  8. Modeling cytoskeletal flow over adhesion sites: competition between stochastic bond dynamics and intracellular relaxation

    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.

  9. A deterministic and stochastic model for the system dynamics of tumor-immune responses to chemotherapy

    Science.gov (United States)

    Liu, Xiangdong; Li, Qingze; Pan, Jianxin

    2018-06-01

    Modern medical studies show that chemotherapy can help most cancer patients, especially for those diagnosed early, to stabilize their disease conditions from months to years, which means the population of tumor cells remained nearly unchanged in quite a long time after fighting against immune system and drugs. In order to better understand the dynamics of tumor-immune responses under chemotherapy, deterministic and stochastic differential equation models are constructed to characterize the dynamical change of tumor cells and immune cells in this paper. The basic dynamical properties, such as boundedness, existence and stability of equilibrium points, are investigated in the deterministic model. Extended stochastic models include stochastic differential equations (SDEs) model and continuous-time Markov chain (CTMC) model, which accounts for the variability in cellular reproduction, growth and death, interspecific competitions, and immune response to chemotherapy. The CTMC model is harnessed to estimate the extinction probability of tumor cells. Numerical simulations are performed, which confirms the obtained theoretical results.

  10. Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games

    KAUST Repository

    Jaleel, Hassan

    2018-04-08

    Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We address this limitation for the first time and develop a framework for the comparative analysis of stochastic learning dynamics with different update rules but same steady-state behavior. We present the framework in the context of two learning dynamics: Log-Linear Learning (LLL) and Metropolis Learning (ML). Although both of these dynamics have the same stochastically stable states, LLL and ML correspond to different behavioral models for decision making. Moreover, we demonstrate through an example setup of sensor coverage game that for each of these dynamics, the paths to stochastically stable states exhibit distinctive behaviors. Therefore, we propose multiple criteria to analyze and quantify the differences in the short and medium run behavior of stochastic learning dynamics. We derive and compare upper bounds on the expected hitting time to the set of Nash equilibria for both LLL and ML. For the medium to long-run behavior, we identify a set of tools from the theory of perturbed Markov chains that result in a hierarchical decomposition of the state space into collections of states called cycles. We compare LLL and ML based on the proposed criteria and develop invaluable insights into the comparative behavior of the two dynamics.

  11. Dynamic and stochastic multi-project planning

    CERN Document Server

    Melchiors, Philipp

    2015-01-01

    This book deals with dynamic and stochastic methods for multi-project planning. Based on the idea of using queueing networks for the analysis of dynamic-stochastic multi-project environments this book addresses two problems: detailed scheduling of project activities, and integrated order acceptance and capacity planning. In an extensive simulation study, the book thoroughly investigates existing scheduling policies. To obtain optimal and near optimal scheduling policies new models and algorithms are proposed based on the theory of Markov decision processes and Approximate Dynamic programming.

  12. The global dynamics for a stochastic SIS epidemic model with isolation

    Science.gov (United States)

    Chen, Yiliang; Wen, Buyu; Teng, Zhidong

    2018-02-01

    In this paper, we investigate the dynamical behavior for a stochastic SIS epidemic model with isolation which is as an important strategy for the elimination of infectious diseases. It is assumed that the stochastic effects manifest themselves mainly as fluctuation in the transmission coefficient, the death rate and the proportional coefficient of the isolation of infective. It is shown that the extinction and persistence in the mean of the model are determined by a threshold value R0S . That is, if R0S 1, then the disease is stochastic persistent in the means with probability one. Furthermore, the existence of a unique stationary distribution is discussed, and the sufficient conditions are established by using the Lyapunov function method. Finally, some numerical examples are carried out to confirm the analytical results.

  13. Stochastic dynamics modeling solute transport in porous media modeling solute transport in porous media

    CERN Document Server

    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 ...

  14. Nonlinear stochastic exclusion financial dynamics modeling and time-dependent intrinsic detrended cross-correlation

    Science.gov (United States)

    Zhang, Wei; Wang, Jun

    2017-09-01

    In attempt to reproduce price dynamics of financial markets, a stochastic agent-based financial price model is proposed and investigated by stochastic exclusion process. The exclusion process, one of interacting particle systems, is usually thought of as modeling particle motion (with the conserved number of particles) in a continuous time Markov process. In this work, the process is utilized to imitate the trading interactions among the investing agents, in order to explain some stylized facts found in financial time series dynamics. To better understand the correlation behaviors of the proposed model, a new time-dependent intrinsic detrended cross-correlation (TDI-DCC) is introduced and performed, also, the autocorrelation analyses are applied in the empirical research. Furthermore, to verify the rationality of the financial price model, the actual return series are also considered to be comparatively studied with the simulation ones. The comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets.

  15. Stochastic linear dynamical programming in order to apply it in energy modelling

    Energy Technology Data Exchange (ETDEWEB)

    El Hachem, S

    1995-11-01

    This thesis contributes to the development of new algorithms for the computation of stochastic dynamic problem and its mini-maxi variant for the case of imperfect knowledge on random data. The proposed algorithms are scenarios aggregation type. It also contributes to integrate these algorithms in a decision support approach and to discuss the stochastic modeling of two energy problems: the refining and the portfolio gas contracts. (author). 112 refs., 5 tabs.

  16. Modeling and stochastic analysis of dynamic mechanisms of the perception

    Science.gov (United States)

    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.

  17. Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?

    Science.gov (United States)

    Choustova, Olga

    2007-02-01

    We apply the mathematical formalism of Bohmian mechanics to describe dynamics of shares. The main distinguishing feature of the financial Bohmian model is the possibility to take into account market psychology by describing expectations of traders by the pilot wave. We also discuss some objections (coming from conventional financial mathematics of stochastic processes) against the deterministic Bohmian model. In particular, the objection that such a model contradicts to the efficient market hypothesis which is the cornerstone of the modern market ideology. Another objection is of pure mathematical nature: it is related to the quadratic variation of price trajectories. One possibility to reply to this critique is to consider the stochastic Bohm-Vigier model, instead of the deterministic one. We do this in the present note.

  18. Stochastic sensitivity analysis of the variability of dynamics and transition to chaos in the business cycles model

    Science.gov (United States)

    Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana

    2018-01-01

    A problem of mathematical modeling of complex stochastic processes in macroeconomics is discussed. For the description of dynamics of income and capital stock, the well-known Kaldor model of business cycles is used as a basic example. The aim of the paper is to give an overview of the variety of stochastic phenomena which occur in Kaldor model forced by additive and parametric random noise. We study a generation of small- and large-amplitude stochastic oscillations, and their mixed-mode intermittency. To analyze these phenomena, we suggest a constructive approach combining the study of the peculiarities of deterministic phase portrait, and stochastic sensitivity of attractors. We show how parametric noise can stabilize the unstable equilibrium and transform dynamics of Kaldor system from order to chaos.

  19. Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games

    KAUST Repository

    Jaleel, Hassan; Shamma, Jeff S.

    2018-01-01

    dynamics: Log-Linear Learning (LLL) and Metropolis Learning (ML). Although both of these dynamics have the same stochastically stable states, LLL and ML correspond to different behavioral models for decision making. Moreover, we demonstrate through

  20. Automated Flight Routing Using Stochastic Dynamic Programming

    Science.gov (United States)

    Ng, Hok K.; Morando, Alex; Grabbe, Shon

    2010-01-01

    Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.

  1. Stochastic dynamics of melt ponds and sea ice-albedo climate feedback

    Science.gov (United States)

    Sudakov, Ivan

    Evolution of melt ponds on the Arctic sea surface is a complicated stochastic process. We suggest a low-order model with ice-albedo feedback which describes stochastic dynamics of melt ponds geometrical characteristics. The model is a stochastic dynamical system model of energy balance in the climate system. We describe the equilibria in this model. We conclude the transition in fractal dimension of melt ponds affects the shape of the sea ice albedo curve.

  2. Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics

    KAUST Repository

    Bressloff, Paul C.

    2010-01-01

    We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N→∞, where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand

  3. Stochastic modeling of lift and drag dynamics to obtain aerodynamic forces with local dynamics on rotor blade under unsteady wind inflow

    International Nuclear Information System (INIS)

    Luhur, M.R.

    2014-01-01

    This contribution provides the development of a stochastic lift and drag model for an airfoil FX 79-W-151A under unsteady wind inflow based on wind tunnel measurements. Here we present the integration of the stochastic model into a well-known standard BEM (Blade Element Momentum) model to obtain the corresponding aerodynamic forces on a rotating blade element. The stochastic model is integrated as an alternative to static tabulated data used by classical BEM. The results show that in comparison to classical BEM, the BEM with stochastic approach additionally reflects the local force dynamics and therefore provides more information on aerodynamic forces that can be used by wind turbine simulation codes. (author)

  4. Stochastic Modeling of Lift and Drag Dynamics to Obtain Aerodynamic Forces with Local Dynamics on Rotor Blade under Unsteady Wind Inflow

    Directory of Open Access Journals (Sweden)

    Muhammad Ramzan Luhur

    2014-01-01

    Full Text Available This contribution provides the development of a stochastic lift and drag model for an airfoil FX 79-W-151A under unsteady wind inflow based on wind tunnel measurements. Here we present the integration of the stochastic model into a well-known standard BEM (Blade Element Momentum model to obtain the corresponding aerodynamic forces on a rotating blade element. The stochastic model is integrated as an alternative to static tabulated data used by classical BEM. The results show that in comparison to classical BEM, the BEM with stochastic approach additionally reflects the local force dynamics and therefore provides more information on aerodynamic forces that can be used by wind turbine simulation codes

  5. Stochasticity and determinism in models of hematopoiesis.

    Science.gov (United States)

    Kimmel, Marek

    2014-01-01

    This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.

  6. A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

    Science.gov (United States)

    Hagos, Samson; Feng, Zhe; Plant, Robert S.; Houze, Robert A.; Xiao, Heng

    2018-02-01

    A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii) the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. In addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.

  7. Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

    Science.gov (United States)

    Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young

    2017-03-14

    Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.

  8. Inter-species competition-facilitation in stochastic riparian vegetation dynamics.

    Science.gov (United States)

    Tealdi, Stefano; Camporeale, Carlo; Ridolfi, Luca

    2013-02-07

    Riparian vegetation is a highly dynamic community that lives on river banks and which depends to a great extent on the fluvial hydrology. The stochasticity of the discharge and erosion/deposition processes in fact play a key role in determining the distribution of vegetation along a riparian transect. These abiotic processes interact with biotic competition/facilitation mechanisms, such as plant competition for light, water, and nutrients. In this work, we focus on the dynamics of plants characterized by three components: (1) stochastic forcing due to river discharges, (2) competition for resources, and (3) inter-species facilitation due to the interplay between vegetation and fluid dynamics processes. A minimalist stochastic bio-hydrological model is proposed for the dynamics of the biomass of two vegetation species: one species is assumed dominant and slow-growing, the other is subdominant, but fast-growing. The stochastic model is solved analytically and the probability density function of the plant biomasses is obtained as a function of both the hydrologic and biologic parameters. The impact of the competition/facilitation processes on the distribution of vegetation species along the riparian transect is investigated and remarkable effects are observed. Finally, a good qualitative agreement is found between the model results and field data. Copyright © 2012 Elsevier Ltd. All rights reserved.

  9. Stochastic properties of the Friedman dynamical system

    International Nuclear Information System (INIS)

    Szydlowski, M.; Heller, M.; Golda, Z.

    1985-01-01

    Some mathematical aspects of the stochastic cosmology are discussed in the corresponding ordinary Friedman world models. In particulare, it is shown that if the strong and Lorentz energy conditions are known, or the potential function is given, or a stochastic measure is suitably defined then the structure of the phase plane of the Friedman dynamical system is determined. 11 refs., 2 figs. (author)

  10. 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.

  11. Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator

    Science.gov (United States)

    González Ochoa, Héctor O.; Perales, Gualberto Solís; Epstein, Irving R.; Femat, Ricardo

    2018-05-01

    We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.

  12. Sparse learning of stochastic dynamical equations

    Science.gov (United States)

    Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia

    2018-06-01

    With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.

  13. Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons.

    Science.gov (United States)

    Buesing, Lars; Bill, Johannes; Nessler, Bernhard; Maass, Wolfgang

    2011-11-01

    The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.

  14. Forecasting financial asset processes: stochastic dynamics via learning neural networks.

    Science.gov (United States)

    Giebel, S; Rainer, M

    2010-01-01

    Models for financial asset dynamics usually take into account their inherent unpredictable nature by including a suitable stochastic component into their process. Unknown (forward) values of financial assets (at a given time in the future) are usually estimated as expectations of the stochastic asset under a suitable risk-neutral measure. This estimation requires the stochastic model to be calibrated to some history of sufficient length in the past. Apart from inherent limitations, due to the stochastic nature of the process, the predictive power is also limited by the simplifying assumptions of the common calibration methods, such as maximum likelihood estimation and regression methods, performed often without weights on the historic time series, or with static weights only. Here we propose a novel method of "intelligent" calibration, using learning neural networks in order to dynamically adapt the parameters of the stochastic model. Hence we have a stochastic process with time dependent parameters, the dynamics of the parameters being themselves learned continuously by a neural network. The back propagation in training the previous weights is limited to a certain memory length (in the examples we consider 10 previous business days), which is similar to the maximal time lag of autoregressive processes. We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts for the EURTRY and EUR-HUF exchange rates each.

  15. Stochastic lattice model of synaptic membrane protein domains.

    Science.gov (United States)

    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.

  16. Threshold Dynamics of a Stochastic SIR Model with Vertical Transmission and Vaccination

    OpenAIRE

    Miao, Anqi; Zhang, Jian; Zhang, Tongqian; Pradeep, B. G. Sampath Aruna

    2017-01-01

    A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control.

  17. Stochastic beam dynamics in storage rings

    International Nuclear Information System (INIS)

    Pauluhn, A.

    1993-12-01

    In this thesis several approaches to stochastic dynamics in storage rings are investigated. In the first part the theory of stochastic differential equations and Fokker-Planck equations is used to describe the processes which have been assumed to be Markov processes. The mathematical theory of Markov processes is well known. Nevertheless, analytical solutions can be found only in special cases and numerical algorithms are required. Several numerical integration schemes for stochastic differential equations will therefore be tested in analytical solvable examples and then applied to examples from accelerator physics. In particular the stochastically perturbed synchrotron motion is treated. For the special case of a double rf system several perturbation theoretical methods for deriving the Fokker-Planck equation in the action variable are used and compared with numerical results. The second part is concerned with the dynamics of electron storage rings. Due to the synchrotron radiation the electron motion is influenced by damping and exciting forces. An algorithm for the computation of the density function in the phase space of such a dissipative stochastically excited system is introduced. The density function contains all information of a process, e.g. it determines the beam dimensions and the lifetime of a stored electron beam. The new algorithm consists in calculating a time propagator for the density function. By means of this propagator the time evolution of the density is modelled very computing time efficient. The method is applied to simple models of the beam-beam interaction (one-dimensional, round beams) and the results of the density calculations are compared with results obtained from multiparticle tracking. Furthermore some modifications of the algorithm are introduced to improve its efficiency concerning computing time and storage requirements. Finally, extensions to two-dimensional beam-beam models are described. (orig.)

  18. Modeling and simulation of a controlled steam generator in the context of dynamic reliability using a Stochastic Hybrid Automaton

    International Nuclear Information System (INIS)

    Babykina, Génia; Brînzei, Nicolae; Aubry, Jean-François; Deleuze, Gilles

    2016-01-01

    The paper proposes a modeling framework to support Monte Carlo simulations of the behavior of a complex industrial system. The aim is to analyze the system dependability in the presence of random events, described by any type of probability distributions. Continuous dynamic evolutions of physical parameters are taken into account by a system of differential equations. Dynamic reliability is chosen as theoretical framework. Based on finite state automata theory, the formal model is built by parallel composition of elementary sub-models using a bottom-up approach. Considerations of a stochastic nature lead to a model called the Stochastic Hybrid Automaton. The Scilab/Scicos open source environment is used for implementation. The case study is carried out on an example of a steam generator of a nuclear power plant. The behavior of the system is studied by exploring its trajectories. Possible system trajectories are analyzed both empirically, using the results of Monte Carlo simulations, and analytically, using the formal system model. The obtained results are show to be relevant. The Stochastic Hybrid Automaton appears to be a suitable tool to address the dynamic reliability problem and to model real systems of high complexity; the bottom-up design provides precision and coherency of the system model. - Highlights: • A part of a nuclear power plant is modeled in the context of dynamic reliability. • Stochastic Hybrid Automaton is used as an input model for Monte Carlo simulations. • The model is formally built using a bottom-up approach. • The behavior of the system is analyzed empirically and analytically. • A formally built SHA shows to be a suitable tool to approach dynamic reliability.

  19. A Stochastic Fractional Dynamics Model of Rainfall Statistics

    Science.gov (United States)

    Kundu, Prasun; Travis, James

    2013-04-01

    Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.

  20. Fast stochastic algorithm for simulating evolutionary population dynamics

    Science.gov (United States)

    Tsimring, Lev; Hasty, Jeff; Mather, William

    2012-02-01

    Evolution and co-evolution of ecological communities are stochastic processes often characterized by vastly different rates of reproduction and mutation and a coexistence of very large and very small sub-populations of co-evolving species. This creates serious difficulties for accurate statistical modeling of evolutionary dynamics. In this talk, we introduce a new exact algorithm for fast fully stochastic simulations of birth/death/mutation processes. It produces a significant speedup compared to the direct stochastic simulation algorithm in a typical case when the total population size is large and the mutation rates are much smaller than birth/death rates. We illustrate the performance of the algorithm on several representative examples: evolution on a smooth fitness landscape, NK model, and stochastic predator-prey system.

  1. Stochastic Relational Presheaves and Dynamic Logic for Contextuality

    Directory of Open Access Journals (Sweden)

    Kohei Kishida

    2014-12-01

    Full Text Available Presheaf models provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in quantum systems. After reviewing what presheaf models represent and what certain operations on them mean in terms of notions such as internal and external choices, composition of systems, and so on, I will show how to extend those models and ideas by combining them with ideas from other category-theoretic approaches to relational models and to stochastic processes. It turns out that my extension yields a transitional formulation of sheaf-theoretic structures that Abramsky and Brandenburger proposed to characterize non-locality and contextuality. An alternative characterization of contextuality will then be given in terms of a dynamic modal logic of the models I put forward.

  2. Threshold Dynamics of a Stochastic SIR Model with Vertical Transmission and Vaccination

    Directory of Open Access Journals (Sweden)

    Anqi Miao

    2017-01-01

    Full Text Available A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control.

  3. Stochastic integer programming by dynamic programming

    NARCIS (Netherlands)

    Lageweg, B.J.; Lenstra, J.K.; Rinnooy Kan, A.H.G.; Stougie, L.; Ermoliev, Yu.; Wets, R.J.B.

    1988-01-01

    Stochastic integer programming is a suitable tool for modeling hierarchical decision situations with combinatorial features. In continuation of our work on the design and analysis of heuristics for such problems, we now try to find optimal solutions. Dynamic programming techniques can be used to

  4. Developing stochastic epidemiological models to quantify the dynamics of infectious diseases in domestic livestock.

    Science.gov (United States)

    MacKenzie, K; Bishop, S C

    2001-08-01

    A stochastic model describing disease transmission dynamics for a microparasitic infection in a structured domestic animal population is developed and applied to hypothetical epidemics on a pig farm. Rational decision making regarding appropriate control strategies for infectious diseases in domestic livestock requires an understanding of the disease dynamics and risk profiles for different groups of animals. This is best achieved by means of stochastic epidemic models. Methodologies are presented for 1) estimating the probability of an epidemic, given the presence of an infected animal, whether this epidemic is major (requires intervention) or minor (dies out without intervention), and how the location of the infected animal on the farm influences the epidemic probabilities; 2) estimating the basic reproductive ratio, R0 (i.e., the expected number of secondary cases on the introduction of a single infected animal) and the variability of the estimate of this parameter; and 3) estimating the total proportion of animals infected during an epidemic and the total proportion infected at any point in time. The model can be used for assessing impact of altering farm structure on disease dynamics, as well as disease control strategies, including altering farm structure, vaccination, culling, and genetic selection.

  5. Two-boundary first exit time of Gauss-Markov processes for stochastic modeling of acto-myosin dynamics.

    Science.gov (United States)

    D'Onofrio, Giuseppe; Pirozzi, Enrica

    2017-05-01

    We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.

  6. Dynamical and hamiltonian dilations of stochastic processes

    International Nuclear Information System (INIS)

    Baumgartner, B.; Gruemm, H.-R.

    1982-01-01

    This is a study of the problem, which stochastic processes could arise from dynamical systems by loss of information. The notions of ''dilation'' and ''approximate dilation'' of a stochastic process are introduced to give exact definitions of this particular relationship. It is shown that every generalized stochastic process is approximately dilatable by a sequence of dynamical systems, but for stochastic processes in full generality one needs nets. (Author)

  7. Stochastic fractional differential equations: Modeling, method and analysis

    International Nuclear Information System (INIS)

    Pedjeu, Jean-C.; Ladde, Gangaram S.

    2012-01-01

    By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.

  8. 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.

  9. Stochastic Control - External Models

    DEFF Research Database (Denmark)

    Poulsen, Niels Kjølstad

    2005-01-01

    This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...

  10. Setting development goals using stochastic dynamical system models.

    Science.gov (United States)

    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.

  11. Multivariate moment closure techniques for stochastic kinetic models

    International Nuclear Information System (INIS)

    Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.

    2015-01-01

    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

  12. 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.

  13. 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...

  14. Dynamics of non-holonomic systems with stochastic transport

    Science.gov (United States)

    Holm, D. D.; Putkaradze, V.

    2018-01-01

    This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.

  15. 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 ...

  16. Is There Really a Global Business Cycle? : A Dynamic Factor Model with Stochastic Factor Selection

    NARCIS (Netherlands)

    T. Berger (Tino); L.C.G. Pozzi (Lorenzo)

    2016-01-01

    textabstractWe investigate the presence of international business cycles in macroeconomic aggregates (output, consumption, investment) using a panel of 60 countries over the period 1961-2014. The paper presents a Bayesian stochastic factor selection approach for dynamic factor models with

  17. Dynamics of stochastic systems

    CERN Document Server

    Klyatskin, Valery I

    2005-01-01

    Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...

  18. Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc [Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003 (United States)

    2016-03-14

    We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.

  19. An effective streamflow process model for optimal reservoir operation using stochastic dual dynamic programming

    OpenAIRE

    Raso , L.; Malaterre , P.O.; Bader , J.C.

    2017-01-01

    International audience; This article presents an innovative streamflow process model for use in reservoir operational rule design in stochastic dual dynamic programming (SDDP). Model features, which can be applied independently, are (1) a multiplicative process model for the forward phase and its linearized version for the backward phase; and (2) a nonuniform time-step length that is inversely proportional to seasonal variability. The advantages are (1) guaranteeing positive streamflow values...

  20. A stochastic model of enzyme kinetics

    Science.gov (United States)

    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.

  1. Nonlinear and stochastic dynamics of coherent structures

    DEFF Research Database (Denmark)

    Rasmussen, Kim

    1997-01-01

    This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree of nonli......This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree...... introduces the nonlinear Schrödinger model in one and two dimensions, discussing the soliton solutions in one dimension and the collapse phenomenon in two dimensions. Also various analytical methods are described. Then a derivation of the nonlinear Schrödinger equation is given, based on a Davydov like...... system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...

  2. Stochastic runaway of dynamical systems

    International Nuclear Information System (INIS)

    Pfirsch, D.; Graeff, P.

    1984-10-01

    One-dimensional, stochastic, dynamical systems are well studied with respect to their stability properties. Less is known for the higher dimensional case. This paper derives sufficient and necessary criteria for the asymptotic divergence of the entropy (runaway) and sufficient ones for the moments of n-dimensional, stochastic, dynamical systems. The crucial implication is the incompressibility of their flow defined by the equations of motion in configuration space. Two possible extensions to compressible flow systems are outlined. (orig.)

  3. 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

  4. A stochastic MILP energy planning model incorporating power market dynamics

    International Nuclear Information System (INIS)

    Koltsaklis, Nikolaos E.; Nazos, Konstantinos

    2017-01-01

    Highlights: •Stochastic MILP model for the optimal energy planning of a power system. •Power market dynamics (offers/bids) are incorporated in the proposed model. •Monte Carlo method for capturing the uncertainty of some key parameters. •Analytical supply cost composition per power producer and activity. •Clean dark and spark spreads are calculated for each power unit. -- Abstract: This paper presents an optimization-based methodological approach to address the problem of the optimal planning of a power system at an annual level in competitive and uncertain power markets. More specifically, a stochastic mixed integer linear programming model (MILP) has been developed, combining advanced optimization techniques with Monte Carlo method in order to deal with uncertainty issues. The main focus of the proposed framework is the dynamic formulation of the strategy followed by all market participants in volatile market conditions, as well as detailed economic assessment of the power system’s operation. The applicability of the proposed approach has been tested on a real case study of the interconnected Greek power system, quantifying in detail all the relevant technical and economic aspects of the system’s operation. The proposed work identifies in the form of probability distributions the optimal power generation mix, electricity trade at a regional level, carbon footprint, as well as detailed total supply cost composition, according to the assumed market structure. The paper demonstrates that the proposed optimization approach is able to provide important insights into the appropriate energy strategies designed by market participants, as well as on the strategic long-term decisions to be made by investors and/or policy makers at a national and/or regional level, underscoring potential risks and providing appropriate price signals on critical energy projects under real market operating conditions.

  5. Enhancement of epidemic spread by noise and stochastic resonance in spatial network models with viral dynamics.

    Science.gov (United States)

    Tuckwell, H C; Toubiana, L; Vibert, J F

    2000-05-01

    We extend a previous dynamical viral network model to include stochastic effects. The dynamical equations for the viral and immune effector densities within a host population of size n are bilinear, and the noise is white, additive, and Gaussian. The individuals are connected with an n x n transmission matrix, with terms which decay exponentially with distance. In a single individual, for the range of noise parameters considered, it is found that increasing the amplitude of the noise tends to decrease the maximum mean virion level, and slightly accelerate its attainment. Two different spatial dynamical models are employed to ascertain the effects of environmental stochasticity on viral spread. In the first model transmission is unrestricted and there is no threshold within individuals. This model has the advantage that it can be analyzed using a Fokker-Planck approach. The noise is found both to synchronize and uniformize the trajectories of the viral levels across the population of infected individuals, and thus to promote the epidemic spread of the virus. Quantitative measures of the speed of spread and overall amplitude of the epidemic are obtained as functions of the noise and virulence parameters. The mean amplitude increases steadily without threshold effects for a fixed value of the virulence as the noise amplitude sigma is increased, and there is no evidence of a stochastic resonance. However, the speed of transmission, both with respect to its mean and variance, undergoes rapid increases as sigma changes by relatively small amounts. In the second, more realistic, model, there is a threshold for infection and an upper limit to the transmission rate. There may be no spread of infection at all in the absence of noise. With increasing noise level and a low threshold, the mean maximum virion level grows quickly and shows a broad-based stochastic resonance effect. When the threshold within individuals is increased, the mean population virion level increases only

  6. Inverse stochastic-dynamic models for high-resolution Greenland ice core records

    DEFF Research Database (Denmark)

    Boers, Niklas; Chekroun, Mickael D.; Liu, Honghu

    2017-01-01

    as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data, (ii) cubic drift terms, (iii) nonlinear coupling terms between the 18O and dust......Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from 18O and dust records of unprecedented, subdecadal...

  7. Agent-based financial dynamics model from stochastic interacting epidemic system and complexity analysis

    International Nuclear Information System (INIS)

    Lu, Yunfan; Wang, Jun; Niu, Hongli

    2015-01-01

    An agent-based financial stock price model is developed and investigated by a stochastic interacting epidemic system, which is one of the statistical physics systems and has been used to model the spread of an epidemic or a forest fire. Numerical and statistical analysis are performed on the simulated returns of the proposed financial model. Complexity properties of the financial time series are explored by calculating the correlation dimension and using the modified multiscale entropy method. In order to verify the rationality of the financial model, the real stock market indexes, Shanghai Composite Index and Shenzhen Component Index, are studied in comparison with the simulation data of the proposed model for the different infectiousness parameters. The empirical research reveals that this financial model can reproduce some important features of the real stock markets. - Highlights: • A new agent-based financial price model is developed by stochastic interacting epidemic system. • The structure of the proposed model allows to simulate the financial dynamics. • Correlation dimension and MMSE are applied to complexity analysis of financial time series. • Empirical results show the rationality of the proposed financial model

  8. Agent-based financial dynamics model from stochastic interacting epidemic system and complexity analysis

    Energy Technology Data Exchange (ETDEWEB)

    Lu, Yunfan, E-mail: yunfanlu@yeah.net; Wang, Jun; Niu, Hongli

    2015-06-12

    An agent-based financial stock price model is developed and investigated by a stochastic interacting epidemic system, which is one of the statistical physics systems and has been used to model the spread of an epidemic or a forest fire. Numerical and statistical analysis are performed on the simulated returns of the proposed financial model. Complexity properties of the financial time series are explored by calculating the correlation dimension and using the modified multiscale entropy method. In order to verify the rationality of the financial model, the real stock market indexes, Shanghai Composite Index and Shenzhen Component Index, are studied in comparison with the simulation data of the proposed model for the different infectiousness parameters. The empirical research reveals that this financial model can reproduce some important features of the real stock markets. - Highlights: • A new agent-based financial price model is developed by stochastic interacting epidemic system. • The structure of the proposed model allows to simulate the financial dynamics. • Correlation dimension and MMSE are applied to complexity analysis of financial time series. • Empirical results show the rationality of the proposed financial model.

  9. Stochastic light-cone CTMRG: a new DMRG approach to stochastic models 02.50.Ey Stochastic processes; 64.60.Ht Dynamic critical phenomena; 02.70.-c Computational techniques; 05.10.Cc Renormalization group methods;

    CERN Document Server

    Kemper, A; Nishino, T; Schadschneider, A; Zittartz, J

    2003-01-01

    We develop a new variant of the recently introduced stochastic transfer matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG, adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process are studied and compared with exact data and Monte Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10 sup 5 shows a considerable improvement on the old stochastic TMRG algorithm.

  10. Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics

    KAUST Repository

    Bressloff, Paul C.

    2010-11-03

    We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N→∞, where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first consider a single excitatory population that exhibits bistability in the deterministic limit. The steady-state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network; the relative weighting of the two maxima depends on the system size. For large but finite N, we calculate the exponentially small rate of noise-induced transitions between the resulting metastable states using a Wentzel-Kramers- Brillouin (WKB) approximation and matched asymptotic expansions. We then consider a two-population excitatory or inhibitory network that supports limit cycle oscillations. Using a diffusion approximation, we reduce the dynamics to a neural Langevin equation, and show how the intrinsic noise amplifies subthreshold oscillations (quasicycles). © 2010 The American Physical Society.

  11. Dynamic Stochastic Superresolution of sparsely observed turbulent systems

    International Nuclear Information System (INIS)

    Branicki, M.; Majda, A.J.

    2013-01-01

    Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum

  12. Stochastic dynamic analysis of marine risers considering Gaussian system uncertainties

    Science.gov (United States)

    Ni, Pinghe; Li, Jun; Hao, Hong; Xia, Yong

    2018-03-01

    This paper performs the stochastic dynamic response analysis of marine risers with material uncertainties, i.e. in the mass density and elastic modulus, by using Stochastic Finite Element Method (SFEM) and model reduction technique. These uncertainties are assumed having Gaussian distributions. The random mass density and elastic modulus are represented by using the Karhunen-Loève (KL) expansion. The Polynomial Chaos (PC) expansion is adopted to represent the vibration response because the covariance of the output is unknown. Model reduction based on the Iterated Improved Reduced System (IIRS) technique is applied to eliminate the PC coefficients of the slave degrees of freedom to reduce the dimension of the stochastic system. Monte Carlo Simulation (MCS) is conducted to obtain the reference response statistics. Two numerical examples are studied in this paper. The response statistics from the proposed approach are compared with those from MCS. It is noted that the computational time is significantly reduced while the accuracy is kept. The results demonstrate the efficiency of the proposed approach for stochastic dynamic response analysis of marine risers.

  13. 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.

  14. Stochastic population dynamics in spatially extended predator-prey systems

    Science.gov (United States)

    Dobramysl, Ulrich; Mobilia, Mauro; Pleimling, Michel; Täuber, Uwe C.

    2018-02-01

    Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting many-particle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator-prey competition invalidates the neutral Lotka-Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator-prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi-Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steady-state and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species’ population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with ‘rock-paper-scissors’ interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May-Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a complex

  15. Stochastic ice stream dynamics.

    Science.gov (United States)

    Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca

    2016-08-09

    Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.

  16. Geometric integrators for stochastic rigid body dynamics

    KAUST Repository

    Tretyakov, Mikhail

    2016-01-05

    Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.

  17. Geometric integrators for stochastic rigid body dynamics

    KAUST Repository

    Tretyakov, Mikhail

    2016-01-01

    Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.

  18. A stochastic agent-based model of pathogen propagation in dynamic multi-relational social networks

    Science.gov (United States)

    Khan, Bilal; Dombrowski, Kirk; Saad, Mohamed

    2015-01-01

    We describe a general framework for modeling and stochastic simulation of epidemics in realistic dynamic social networks, which incorporates heterogeneity in the types of individuals, types of interconnecting risk-bearing relationships, and types of pathogens transmitted across them. Dynamism is supported through arrival and departure processes, continuous restructuring of risk relationships, and changes to pathogen infectiousness, as mandated by natural history; dynamism is regulated through constraints on the local agency of individual nodes and their risk behaviors, while simulation trajectories are validated using system-wide metrics. To illustrate its utility, we present a case study that applies the proposed framework towards a simulation of HIV in artificial networks of intravenous drug users (IDUs) modeled using data collected in the Social Factors for HIV Risk survey. PMID:25859056

  19. Stochastic dynamical models for ecological regime shifts

    DEFF Research Database (Denmark)

    Møller, Jan Kloppenborg; Carstensen, Jacob; Madsen, Henrik

    the physical and biological knowledge of the system, and nonlinearities introduced here can generate regime shifts or enhance the probability of regime shifts in the case of stochastic models, typically characterized by a threshold value for the known driver. A simple model for light competition between...... definition and stability of regimes become less subtle. Ecological regime shifts and their modeling must be viewed in a probabilistic manner, particularly if such model results are to be used in ecosystem management....

  20. Assessing predictability of a hydrological stochastic-dynamical system

    Science.gov (United States)

    Gelfan, Alexander

    2014-05-01

    The water cycle includes the processes with different memory that creates potential for predictability of hydrological system based on separating its long and short memory components and conditioning long-term prediction on slower evolving components (similar to approaches in climate prediction). In the face of the Panta Rhei IAHS Decade questions, it is important to find a conceptual approach to classify hydrological system components with respect to their predictability, define predictable/unpredictable patterns, extend lead-time and improve reliability of hydrological predictions based on the predictable patterns. Representation of hydrological systems as the dynamical systems subjected to the effect of noise (stochastic-dynamical systems) provides possible tool for such conceptualization. A method has been proposed for assessing predictability of hydrological system caused by its sensitivity to both initial and boundary conditions. The predictability is defined through a procedure of convergence of pre-assigned probabilistic measure (e.g. variance) of the system state to stable value. The time interval of the convergence, that is the time interval during which the system losses memory about its initial state, defines limit of the system predictability. The proposed method was applied to assess predictability of soil moisture dynamics in the Nizhnedevitskaya experimental station (51.516N; 38.383E) located in the agricultural zone of the central European Russia. A stochastic-dynamical model combining a deterministic one-dimensional model of hydrothermal regime of soil with a stochastic model of meteorological inputs was developed. The deterministic model describes processes of coupled heat and moisture transfer through unfrozen/frozen soil and accounts for the influence of phase changes on water flow. The stochastic model produces time series of daily meteorological variables (precipitation, air temperature and humidity), whose statistical properties are similar

  1. Inverse stochastic-dynamic models for high-resolution Greenland ice core records

    Science.gov (United States)

    Boers, Niklas; Chekroun, Mickael D.; Liu, Honghu; Kondrashov, Dmitri; Rousseau, Denis-Didier; Svensson, Anders; Bigler, Matthias; Ghil, Michael

    2017-12-01

    Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from δ18O and dust records of unprecedented, subdecadal temporal resolution. The records stem from the North Greenland Ice Core Project (NGRIP), and we focus on the time interval 59-22 ka b2k. Our model reproduces the dynamical characteristics of both the δ18O and dust proxy records, including the millennial-scale Dansgaard-Oeschger variability, as well as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data, (ii) cubic drift terms, (iii) nonlinear coupling terms between the δ18O and dust time series, and (iv) non-Markovian contributions that represent short-term memory effects.

  2. Direct characterization of chaotic and stochastic dynamics in a population model with strong periodicity

    International Nuclear Information System (INIS)

    Tung Wenwen; Qi Yan; Gao, J.B.; Cao Yinhe; Billings, Lora

    2005-01-01

    In recent years it has been increasingly recognized that noise and determinism may have comparable but different influences on population dynamics. However, no simple analysis methods have been introduced into ecology which can readily characterize those impacts. In this paper, we study a population model with strong periodicity and both with and without noise. The noise-free model generates both quasi-periodic and chaotic dynamics for certain parameter values. Due to the strong periodicity, however, the generated chaotic dynamics have not been satisfactorily described. The dynamics becomes even more complicated when there is noise. Characterizing the chaotic and stochastic dynamics in this model thus represents a challenging problem. Here we show how the chaotic dynamics can be readily characterized by the direct dynamical test for deterministic chaos developed by [Gao JB, Zheng ZM. Europhys. Lett. 1994;25:485] and how the influence of noise on quasi-periodic motions can be characterized as asymmetric diffusions wandering along the quasi-periodic orbit. It is hoped that the introduced methods will be useful in studying other population models as well as population time series obtained both in field and laboratory experiments

  3. The Theory of Dynamic Public Transit Priority with Dynamic Stochastic Park and Ride

    Directory of Open Access Journals (Sweden)

    Chengming Zhu

    2014-01-01

    Full Text Available Public transit priority is very important for relieving traffic congestion. The connotation of dynamic public transit priority and dynamic stochastic park and ride is presented. Based on the point that the travel cost of public transit is not higher than the travel cost of car, how to determine the level of dynamic public transit priority is discussed. The traffic organization method of dynamic public transit priority is introduced. For dynamic stochastic park and ride, layout principle, scale, and charging standard are discussed. Traveler acceptability is high through the analysis of questionnaire survey. Dynamic public transit priority with dynamic stochastic park and ride has application feasibility.

  4. Extinction in neutrally stable stochastic Lotka-Volterra models

    Science.gov (United States)

    Dobrinevski, Alexander; Frey, Erwin

    2012-05-01

    Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

  5. Stochastic dynamics of new inflation

    International Nuclear Information System (INIS)

    Nakao, Ken-ichi; Nambu, Yasusada; Sasaki, Misao.

    1988-07-01

    We investigate thoroughly the dynamics of an inflation-driving scalar field in terms of an extended version of the stochastic approach proposed by Starobinsky and discuss the spacetime structure of the inflationary universe. To avoid any complications which might arise due to quantum gravity, we concentrate our discussions on the new inflationary universe scenario in which all the energy scales involved are well below the planck mass. The investigation is done both analytically and numerically. In particular, we present a full numerical analysis of the stochastic scalar field dynamics on the phase space. Then implications of the results are discussed. (author)

  6. Complex dynamics of a stochastic discrete modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting

    Directory of Open Access Journals (Sweden)

    A. Elhassanein

    2014-06-01

    Full Text Available This paper introduced a stochastic discretized version of the modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting. The dynamical behavior of the proposed model was investigated. The existence and stability of the equilibria of the skeleton were studied. Numerical simulations were employed to show the model's complex dynamics by means of the largest Lyapunov exponents, bifurcations, time series diagrams and phase portraits. The effects of noise intensity on its dynamics and the intermittency phenomenon were also discussed via simulation.

  7. Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—an analytical theory

    International Nuclear Information System (INIS)

    Qian, Hong

    2011-01-01

    The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z n . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on R n emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed. (invited article)

  8. Hybrid Semantics of Stochastic Programs with Dynamic Reconfiguration

    Directory of Open Access Journals (Sweden)

    Alberto Policriti

    2009-10-01

    Full Text Available We begin by reviewing a technique to approximate the dynamics of stochastic programs --written in a stochastic process algebra-- by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete dynamics is kept stochastic while the continuous evolution is given in terms of ODEs, and the overall technique, therefore, naturally associates a Piecewise Deterministic Markov Process with a stochastic program. The specific contribution in this work consists in an increase of the flexibility of the translation scheme, obtained by allowing a dynamic reconfiguration of the degree of discreteness/continuity of the semantics. We also discuss the relationships of this approach with other hybrid simulation strategies for biochemical systems.

  9. Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

    Science.gov (United States)

    Agarwal, S.; Wettlaufer, J. S.

    2014-12-01

    We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

  10. A stochastic fractional dynamics model of space-time variability of rain

    Science.gov (United States)

    Kundu, Prasun K.; Travis, James E.

    2013-09-01

    varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, which allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.

  11. Stochastic feeding dynamics arise from the need for information and energy.

    Science.gov (United States)

    Scholz, Monika; Dinner, Aaron R; Levine, Erel; Biron, David

    2017-08-29

    Animals regulate their food intake in response to the available level of food. Recent observations of feeding dynamics in small animals showed feeding patterns of bursts and pauses, but their function is unknown. Here, we present a data-driven decision-theoretical model of feeding in Caenorhabditis elegans Our central assumption is that food intake serves a dual purpose: to gather information about the external food level and to ingest food when the conditions are good. The model recapitulates experimentally observed feeding patterns. It naturally implements trade-offs between speed versus accuracy and exploration versus exploitation in responding to a dynamic environment. We find that the model predicts three distinct regimes in responding to a dynamical environment, with a transition region where animals respond stochastically to periodic signals. This stochastic response accounts for previously unexplained experimental data.

  12. Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

    Science.gov (United States)

    Gay-Balmaz, François; Holm, Darryl D.

    2018-01-01

    Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

  13. Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

    Science.gov (United States)

    Gay-Balmaz, François; Holm, Darryl D.

    2018-06-01

    Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

  14. Compositional Modelling of Stochastic Hybrid Systems

    NARCIS (Netherlands)

    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

  15. Age distribution dynamics with stochastic jumps in mortality.

    Science.gov (United States)

    Calabrese, Salvatore; Porporato, Amilcare; Laio, Francesco; D'Odorico, Paolo; Ridolfi, Luca

    2017-11-01

    While deterministic age distribution models have been extensively studied and applied in various disciplines, little work has been devoted to understanding the role of stochasticity in birth and mortality terms. In this paper, we analyse a stochastic M'Kendrick-von Foerster equation in which jumps in mortality represent intense losses of population due to external events. We present explicit solutions for the probability density functions of the age distribution and the total population and for the temporal dynamics of their moments. We also derive the dynamics of the mean age of the population and its harmonic mean. The framework is then used to calculate the age distribution of salt in the soil root zone, where the accumulation of salt by atmospheric deposition is counteracted by plant uptake and by jump losses due to percolation events.

  16. 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)

  17. Testing the robustness of deterministic models of optimal dynamic pricing and lot-sizing for deteriorating items under stochastic conditions

    DEFF Research Database (Denmark)

    Ghoreishi, Maryam

    2018-01-01

    Many models within the field of optimal dynamic pricing and lot-sizing models for deteriorating items assume everything is deterministic and develop a differential equation as the core of analysis. Two prominent examples are the papers by Rajan et al. (Manag Sci 38:240–262, 1992) and Abad (Manag......, we will try to expose the model by Abad (1996) and Rajan et al. (1992) to stochastic inputs; however, designing these stochastic inputs such that they as closely as possible are aligned with the assumptions of those papers. We do our investigation through a numerical test where we test the robustness...... of the numerical results reported in Rajan et al. (1992) and Abad (1996) in a simulation model. Our numerical results seem to confirm that the results stated in these papers are indeed robust when being imposed to stochastic inputs....

  18. 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.

  19. Stochastic Simulation of Cardiac Ventricular Myocyte Calcium Dynamics and Waves

    OpenAIRE

    Tuan, Hoang-Trong Minh; Williams, George S. B.; Chikando, Aristide C.; Sobie, Eric A.; Lederer, W. Jonathan; Jafri, M. Saleet

    2011-01-01

    A three dimensional model of calcium dynamics in the rat ventricular myocyte was developed to study the mechanism of calcium homeostasis and pathological calcium dynamics during calcium overload. The model contains 20,000 calcium release units (CRUs) each containing 49 ryanodine receptors. The model simulates calcium sparks with a realistic spontaneous calcium spark rate. It suggests that in addition to the calcium spark-based leak, there is an invisible calcium leak caused by the stochastic ...

  20. Multiparameter Stochastic Dynamics of Ecological Tourism System with Continuous Visitor Education Interventions

    Directory of Open Access Journals (Sweden)

    Dongping Wei

    2015-01-01

    Full Text Available Management of ecological tourism in protected areas faces many challenges, with visitation-related resource degradations and cultural impacts being two of them. To address those issues, several strategies including regulations, site managements, and visitor education programs have been commonly used in China and other countries. This paper presents a multiparameter stochastic differential equation model of an Ecological Tourism System to study how the populations of stakeholders vary in a finite time. The solution of Ordinary Differential Equation of Ecological Tourism System reveals that the system collapses when there is a lack of visitor educational intervention. Hence, the Stochastic Dynamic of Ecological Tourism System is introduced to suppress the explosion of the system. But the simulation results of the Stochastic Dynamic of Ecological Tourism System show that the system is still unstable and chaos in some small time interval. The Multiparameters Stochastic Dynamics of Ecological Tourism System is proposed to improve the performance in this paper. The Multiparameters Stochastic Dynamics of Ecological Tourism System not only suppresses the explosion of the system in a finite time, but also keeps the populations of stakeholders in an acceptable level. In conclusion, the Ecological Tourism System develops steadily and sustainably when land managers employ effective visitor education intervention programs to deal with recreation impacts.

  1. Computational Methods in Stochastic Dynamics Volume 2

    CERN Document Server

    Stefanou, George; Papadopoulos, Vissarion

    2013-01-01

    The considerable influence of inherent uncertainties on structural behavior has led the engineering community to recognize the importance of a stochastic approach to structural problems. Issues related to uncertainty quantification and its influence on the reliability of the computational models are continuously gaining in significance. In particular, the problems of dynamic response analysis and reliability assessment of structures with uncertain system and excitation parameters have been the subject of continuous research over the last two decades as a result of the increasing availability of powerful computing resources and technology.   This book is a follow up of a previous book with the same subject (ISBN 978-90-481-9986-0) and focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The selected chapters are authored by some of the most active scholars in their respective areas and...

  2. Deterministic and stochastic CTMC models from Zika disease transmission

    Science.gov (United States)

    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.

  3. 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...

  4. 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...

  5. Effects of stochastic noise on dynamical decoupling procedures

    Energy Technology Data Exchange (ETDEWEB)

    Bernad, Jozsef Zsolt; Frydrych, Holger; Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)

    2013-07-01

    Dynamical decoupling is a well-established technique to protect quantum systems from unwanted influences of their environment by exercising active control. It has been used experimentally to drastically increase the lifetime of qubit states in various implementations. The efficiency of different dynamical decoupling schemes defines the lifetime. However, errors in control operations always limit this efficiency. We propose a stochastic model as a possible description of imperfect control pulses and discuss the impact of this kind of error on different decoupling schemes. In the limit of continuous control, i.e. if the number of pulses N → ∞, we derive a stochastic differential equation for the evolution of the density operator of the controlled system and its environment. In the context of this modified time evolution we discuss possibilities of protecting qubit states against environmental noise.

  6. From complex to simple: interdisciplinary stochastic models

    International Nuclear Information System (INIS)

    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 for certain physical quantities, such as the time dependence of the length of the microtubules, and diffusion coefficients. The second one is a stochastic adsorption model with applications in surface deposition, epidemics and voter systems. We introduce the ‘empty interval method’ and show sample calculations for the time-dependent particle density. These models can serve as an introduction to the field of non-equilibrium statistical physics, and can also be used as a pedagogical tool to exemplify standard statistical physics concepts, such as random walks or the kinetic approach of the master equation. (paper)

  7. The Theory of Dynamic Public Transit Priority with Dynamic Stochastic Park and Ride

    OpenAIRE

    Zhu, Chengming; Chen, Yanyan; Ma, Changxi

    2014-01-01

    Public transit priority is very important for relieving traffic congestion. The connotation of dynamic public transit priority and dynamic stochastic park and ride is presented. Based on the point that the travel cost of public transit is not higher than the travel cost of car, how to determine the level of dynamic public transit priority is discussed. The traffic organization method of dynamic public transit priority is introduced. For dynamic stochastic park and ride, layout principle, scal...

  8. Stochastic volatility models and Kelvin waves

    Science.gov (United States)

    Lipton, Alex; Sepp, Artur

    2008-08-01

    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.

  9. 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

  10. Stochastic volatility models and Kelvin waves

    Energy Technology Data Exchange (ETDEWEB)

    Lipton, Alex [Merrill Lynch, Mlfc Main, 2 King Edward Street, London EC1A 1HQ (United Kingdom); Sepp, Artur [Merrill Lynch, 4 World Financial Center, New York, NY 10080 (United States)], E-mail: Alex_Lipton@ml.com, E-mail: Artur_Sepp@ml.com

    2008-08-29

    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.

  11. Collisionally induced stochastic dynamics of fast ions in solids

    International Nuclear Information System (INIS)

    Burgdoerfer, J.

    1989-01-01

    Recent developments in the theory of excited state formation in collisions of fast highly charged ions with solids are reviewed. We discuss a classical transport theory employing Monte-Carlo sampling of solutions of a microscopic Langevin equation. Dynamical screening by the dielectric medium as well as multiple collisions are incorporated through the drift and stochastic forces in the Langevin equation. The close relationship between the extrinsically stochastic dynamics described by the Langevin and the intrinsic stochasticity in chaotic nonlinear dynamical systems is stressed. Comparison with experimental data and possible modification by quantum corrections are discussed. 49 refs., 11 figs

  12. Optimal Strategy for Integrated Dynamic Inventory Control and Supplier Selection in Unknown Environment via Stochastic Dynamic Programming

    International Nuclear Information System (INIS)

    Sutrisno; Widowati; Solikhin

    2016-01-01

    In this paper, we propose a mathematical model in stochastic dynamic optimization form to determine the optimal strategy for an integrated single product inventory control problem and supplier selection problem where the demand and purchasing cost parameters are random. For each time period, by using the proposed model, we decide the optimal supplier and calculate the optimal product volume purchased from the optimal supplier so that the inventory level will be located at some point as close as possible to the reference point with minimal cost. We use stochastic dynamic programming to solve this problem and give several numerical experiments to evaluate the model. From the results, for each time period, the proposed model was generated the optimal supplier and the inventory level was tracked the reference point well. (paper)

  13. Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

    Science.gov (United States)

    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.

  14. Approaches for modeling within subject variability in pharmacometric count data analysis: dynamic inter-occasion variability and stochastic differential equations.

    Science.gov (United States)

    Deng, Chenhui; Plan, Elodie L; Karlsson, Mats O

    2016-06-01

    Parameter variation in pharmacometric analysis studies can be characterized as within subject parameter variability (WSV) in pharmacometric models. WSV has previously been successfully modeled using inter-occasion variability (IOV), but also stochastic differential equations (SDEs). In this study, two approaches, dynamic inter-occasion variability (dIOV) and adapted stochastic differential equations, were proposed to investigate WSV in pharmacometric count data analysis. These approaches were applied to published count models for seizure counts and Likert pain scores. Both approaches improved the model fits significantly. In addition, stochastic simulation and estimation were used to explore further the capability of the two approaches to diagnose and improve models where existing WSV is not recognized. The results of simulations confirmed the gain in introducing WSV as dIOV and SDEs when parameters vary randomly over time. Further, the approaches were also informative as diagnostics of model misspecification, when parameters changed systematically over time but this was not recognized in the structural model. The proposed approaches in this study offer strategies to characterize WSV and are not restricted to count data.

  15. Stochastic models, estimation, and control

    CERN Document Server

    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.

  16. Ensemble assimilation of JASON/ENVISAT and JASON/AltiKA altimetric observations with stochastic parameterization of the model dynamical uncertainties

    Science.gov (United States)

    Brasseur, Pierre; Candille, Guillem; Bouttier, Pierre-Antoine; Brankart, Jean-Michel; Verron, Jacques

    2015-04-01

    The objective of this study is to explicitly simulate and quantify the uncertainty related to sea-level anomalies diagnosed from eddy-resolving ocean circulation models, in order to develop advanced methods suitable for addressing along-track altimetric data assimilation into such models. This work is carried out jointly with the MyOcean and SANGOMA (Stochastic Assimilation for the Next Generation Ocean Model Applications) consortium, funded by EU under the GMES umbrella over the 2012-2015 period. In this framework, a realistic circulation model of the North Atlantic ocean at 1/4° resolution (NATL025 configuration) has been adapted to include effects of unresolved scales on the dynamics. This is achieved by introducing stochastic perturbations of the equation of state to represent the associated model uncertainty. Assimilation experiments are designed using altimetric data from past and on-going missions (Jason-2 and Saral/AltiKA experiments, and Cryosat-2 for fully independent altimetric validation) to better control the Gulf Stream circulation, especially the frontal regions which are predominantly affected by the non-resolved dynamical scales. An ensemble based on such stochastic perturbations is then produced and evaluated -through the probabilistic criteria: the reliability and the resolution- using the model equivalent of along-track altimetric observations. These three elements (stochastic parameterization, ensemble simulation and 4D observation operator) are used together to perform optimal 4D analysis of along-track altimetry over 10-day assimilation windows. In this presentation, the results show that the free ensemble -before starting the assimilation process- well reproduces the climatological variability over the Gulf Stream area: the system is then pretty reliable but no informative (null probabilistic resolution). Updating the free ensemble with altimetric data leads to a better reliability and to an improvement of the information (resolution

  17. Stochastic bifurcation in a model of love with colored noise

    Science.gov (United States)

    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.

  18. Stochastic volatility and multi-dimensional modeling in the European energy market

    Energy Technology Data Exchange (ETDEWEB)

    Vos, Linda

    2012-07-01

    In energy prices there is evidence for stochastic volatility. Stochastic volatility has effect on the price of path-dependent options and therefore has to be modeled properly. We introduced a multi-dimensional non-Gaussian stochastic volatility model with leverage which can be used in energy pricing. It captures special features of energy prices like price spikes, mean-reversion, stochastic volatility and inverse leverage. Moreover it allows modeling dependencies between different commodities.The derived forward price dynamics based on this multi-variate spot price model, provides a very flexible structure. It includes cotango, backwardation and hump shape forward curves.Alternatively energy prices could be modeled by a 2-factor model consisting of a non-Gaussian stable CARMA process and a non-stationary trend models by a Levy process. Also this model is able to capture special features like price spikes, mean reversion and the low frequency dynamics in the market. An robust L1-filter is introduced to filter out the states of the CARMA process. When applying to German electricity EEX exchange data an overall negative risk-premium is found. However close to delivery a positive risk-premium is observed.(Author)

  19. Effects of demographic structure on key properties of stochastic density-independent population dynamics.

    Science.gov (United States)

    Vindenes, Yngvild; Sæther, Bernt-Erik; Engen, Steinar

    2012-12-01

    The development of stochastic demography has largely been based on age structured populations, although other types of demographic structure, especially permanent and dynamic heterogeneity, are likely common in natural populations. The combination of stochasticity and demographic structure is a challenge for analyses of population dynamics and extinction risk, because the population structure will fluctuate around the stable structure and the population size shows transient fluctuations. However, by using a diffusion approximation for the total reproductive value, density-independent dynamics of structured populations can be described with only three population parameters: the expected population growth rate, the environmental variance and the demographic variance. These parameters depend on population structure via the state-specific vital rates and transition rates. Once they are found, the diffusion approximation represents a substantial reduction in model complexity. Here, we review and compare the key population parameters across a wide range of demographic structure, from the case of no structure to the most general case of dynamic heterogeneity, and for both discrete and continuous types. We focus on the demographic variance, but also show how environmental stochasticity can be included. This study brings together results from recent models, each considering a specific type of population structure, and places them in a general framework for structured populations. Comparison across different types of demographic structure reveals that the reproductive value is an essential concept for understanding how population structure affects stochastic dynamics and extinction risk. Copyright © 2011 Elsevier Inc. All rights reserved.

  20. A stochastic SIRS epidemic model with infectious force under intervention strategies

    Science.gov (United States)

    Cai, Yongli; Kang, Yun; Banerjee, Malay; Wang, Weiming

    2015-12-01

    In this paper, we extend a classical SIRS epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation (SDE) one through introducing random fluctuations. The value of our study lies in two aspects. Mathematically, by using the Markov semigroups theory, we prove that the reproduction number R0S can be used to govern the stochastic dynamics of SDE model. If R0S 1, under mild extra conditions, it has an endemic stationary distribution which leads to the stochastical persistence of the disease. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.

  1. Stochastic ontogenetic growth model

    Science.gov (United States)

    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.

  2. Stochastic mixed-mode oscillations in a three-species predator-prey model

    Science.gov (United States)

    Sadhu, Susmita; Kuehn, Christian

    2018-03-01

    The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.

  3. Lectures on Dynamics of Stochastic Systems

    CERN Document Server

    Klyatskin, Valery I

    2010-01-01

    Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data. This book is a revised a

  4. The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process

    Science.gov (United States)

    Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko

    2012-06-01

    A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.

  5. Pricing decisions in an experimental dynamic stochastic general equilibrium economy

    NARCIS (Netherlands)

    Noussair, C.N.; Pfajfar, D.; Zsiros, J.

    We construct experimental economies, populated with human subjects, with a structure based on a nonlinear version of the New Keynesian dynamic stochastic general equilibrium (DSGE) model. We analyze the behavior of firms’ pricing decisions in four different experimental economies. We consider how

  6. Hybrid approaches for multiple-species stochastic reaction–diffusion models

    International Nuclear Information System (INIS)

    Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

    2015-01-01

    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. - 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

  7. 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.

  8. Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics

    International Nuclear Information System (INIS)

    Ao, P.

    2008-01-01

    The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach: One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium

  9. Quantitative sociodynamics stochastic methods and models of social interaction processes

    CERN Document Server

    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...

  10. Quantitative Sociodynamics Stochastic Methods and Models of Social Interaction Processes

    CERN Document Server

    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...

  11. Modelling the Dynamics of an Aedes albopictus Population

    Directory of Open Access Journals (Sweden)

    Thomas Anung Basuki

    2010-08-01

    Full Text Available We present a methodology for modelling population dynamics with formal means of computer science. This allows unambiguous description of systems and application of analysis tools such as simulators and model checkers. In particular, the dynamics of a population of Aedes albopictus (a species of mosquito and its modelling with the Stochastic Calculus of Looping Sequences (Stochastic CLS are considered. The use of Stochastic CLS to model population dynamics requires an extension which allows environmental events (such as changes in the temperature and rainfalls to be taken into account. A simulator for the constructed model is developed via translation into the specification language Maude, and used to compare the dynamics obtained from the model with real data.

  12. Exercise effects in a virtual type 1 diabetes patient: Using stochastic differential equations for model extension

    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...

  13. Stochastic Modeling of Past Volcanic Crises

    Science.gov (United States)

    Woo, Gordon

    2018-01-01

    The statistical foundation of disaster risk analysis is past experience. From a scientific perspective, history is just one realization of what might have happened, given the randomness and chaotic dynamics of Nature. Stochastic analysis of the past is an exploratory exercise in counterfactual history, considering alternative possible scenarios. In particular, the dynamic perturbations that might have transitioned a volcano from an unrest to an eruptive state need to be considered. The stochastic modeling of past volcanic crises leads to estimates of eruption probability that can illuminate historical volcanic crisis decisions. It can also inform future economic risk management decisions in regions where there has been some volcanic unrest, but no actual eruption for at least hundreds of years. Furthermore, the availability of a library of past eruption probabilities would provide benchmark support for estimates of eruption probability in future volcanic crises.

  14. A stochastic analysis for a phytoplankton-zooplankton model

    International Nuclear Information System (INIS)

    Ge, G; Wang, H-L; Xu, J

    2008-01-01

    A simple phytoplankton-zooplankton nonlinear dynamical model was proposed to study the coexistence of all the species and a Hopf bifurcation was observed. In order to study the effect of environmental robustness on this system, we have stochastically perturbed the system with respect to white noise around its positive interior equilibrium. We have observed that the system remains stochastically stable around the positive equilibrium for same parametric values in the deterministic situation

  15. Stochastic processes, multiscale modeling, and numerical methods for computational cellular biology

    CERN Document Server

    2017-01-01

    This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of s...

  16. Stochastic neuron models

    CERN Document Server

    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...

  17. Dynamic-stochastic modeling of snow cover formation on the European territory of Russia

    Directory of Open Access Journals (Sweden)

    A. N. Gelfan

    2014-01-01

    Full Text Available A dynamic-stochastic model, which combines a deterministic model of snow cover formation with a stochastic weather generator, has been developed. The deterministic snow model describes temporal change of the snow depth, content of ice and liquid water, snow density, snowmelt, sublimation, re-freezing of melt water, and snow metamorphism. The model has been calibrated and validated against the long-term data of snow measurements over the territory of the European Russia. The model showed good performance in simulating time series of the snow water equivalent and snow depth. The developed weather generator (NEsted Weather Generator, NewGen includes nested generators of annual, monthly and daily time series of weather variables (namely, precipitation, air temperature, and air humidity. The parameters of the NewGen have been adjusted through calibration against the long-term meteorological data in the European Russia. A disaggregation procedure has been proposed for transforming parameters of the annual weather generator into the parameters of the monthly one and, subsequently, into the parameters of the daily generator. Multi-year time series of the simulated daily weather variables have been used as an input to the snow model. Probability properties of the snow cover, such as snow water equivalent and snow depth for return periods of 25 and 100 years, have been estimated against the observed data, showing good correlation coefficients. The described model has been applied to different landscapes of European Russia, from steppe to taiga regions, to show the robustness of the proposed technique.

  18. 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

  19. Stochastic two-delay differential model of delayed visual feedback effects on postural dynamics.

    Science.gov (United States)

    Boulet, Jason; Balasubramaniam, Ramesh; Daffertshofer, Andreas; Longtin, André

    2010-01-28

    We report on experiments and modelling involving the 'visuo-postural control loop' in the upright stance. We experimentally manipulated an artificial delay to the visual feedback during standing, presented at delays ranging from 0 to 1 s in increments of 250 ms. Using stochastic delay differential equations, we explicitly modelled the centre-of-pressure (COP) and centre-of-mass (COM) dynamics with two independent delay terms for vision and proprioception. A novel 'drifting fixed point' hypothesis was used to describe the fluctuations of the COM with the COP being modelled as a faster, corrective process of the COM. The model was in good agreement with the data in terms of probability density functions, power spectral densities, short- and long-term correlations (Hurst exponents) as well the critical time between the two ranges. This journal is © 2010 The Royal Society

  20. Stochastic dynamic stiffness of surface footing for offshore wind turbines

    DEFF Research Database (Denmark)

    Vahdatirad, Mohammadjavad; Andersen, Lars Vabbersgaard; Ibsen, Lars Bo

    2014-01-01

    Highlights •This study concerns the stochastic dynamic stiffness of foundations for large offshore wind turbines. •A simple model of wind turbine structure with equivalent coupled springs at the base is utilized. •The level of uncertainties is quantified through a sensitivity analysis. •Estimation...

  1. Modeling dynamic swarms

    KAUST Repository

    Ghanem, Bernard; Ahuja, Narendra

    2013-01-01

    This paper proposes the problem of modeling video sequences of dynamic swarms (DSs). We define a DS as a large layout of stochastically repetitive spatial configurations of dynamic objects (swarm elements) whose motions exhibit local spatiotemporal

  2. Developing stochastic model of thrust and flight dynamics for small UAVs

    Science.gov (United States)

    Tjhai, Chandra

    This thesis presents a stochastic thrust model and aerodynamic model for small propeller driven UAVs whose power plant is a small electric motor. First a model which relates thrust generated by a small propeller driven electric motor as a function of throttle setting and commanded engine RPM is developed. A perturbation of this model is then used to relate the uncertainty in throttle and engine RPM commanded to the error in the predicted thrust. Such a stochastic model is indispensable in the design of state estimation and control systems for UAVs where the performance requirements of the systems are specied in stochastic terms. It is shown that thrust prediction models for small UAVs are not a simple, explicit functions relating throttle input and RPM command to thrust generated. Rather they are non-linear, iterative procedures which depend on a geometric description of the propeller and mathematical model of the motor. A detailed derivation of the iterative procedure is presented and the impact of errors which arise from inaccurate propeller and motor descriptions are discussed. Validation results from a series of wind tunnel tests are presented. The results show a favorable statistical agreement between the thrust uncertainty predicted by the model and the errors measured in the wind tunnel. The uncertainty model of aircraft aerodynamic coefficients developed based on wind tunnel experiment will be discussed at the end of this thesis.

  3. Hybrid approaches for multiple-species stochastic reaction-diffusion models

    Science.gov (United States)

    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.

  4. Hybrid approaches for multiple-species stochastic reaction-diffusion models.

    KAUST Repository

    Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen

    2015-01-01

    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.

  5. Hybrid approaches for multiple-species stochastic reaction-diffusion models.

    KAUST Repository

    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.

  6. Dynamics and Physiological Roles of Stochastic Firing Patterns Near Bifurcation Points

    Science.gov (United States)

    Jia, Bing; Gu, Huaguang

    2017-06-01

    Different stochastic neural firing patterns or rhythms that appeared near polarization or depolarization resting states were observed in biological experiments on three nervous systems, and closely matched those simulated near bifurcation points between stable equilibrium point and limit cycle in a theoretical model with noise. The distinct dynamics of spike trains and interspike interval histogram (ISIH) of these stochastic rhythms were identified and found to build a relationship to the coexisting behaviors or fixed firing frequency of four different types of bifurcations. Furthermore, noise evokes coherence resonances near bifurcation points and plays important roles in enhancing information. The stochastic rhythms corresponding to Hopf bifurcation points with fixed firing frequency exhibited stronger coherence degree and a sharper peak in the power spectrum of the spike trains than those corresponding to saddle-node bifurcation points without fixed firing frequency. Moreover, the stochastic firing patterns changed to a depolarization resting state as the extracellular potassium concentration increased for the injured nerve fiber related to pathological pain or static blood pressure level increased for aortic depressor nerve fiber, and firing frequency decreased, which were different from the physiological viewpoint that firing frequency increased with increasing pressure level or potassium concentration. This shows that rhythms or firing patterns can reflect pressure or ion concentration information related to pathological pain information. Our results present the dynamics of stochastic firing patterns near bifurcation points, which are helpful for the identification of both dynamics and physiological roles of complex neural firing patterns or rhythms, and the roles of noise.

  7. Stochastic biomathematical models with applications to neuronal modeling

    CERN Document Server

    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.

  8. Deterministic and stochastic trends in the Lee-Carter mortality model

    DEFF Research Database (Denmark)

    Callot, Laurent; Haldrup, Niels; Kallestrup-Lamb, Malene

    The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics loads with identical weights when describing the development of age specific mortality rates. Effectively this means that the main characteristics of the model simplifies to a random walk model...... that characterizes mortality data. We find empirical evidence that this feature of the Lee-Carter model overly restricts the system dynamics and we suggest to separate the deterministic and stochastic time series components at the benefit of improved fit and forecasting performance. In fact, we find...... that the classical Lee-Carter model will otherwise over estimate the reduction of mortality for the younger age groups and will under estimate the reduction of mortality for the older age groups. In practice, our recommendation means that the Lee-Carter model instead of a one-factor model should be formulated...

  9. A stochastic model for magnetic dynamics in single-molecule magnets

    Energy Technology Data Exchange (ETDEWEB)

    López-Ruiz, R., E-mail: rlruiz@ifi.unicamp.br [Instituto de Física Gleb Wataghin - Universidade Estadual de Campinas, 13083-859 Campinas (SP) (Brazil); Almeida, P.T. [Instituto de Física Gleb Wataghin - Universidade Estadual de Campinas, 13083-859 Campinas (SP) (Brazil); Vaz, M.G.F. [Instituto de Química, Universidade Federal Fluminense, 24020-150 Niterói (RJ) (Brazil); Novak, M.A. [Instituto de Física - Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro (RJ) (Brazil); Béron, F.; Pirota, K.R. [Instituto de Física Gleb Wataghin - Universidade Estadual de Campinas, 13083-859 Campinas (SP) (Brazil)

    2016-04-01

    Hysteresis and magnetic relaxation curves were performed on double well potential systems with quantum tunneling possibility via stochastic simulations. Simulation results are compared with experimental ones using the Mn{sub 12} single-molecule magnet, allowing us to introduce time dependence in the model. Despite being a simple simulation model, it adequately reproduces the phenomenology of a thermally activated quantum tunneling and can be extended to other systems with different parameters. Assuming competition between the reversal modes, thermal (over) and tunneling (across) the anisotropy barrier, a separation of classical and quantum contributions to relaxation time can be obtained. - Highlights: • Single-molecule magnets are modeled using a simple stochastic approach. • Simulation reproduces thermally-activated tunnelling magnetization reversal features. • The time is introduced in hysteresis and relaxation simulations. • We can separate the quantum and classical contributions to decay time.

  10. Stochastic modeling analysis and simulation

    CERN Document Server

    Nelson, Barry L

    1995-01-01

    A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Suitable for advanced undergraduates and graduate-level industrial engineers and management science majors, it proposes modeling systems in terms of their simulation, regardless of whether simulation is employed for analysis. Beginning with a view of the conditions that permit a mathematical-numerical analysis, the text explores Poisson and renewal processes, Markov chains in discrete and continuous time, se

  11. Dynamic analysis of a stochastic rumor propagation model

    Science.gov (United States)

    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.

  12. Stochastic control theory dynamic programming principle

    CERN Document Server

    Nisio, Makiko

    2015-01-01

    This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-ma...

  13. Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports.

    Science.gov (United States)

    Schilde, M; Doerner, K F; Hartl, R F

    2011-12-01

    The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15%. Moreover, improvements of up to 41% can be achieved for some test instances.

  14. Nonlinear dynamics and bifurcation characteristics of shape memory alloy thin films subjected to in-plane stochastic excitation

    International Nuclear Information System (INIS)

    Zhu, Zhi-Wen; Zhang, Qing-Xin; Xu, Jia

    2014-01-01

    A kind of shape memory alloy (SMA) hysteretic nonlinear model was developed, and the nonlinear dynamics and bifurcation characteristics of the SMA thin film subjected to in-plane stochastic excitation were investigated. Van der Pol difference item was introduced to describe the hysteretic phenomena of the SMA strain–stress curves, and the nonlinear dynamic model of the SMA thin film subjected to in-plane stochastic excitation was developed. The conditions of global stochastic stability of the system were determined in singular boundary theory, and the probability density function of the system response was obtained. Finally, the conditions of stochastic Hopf bifurcation were analyzed. The results of theoretical analysis and numerical simulation indicate that self-excited vibration is induced by the hysteretic nonlinear characteristics of SMA, and stochastic Hopf bifurcation appears when the bifurcation parameter was changed; there are two limit cycles in the stationary probability density of the dynamic response of the system in some cases, which means that there are two vibration amplitudes whose probabilities are both very high, and jumping phenomena between the two vibration amplitudes appear with the change in conditions. The results obtained in this current paper are helpful for the application of the SMA thin film in stochastic vibration fields. - Highlights: • Hysteretic nonlinear model of shape memory alloy was developed. • Van der Pol item was introduced to interpret hysteretic strain–stress curves. • Nonlinear dynamic characteristics of the shape memory alloy film were analyzed. • Jumping phenomena were observed in the change of the parameters

  15. State vector reduction - 2: Elements of physical reality, nonlocality and stochasticity in relativistic dynamical reduction models

    International Nuclear Information System (INIS)

    Ghirardi, G.C.; Pearle, P.

    1991-02-01

    The problem of getting a relativistic generalization of the CSL dynamical reduction model, which has been presented in part I, is discussed. In so doing we have the opportunity to introduce the idea of a stochastically invariant theory. The theoretical model we present, that satisfies this kind of invariance requirement, offers us the possibility to reconsider, from a new point of view, some conceptually relevant issues such as nonlocality, the legitimacy of attributing elements of physical reality to physical systems and the problem of establishing causal relations between physical events. (author). Refs, 3 figs

  16. Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage

    Science.gov (United States)

    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.

  17. Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

    Science.gov (United States)

    Varga, Katherine Yvonne

    2015-01-01

    We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

  18. Parallel Stochastic discrete event simulation of calcium dynamics in neuron.

    Science.gov (United States)

    Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W

    2017-09-26

    The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.

  19. Reliability-based Dynamic Network Design with Stochastic Networks

    NARCIS (Netherlands)

    Li, H.

    2009-01-01

    Transportation systems are stochastic and dynamic systems. The road capacities and the travel demand are fluctuating from time to time within a day and at the same time from day to day. For road users, the travel time and travel costs experienced over time and space are stochastic, thus desire

  20. Path integral methods for the dynamics of stochastic and disordered systems

    International Nuclear Information System (INIS)

    Hertz, John A; Roudi, Yasser; Sollich, Peter

    2017-01-01

    We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models. (topical review)

  1. Dynamic electricity pricing for electric vehicles using stochastic programming

    International Nuclear Information System (INIS)

    Soares, João; Ghazvini, Mohammad Ali Fotouhi; Borges, Nuno; Vale, Zita

    2017-01-01

    Electric Vehicles (EVs) are an important source of uncertainty, due to their variable demand, departure time and location. In smart grids, the electricity demand can be controlled via Demand Response (DR) programs. Smart charging and vehicle-to-grid seem highly promising methods for EVs control. However, high capital costs remain a barrier to implementation. Meanwhile, incentive and price-based schemes that do not require high level of control can be implemented to influence the EVs' demand. Having effective tools to deal with the increasing level of uncertainty is increasingly important for players, such as energy aggregators. This paper formulates a stochastic model for day-ahead energy resource scheduling, integrated with the dynamic electricity pricing for EVs, to address the challenges brought by the demand and renewable sources uncertainty. The two-stage stochastic programming approach is used to obtain the optimal electricity pricing for EVs. A realistic case study projected for 2030 is presented based on Zaragoza network. The results demonstrate that it is more effective than the deterministic model and that the optimal pricing is preferable. This study indicates that adequate DR schemes like the proposed one are promising to increase the customers' satisfaction in addition to improve the profitability of the energy aggregation business. - Highlights: • A stochastic model for energy scheduling tackling several uncertainty sources. • A two-stage stochastic programming is used to tackle the developed model. • Optimal EV electricity pricing seems to improve the profits. • The propose results suggest to increase the customers' satisfaction.

  2. Stochastic population dynamics of a montane ground-dwelling squirrel.

    Directory of Open Access Journals (Sweden)

    Jeffrey A Hostetler

    Full Text Available Understanding the causes and consequences of population fluctuations is a central goal of ecology. We used demographic data from a long-term (1990-2008 study and matrix population models to investigate factors and processes influencing the dynamics and persistence of a golden-mantled ground squirrel (Callospermophilus lateralis population, inhabiting a dynamic subalpine habitat in Colorado, USA. The overall deterministic population growth rate λ was 0.94±SE 0.05 but it varied widely over time, ranging from 0.45±0.09 in 2006 to 1.50±0.12 in 2003, and was below replacement (λ<1 for 9 out of 18 years. The stochastic population growth rate λ(s was 0.92, suggesting a declining population; however, the 95% CI on λ(s included 1.0 (0.52-1.60. Stochastic elasticity analysis showed that survival of adult females, followed by survival of juvenile females and litter size, were potentially the most influential vital rates; analysis of life table response experiments revealed that the same three life history variables made the largest contributions to year-to year changes in λ. Population viability analysis revealed that, when the influences of density dependence and immigration were not considered, the population had a high (close to 1.0 in 50 years probability of extinction. However, probability of extinction declined to as low as zero when density dependence and immigration were considered. Destabilizing effects of stochastic forces were counteracted by regulating effects of density dependence and rescue effects of immigration, which allowed our study population to bounce back from low densities and prevented extinction. These results suggest that dynamics and persistence of our study population are determined synergistically by density-dependence, stochastic forces, and immigration.

  3. Modelling the heat dynamics of a building using stochastic differential equations

    DEFF Research Database (Denmark)

    Andersen, Klaus Kaae; Madsen, Henrik; Hansen, Lars Henrik

    2000-01-01

    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...

  4. Deterministic and stochastic trends in the Lee-Carter mortality model

    DEFF Research Database (Denmark)

    Callot, Laurent; Haldrup, Niels; Kallestrup-Lamb, Malene

    2015-01-01

    The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics load with identical weights when describing the development of age-specific mortality rates. Effectively this means that the main characteristics of the model simplify to a random walk model with age...... mortality data. We find empirical evidence that this feature of the Lee–Carter model overly restricts the system dynamics and we suggest to separate the deterministic and stochastic time series components at the benefit of improved fit and forecasting performance. In fact, we find that the classical Lee......–Carter model will otherwise overestimate the reduction of mortality for the younger age groups and will underestimate the reduction of mortality for the older age groups. In practice, our recommendation means that the Lee–Carter model instead of a one-factor model should be formulated as a two- (or several...

  5. On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs.

    Science.gov (United States)

    Gerhard, Felipe; Deger, Moritz; Truccolo, Wilson

    2017-02-01

    Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a

  6. Spreading dynamics on complex networks: a general stochastic approach.

    Science.gov (United States)

    Noël, Pierre-André; Allard, Antoine; Hébert-Dufresne, Laurent; Marceau, Vincent; Dubé, Louis J

    2014-12-01

    Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.

  7. Numerical simulation of stochastic point kinetic equation in the dynamical system of nuclear reactor

    International Nuclear Information System (INIS)

    Saha Ray, S.

    2012-01-01

    Highlights: ► In this paper stochastic neutron point kinetic equations have been analyzed. ► Euler–Maruyama method and Strong Taylor 1.5 order method have been discussed. ► These methods are applied for the solution of stochastic point kinetic equations. ► Comparison between the results of these methods and others are presented in tables. ► Graphs for neutron and precursor sample paths are also presented. -- Abstract: In the present paper, the numerical approximation methods, applied to efficiently calculate the solution for stochastic point kinetic equations () in nuclear reactor dynamics, are investigated. A system of Itô stochastic differential equations has been analyzed to model the neutron density and the delayed neutron precursors in a point nuclear reactor. The resulting system of Itô stochastic differential equations are solved over each time-step size. The methods are verified by considering different initial conditions, experimental data and over constant reactivities. The computational results indicate that the methods are simple and suitable for solving stochastic point kinetic equations. In this article, a numerical investigation is made in order to observe the random oscillations in neutron and precursor population dynamics in subcritical and critical reactors.

  8. Reformulation of a stochastic action principle for irregular dynamics

    International Nuclear Information System (INIS)

    Wang, Q.A.; Bangoup, S.; Dzangue, F.; Jeatsa, A.; Tsobnang, F.; Le Mehaute, A.

    2009-01-01

    A stochastic action principle for random dynamics is revisited. Numerical diffusion experiments are carried out to show that the diffusion path probability depends exponentially on the Lagrangian action A=∫ a b Ldt. This result is then used to derive the Shannon measure for path uncertainty. It is shown that the maximum entropy principle and the least action principle of classical mechanics can be unified into δA-bar=0 where the average is calculated over all possible paths of the stochastic motion between two configuration points a and b. It is argued that this action principle and the maximum entropy principle are a consequence of the mechanical equilibrium condition extended to the case of stochastic dynamics.

  9. Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

    International Nuclear Information System (INIS)

    Wang Zhi-Gang; Gao Rui-Mei; Fan Xiao-Ming; Han Qi-Xing

    2014-01-01

    We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ 0 , a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ 0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ 0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ 0 , when the stochastic system obeys some conditions and ℛ 0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations. (general)

  10. Stochastic modelling of conjugate heat transfer in near-wall turbulence

    International Nuclear Information System (INIS)

    Pozorski, Jacek; Minier, Jean-Pierre

    2006-01-01

    The paper addresses the conjugate heat transfer in turbulent flows with temperature assumed to be a passive scalar. The Lagrangian approach is applied and the heat transfer is modelled with the use of stochastic particles. The intensity of thermal fluctuations in near-wall turbulence is determined from the scalar probability density function (PDF) with externally provided dynamical statistics. A stochastic model for the temperature field in the wall material is proposed and boundary conditions for stochastic particles at the solid-fluid interface are formulated. The heated channel flow with finite-thickness walls is considered as a validation case. Computation results for the mean temperature profiles and the variance of thermal fluctuations are presented and compared with available DNS data

  11. Stochastic modelling of conjugate heat transfer in near-wall turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Pozorski, Jacek [Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80952 Gdansk (Poland)]. E-mail: jp@imp.gda.pl; Minier, Jean-Pierre [Research and Development Division, Electricite de France, 6 quai Watier, 78400 Chatou (France)

    2006-10-15

    The paper addresses the conjugate heat transfer in turbulent flows with temperature assumed to be a passive scalar. The Lagrangian approach is applied and the heat transfer is modelled with the use of stochastic particles. The intensity of thermal fluctuations in near-wall turbulence is determined from the scalar probability density function (PDF) with externally provided dynamical statistics. A stochastic model for the temperature field in the wall material is proposed and boundary conditions for stochastic particles at the solid-fluid interface are formulated. The heated channel flow with finite-thickness walls is considered as a validation case. Computation results for the mean temperature profiles and the variance of thermal fluctuations are presented and compared with available DNS data.

  12. Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

    Science.gov (United States)

    Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

    2015-05-01

    Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

  13. Stochastic Dynamic AC Optimal Power Flow Based on a Multivariate Short-Term Wind Power Scenario Forecasting Model

    Directory of Open Access Journals (Sweden)

    Wenlei Bai

    2017-12-01

    Full Text Available The deterministic methods generally used to solve DC optimal power flow (OPF do not fully capture the uncertainty information in wind power, and thus their solutions could be suboptimal. However, the stochastic dynamic AC OPF problem can be used to find an optimal solution by fully capturing the uncertainty information of wind power. That uncertainty information of future wind power can be well represented by the short-term future wind power scenarios that are forecasted using the generalized dynamic factor model (GDFM—a novel multivariate statistical wind power forecasting model. Furthermore, the GDFM can accurately represent the spatial and temporal correlations among wind farms through the multivariate stochastic process. Fully capturing the uncertainty information in the spatially and temporally correlated GDFM scenarios can lead to a better AC OPF solution under a high penetration level of wind power. Since the GDFM is a factor analysis based model, the computational time can also be reduced. In order to further reduce the computational time, a modified artificial bee colony (ABC algorithm is used to solve the AC OPF problem based on the GDFM forecasting scenarios. Using the modified ABC algorithm based on the GDFM forecasting scenarios has resulted in better AC OPF’ solutions on an IEEE 118-bus system at every hour for 24 h.

  14. Dynamics of the stochastic low concentration trimolecular oscillatory chemical system with jumps

    Science.gov (United States)

    Wei, Yongchang; Yang, Qigui

    2018-06-01

    This paper is devoted to discern long time dynamics through the stochastic low concentration trimolecular oscillatory chemical system with jumps. By Lyapunov technique, this system is proved to have a unique global positive solution, and the asymptotic stability in mean square of such model is further established. Moreover, the existence of random attractor and Lyapunov exponents are obtained for the stochastic homeomorphism flow generated by the corresponding global positive solution. And some numerical simulations are given to illustrate the presented results.

  15. Integrating stochastic age-structured population dynamics into complex fisheries economic models for management evaluations: the North Sea saithe fishery as a case study

    NARCIS (Netherlands)

    Simons, S.L.; Bartelings, H.; Hamon, K.G.; Kempf, A.J.; Doring, R.; Temming, A.

    2014-01-01

    There is growing interest in bioeconomic models as tools for understanding pathways of fishery behaviour in order to assess the impact of alternative policies on natural resources. A model system is presented that combines stochastic age-structured population dynamics with complex fisheries

  16. Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes

    DEFF Research Database (Denmark)

    Starke, Jens; Reichert, Christian; Eiswirth, Markus

    2007-01-01

    of stochastic origin can be observed in experiments. The models include a new approach to the platinum phase transition, which allows for a unification of existing models for Pt(100) and Pt(110). The rich nonlinear dynamical behavior of the macroscopic reaction kinetics is investigated and shows good agreement...

  17. Model predictive control classical, robust and stochastic

    CERN Document Server

    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...

  18. Stochastic climate theory

    NARCIS (Netherlands)

    Gottwald, G.A.; Crommelin, D.T.; Franzke, C.L.E.; Franzke, C.L.E.; O'Kane, T.J.

    2017-01-01

    In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations contain a Markov term, a memory term and a term suggestive of

  19. Nambu mechanics for stochastic magnetization dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Thibaudeau, Pascal, E-mail: pascal.thibaudeau@cea.fr [CEA DAM/Le Ripault, BP 16, F-37260 Monts (France); Nussle, Thomas, E-mail: thomas.nussle@cea.fr [CEA DAM/Le Ripault, BP 16, F-37260 Monts (France); CNRS-Laboratoire de Mathématiques et Physique Théorique (UMR 7350), Fédération de Recherche “Denis Poisson” (FR2964), Département de Physique, Université de Tours, Parc de Grandmont, F-37200 Tours (France); Nicolis, Stam, E-mail: stam.nicolis@lmpt.univ-tours.fr [CNRS-Laboratoire de Mathématiques et Physique Théorique (UMR 7350), Fédération de Recherche “Denis Poisson” (FR2964), Département de Physique, Université de Tours, Parc de Grandmont, F-37200 Tours (France)

    2017-06-15

    Highlights: • The LLG equation can be formulated in the framework of dissipative Nambu mechanics. • A master equation is derived for the spin dynamics for additive/multiplicative noises. • The derived stochastic equations are compared to moment equations obtained by closures. - Abstract: The Landau–Lifshitz–Gilbert (LLG) equation describes the dynamics of a damped magnetization vector that can be understood as a generalization of Larmor spin precession. The LLG equation cannot be deduced from the Hamiltonian framework, by introducing a coupling to a usual bath, but requires the introduction of additional constraints. It is shown that these constraints can be formulated elegantly and consistently in the framework of dissipative Nambu mechanics. This has many consequences for both the variational principle and for topological aspects of hidden symmetries that control conserved quantities. We particularly study how the damping terms of dissipative Nambu mechanics affect the consistent interaction of magnetic systems with stochastic reservoirs and derive a master equation for the magnetization. The proposals are supported by numerical studies using symplectic integrators that preserve the topological structure of Nambu equations. These results are compared to computations performed by direct sampling of the stochastic equations and by using closure assumptions for the moment equations, deduced from the master equation.

  20. Biochemical Network Stochastic Simulator (BioNetS: software for stochastic modeling of biochemical networks

    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.

  1. Dynamics of the stochastic Lorenz chaotic system with long memory effects

    Energy Technology Data Exchange (ETDEWEB)

    Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China)

    2015-12-15

    Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.

  2. Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

    Science.gov (United States)

    Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto

    2016-12-01

    It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low

  3. Stochastic Boolean networks: An efficient approach to modeling gene regulatory networks

    Directory of Open Access Journals (Sweden)

    Liang Jinghang

    2012-08-01

    Full Text Available Abstract Background Various computational models have been of interest due to their use in the modelling of gene regulatory networks (GRNs. As a logical model, probabilistic Boolean networks (PBNs consider molecular and genetic noise, so the study of PBNs provides significant insights into the understanding of the dynamics of GRNs. This will ultimately lead to advances in developing therapeutic methods that intervene in the process of disease development and progression. The applications of PBNs, however, are hindered by the complexities involved in the computation of the state transition matrix and the steady-state distribution of a PBN. For a PBN with n genes and N Boolean networks, the complexity to compute the state transition matrix is O(nN22n or O(nN2n for a sparse matrix. Results This paper presents a novel implementation of PBNs based on the notions of stochastic logic and stochastic computation. This stochastic implementation of a PBN is referred to as a stochastic Boolean network (SBN. An SBN provides an accurate and efficient simulation of a PBN without and with random gene perturbation. The state transition matrix is computed in an SBN with a complexity of O(nL2n, where L is a factor related to the stochastic sequence length. Since the minimum sequence length required for obtaining an evaluation accuracy approximately increases in a polynomial order with the number of genes, n, and the number of Boolean networks, N, usually increases exponentially with n, L is typically smaller than N, especially in a network with a large number of genes. Hence, the computational efficiency of an SBN is primarily limited by the number of genes, but not directly by the total possible number of Boolean networks. Furthermore, a time-frame expanded SBN enables an efficient analysis of the steady-state distribution of a PBN. These findings are supported by the simulation results of a simplified p53 network, several randomly generated networks and a

  4. Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience

    Directory of Open Access Journals (Sweden)

    Yan Chen

    2017-01-01

    Full Text Available This paper considers a d-dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in d-dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts law; that is, the longer the time of a reaching movement, the higher the accuracy of arriving at the target position, and the results can be directly applied to designing a reaching movement performed by a robotic arm in a more general environment.

  5. Design and validation of a dynamic discrete event stochastic simulation model of mastitis control in dairy herds.

    Science.gov (United States)

    Allore, H G; Schruben, L W; Erb, H N; Oltenacu, P A

    1998-03-01

    A dynamic stochastic simulation model for discrete events, SIMMAST, was developed to simulate the effect of mastitis on the composition of the bulk tank milk of dairy herds. Intramammary infections caused by Streptococcus agalactiae, Streptococcus spp. other than Strep. agalactiae, Staphylococcus aureus, and coagulase-negative staphylococci were modeled as were the milk, fat, and protein test day solutions for individual cows, which accounted for the fixed effects of days in milk, age at calving, season of calving, somatic cell count (SCC), and random effects of test day, cow yield differences from herdmates, and autocorrelated errors. Probabilities for the transitions among various states of udder health (uninfected or subclinically or clinically infected) were calculated to account for exposure, heifer infection, spontaneous recovery, lactation cure, infection or cure during the dry period, month of lactation, parity, within-herd yields, and the number of quarters with clinical intramammary infection in the previous and current lactations. The stochastic simulation model was constructed using estimates from the literature and also using data from 164 herds enrolled with Quality Milk Promotion Services that each had bulk tank SCC between 500,000 and 750,000/ml. Model parameters and outputs were validated against a separate data file of 69 herds from the Northeast Dairy Herd Improvement Association, each with a bulk tank SCC that was > or = 500,000/ml. Sensitivity analysis was performed on all input parameters for control herds. Using the validated stochastic simulation model, the control herds had a stable time average bulk tank SCC between 500,000 and 750,000/ml.

  6. Frictions, Persistence, and Central Bank Policy in an Experimental Dynamic Stochastic General Equilibrium Economy

    NARCIS (Netherlands)

    Noussair, C.N.; Pfajfar, D.; Zsiros, J.

    2011-01-01

    New Keynesian dynamic stochastic general equilibrium models are the principal paradigm currently employed for central bank policymaking. In this paper, we construct experimental economies, populated with human subjects, with the structure of a New Keynesian DSGE model. We give individuals monetary

  7. A stochastic differential equation analysis of cerebrospinal fluid dynamics.

    Science.gov (United States)

    Raman, Kalyan

    2011-01-18

    Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

  8. Stochastic Still Water Response Model

    DEFF Research Database (Denmark)

    Friis-Hansen, Peter; Ditlevsen, Ove Dalager

    2002-01-01

    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 is...... out that an important parameter of the stochastic cargo field model is the mean number of containers delivered by each customer.......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...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...

  9. Molecular dynamics with deterministic and stochastic numerical methods

    CERN Document Server

    Leimkuhler, Ben

    2015-01-01

    This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications.  Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method...

  10. Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model

    Directory of Open Access Journals (Sweden)

    Akio Suzuki

    2011-09-01

    Full Text Available The dynamics of ventricular fibrillation (VF has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.

  11. A stochastic differential equation framework for the timewise dynamics of turbulent velocities

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen

    2008-01-01

    We discuss a stochastic differential equation as a modeling framework for the timewise dynamics of turbulent velocities. The equation is capable of capturing basic stylized facts of the statistics of temporal velocity increments. In particular, we focus on the evolution of the probability density...

  12. Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory

    Science.gov (United States)

    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.

  13. 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)

  14. Stochastic-field cavitation model

    International Nuclear Information System (INIS)

    Dumond, J.; Magagnato, F.; Class, A.

    2013-01-01

    Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations

  15. Stochastic-field cavitation model

    Science.gov (United States)

    Dumond, J.; Magagnato, F.; Class, A.

    2013-07-01

    Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

  16. 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......-space model formulation include the ability to provide estimates of exploitable biomass and fishing mortality at any point in time from data sampled at arbitrary and possibly irregular intervals. We show in a simulation that the ability to analyse subannual data can increase the effective sample size...

  17. Incorporating Daily Flood Control Objectives Into a Monthly Stochastic Dynamic Programing Model for a Hydroelectric Complex

    Science.gov (United States)

    Druce, Donald J.

    1990-01-01

    A monthly stochastic dynamic programing model was recently developed and implemented at British Columbia (B.C.) Hydro to provide decision support for short-term energy exports and, if necessary, for flood control on the Peace River in northern British Columbia. The model establishes the marginal cost of supplying energy from the B.C. Hydro system, as well as a monthly operating policy for the G.M. Shrum and Peace Canyon hydroelectric plants and the Williston Lake storage reservoir. A simulation model capable of following the operating policy then determines the probability of refilling Williston Lake and possible spill rates and volumes. Reservoir inflows are input to both models in daily and monthly formats. The results indicate that flood control can be accommodated without sacrificing significant export revenue.

  18. Incorporating daily flood control objectives into a monthly stochastic dynamic programming model for a hydroelectric complex

    Energy Technology Data Exchange (ETDEWEB)

    Druce, D.J. (British Columbia Hydro and Power Authority, Vancouver, British Columbia (Canada))

    1990-01-01

    A monthly stochastic dynamic programing model was recently developed and implemented at British Columbia (B.C.) Hydro to provide decision support for short-term energy exports and, if necessary, for flood control on the Peace River in northern British Columbia. The model established the marginal cost of supplying energy from the B.C. Hydro system, as well as a monthly operating policy for the G.M. Shrum and Peace Canyon hydroelectric plants and the Williston Lake storage reservoir. A simulation model capable of following the operating policy then determines the probability of refilling Williston Lake and possible spill rates and volumes. Reservoir inflows are input to both models in daily and monthly formats. The results indicate that flood control can be accommodated without sacrificing significant export revenue.

  19. Potential and flux field landscape theory. II. Non-equilibrium thermodynamics of spatially inhomogeneous stochastic dynamical systems

    International Nuclear Information System (INIS)

    Wu, Wei; Wang, Jin

    2014-01-01

    We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series

  20. Dynamic analysis of stochastic transcription cycles.

    Directory of Open Access Journals (Sweden)

    Claire V Harper

    2011-04-01

    Full Text Available In individual mammalian cells the expression of some genes such as prolactin is highly variable over time and has been suggested to occur in stochastic pulses. To investigate the origins of this behavior and to understand its functional relevance, we quantitatively analyzed this variability using new mathematical tools that allowed us to reconstruct dynamic transcription rates of different reporter genes controlled by identical promoters in the same living cell. Quantitative microscopic analysis of two reporter genes, firefly luciferase and destabilized EGFP, was used to analyze the dynamics of prolactin promoter-directed gene expression in living individual clonal and primary pituitary cells over periods of up to 25 h. We quantified the time-dependence and cyclicity of the transcription pulses and estimated the length and variation of active and inactive transcription phases. We showed an average cycle period of approximately 11 h and demonstrated that while the measured time distribution of active phases agreed with commonly accepted models of transcription, the inactive phases were differently distributed and showed strong memory, with a refractory period of transcriptional inactivation close to 3 h. Cycles in transcription occurred at two distinct prolactin-promoter controlled reporter genes in the same individual clonal or primary cells. However, the timing of the cycles was independent and out-of-phase. For the first time, we have analyzed transcription dynamics from two equivalent loci in real-time in single cells. In unstimulated conditions, cells showed independent transcription dynamics at each locus. A key result from these analyses was the evidence for a minimum refractory period in the inactive-phase of transcription. The response to acute signals and the result of manipulation of histone acetylation was consistent with the hypothesis that this refractory period corresponded to a phase of chromatin remodeling which significantly

  1. Stochastic E2F activation and reconciliation of phenomenological cell-cycle models.

    Science.gov (United States)

    Lee, Tae J; Yao, Guang; Bennett, Dorothy C; Nevins, Joseph R; You, Lingchong

    2010-09-21

    The transition of the mammalian cell from quiescence to proliferation is a highly variable process. Over the last four decades, two lines of apparently contradictory, phenomenological models have been proposed to account for such temporal variability. These include various forms of the transition probability (TP) model and the growth control (GC) model, which lack mechanistic details. The GC model was further proposed as an alternative explanation for the concept of the restriction point, which we recently demonstrated as being controlled by a bistable Rb-E2F switch. Here, through a combination of modeling and experiments, we show that these different lines of models in essence reflect different aspects of stochastic dynamics in cell cycle entry. In particular, we show that the variable activation of E2F can be described by stochastic activation of the bistable Rb-E2F switch, which in turn may account for the temporal variability in cell cycle entry. Moreover, we show that temporal dynamics of E2F activation can be recast into the frameworks of both the TP model and the GC model via parameter mapping. This mapping suggests that the two lines of phenomenological models can be reconciled through the stochastic dynamics of the Rb-E2F switch. It also suggests a potential utility of the TP or GC models in defining concise, quantitative phenotypes of cell physiology. This may have implications in classifying cell types or states.

  2. Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

    Science.gov (United States)

    Wang, Ting; Plecháč, Petr

    2017-12-01

    Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed.

  3. Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis.

    Science.gov (United States)

    Wang, Ting; Plecháč, Petr

    2017-12-21

    Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed.

  4. A stochastic spatial model of HIV dynamics with an asymmetric battle between the virus and the immune system

    International Nuclear Information System (INIS)

    Lin Hai; Shuai, J W

    2010-01-01

    A stochastic spatial model based on the Monte Carlo approach is developed to study the dynamics of human immunodeficiency virus (HIV) infection. We aim to propose a more detailed and realistic simulation frame by incorporating many important features of HIV dynamics, which include infections, replications and mutations of viruses, antigen recognitions, activations and proliferations of lymphocytes, and diffusions, encounters and interactions of virions and lymphocytes. Our model successfully reproduces the three-phase pattern observed in HIV infection, and the simulation results for the time distribution from infection to AIDS onset are also in good agreement with the clinical data. The interactions of viruses and the immune system in all the three phases are investigated. We assess the relative importance of various immune system components in the acute phase. The dynamics of how the two important factors, namely the viral diversity and the asymmetric battle between HIV and the immune system, result in AIDS are investigated in detail with the model.

  5. Bayesian inference for hybrid discrete-continuous stochastic kinetic models

    International Nuclear Information System (INIS)

    Sherlock, Chris; Golightly, Andrew; Gillespie, Colin S

    2014-01-01

    We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model. (paper)

  6. Further Results on Dynamic Additive Hazard Rate Model

    Directory of Open Access Journals (Sweden)

    Zhengcheng Zhang

    2014-01-01

    Full Text Available In the past, the proportional and additive hazard rate models have been investigated in the works. Nanda and Das (2011 introduced and studied the dynamic proportional (reversed hazard rate model. In this paper we study the dynamic additive hazard rate model, and investigate its aging properties for different aging classes. The closure of the model under some stochastic orders has also been investigated. Some examples are also given to illustrate different aging properties and stochastic comparisons of the model.

  7. Stochastic population dynamics of a montane ground-dwelling squirrel.

    Science.gov (United States)

    Hostetler, Jeffrey A; Kneip, Eva; Van Vuren, Dirk H; Oli, Madan K

    2012-01-01

    Understanding the causes and consequences of population fluctuations is a central goal of ecology. We used demographic data from a long-term (1990-2008) study and matrix population models to investigate factors and processes influencing the dynamics and persistence of a golden-mantled ground squirrel (Callospermophilus lateralis) population, inhabiting a dynamic subalpine habitat in Colorado, USA. The overall deterministic population growth rate λ was 0.94±SE 0.05 but it varied widely over time, ranging from 0.45±0.09 in 2006 to 1.50±0.12 in 2003, and was below replacement (λbounce back from low densities and prevented extinction. These results suggest that dynamics and persistence of our study population are determined synergistically by density-dependence, stochastic forces, and immigration.

  8. The Dynamic Programming Method of Stochastic Differential Game for Functional Forward-Backward Stochastic System

    Directory of Open Access Journals (Sweden)

    Shaolin Ji

    2013-01-01

    Full Text Available This paper is devoted to a stochastic differential game (SDG of decoupled functional forward-backward stochastic differential equation (FBSDE. For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs. Applying the Girsanov transformation method introduced by Buckdahn and Li (2008, the upper and the lower value functions are shown to be deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI equations to the path-dependent ones. By establishing the dynamic programming principal (DPP, we derive that the upper and the lower value functions are the viscosity solutions of the corresponding upper and the lower path-dependent HJBI equations, respectively.

  9. Inexact Multistage Stochastic Chance Constrained Programming Model for Water Resources Management under Uncertainties

    Directory of Open Access Journals (Sweden)

    Hong Zhang

    2017-01-01

    Full Text Available In order to formulate water allocation schemes under uncertainties in the water resources management systems, an inexact multistage stochastic chance constrained programming (IMSCCP model is proposed. The model integrates stochastic chance constrained programming, multistage stochastic programming, and inexact stochastic programming within a general optimization framework to handle the uncertainties occurring in both constraints and objective. These uncertainties are expressed as probability distributions, interval with multiply distributed stochastic boundaries, dynamic features of the long-term water allocation plans, and so on. Compared with the existing inexact multistage stochastic programming, the IMSCCP can be used to assess more system risks and handle more complicated uncertainties in water resources management systems. The IMSCCP model is applied to a hypothetical case study of water resources management. In order to construct an approximate solution for the model, a hybrid algorithm, which incorporates stochastic simulation, back propagation neural network, and genetic algorithm, is proposed. The results show that the optimal value represents the maximal net system benefit achieved with a given confidence level under chance constraints, and the solutions provide optimal water allocation schemes to multiple users over a multiperiod planning horizon.

  10. Models of the stochastic activity of neurones

    CERN Document Server

    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...

  11. Stochastic modelling of avascular tumour growth and therapy

    International Nuclear Information System (INIS)

    Sahoo, S; Sahoo, A; Shearer, S F C

    2011-01-01

    In this paper, a generalized stochastic model for the growth of avascular tumours is presented. This model captures the dynamical evolution of avascular tumour cell subpopulations by incorporating Gaussian white noise into the growth rate of the mitotic function. This work generalizes the deterministic model proposed by Sherratt and Chaplain (2001 J. Math. Biol. 43 291) where they formulated a tumour model in an in vivo setting, in terms of continuum densities of proliferating, quiescent and necrotic cells. Detailed simulations of our model show that the inclusion of Gaussian noise in the original model of Sherratt and Chaplain substantially distorts the overall structure of the density profiles in addition to reducing the speed of tumour growth. Within this stochastic carcinogenesis framework the action of therapy is also investigated by replacing Gaussian white noise with a therapy term. We compare a constant therapy protocol with a logarithmic time-dependent protocol. Our results predict that a logarithmic therapy is more effective than the constant therapy protocol.

  12. Dynamic analysis of a stochastic delayed rumor propagation model

    Science.gov (United States)

    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.

  13. Deterministic and stochastic models for middle east respiratory syndrome (MERS)

    Science.gov (United States)

    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.

  14. A stochastic differential equation analysis of cerebrospinal fluid dynamics

    Directory of Open Access Journals (Sweden)

    Raman Kalyan

    2011-01-01

    Full Text Available Abstract Background Clinical measurements of intracranial pressure (ICP over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. Methods The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE that accommodates the fluctuations in ICP. Results The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Conclusions Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

  15. Discriminating chaotic and stochastic dynamics through the permutation spectrum test

    Energy Technology Data Exchange (ETDEWEB)

    Kulp, C. W., E-mail: Kulp@lycoming.edu [Department of Astronomy and Physics, Lycoming College, Williamsport, Pennsylvania 17701 (United States); Zunino, L., E-mail: lucianoz@ciop.unlp.edu.ar [Centro de Investigaciones Ópticas (CONICET La Plata—CIC), C.C. 3, 1897 Gonnet (Argentina); Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata (Argentina)

    2014-09-01

    In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism.

  16. Stochastic dynamics of dengue epidemics.

    Science.gov (United States)

    de Souza, David R; Tomé, Tânia; Pinho, Suani T R; Barreto, Florisneide R; de Oliveira, Mário J

    2013-01-01

    We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice versa, so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible, for any death rate of infected mosquitoes.

  17. Alternative Asymmetric Stochastic Volatility Models

    NARCIS (Netherlands)

    M. Asai (Manabu); M.J. McAleer (Michael)

    2010-01-01

    textabstractThe stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is

  18. The dynamics of stochastic processes

    DEFF Research Database (Denmark)

    Basse-O'Connor, Andreas

    In the present thesis the dynamics of stochastic processes is studied with a special attention to the semimartingale property. This is mainly motivated by the fact that semimartingales provide the class of the processes for which it is possible to define a reasonable stochastic calculus due...... to the Bichteler-Dellacherie Theorem. The semimartingale property of Gaussian processes is characterized in terms of their covariance function, spectral measure and spectral representation. In addition, representation and expansion of filtration results are provided as well. Special attention is given to moving...... average processes, and when the driving process is a Lévy or a chaos process the semimartingale property is characterized in the filtration spanned by the driving process and in the natural filtration when the latter is a Brownian motion. To obtain some of the above results an integrability of seminorm...

  19. Stochastic models for structured populations scaling limits and long time behavior

    CERN Document Server

    Meleard, Sylvie

    2015-01-01

    In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading  to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of  environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured P...

  20. The stochastic system approach for estimating dynamic treatments effect.

    Science.gov (United States)

    Commenges, Daniel; Gégout-Petit, Anne

    2015-10-01

    The problem of assessing the effect of a treatment on a marker in observational studies raises the difficulty that attribution of the treatment may depend on the observed marker values. As an example, we focus on the analysis of the effect of a HAART on CD4 counts, where attribution of the treatment may depend on the observed marker values. This problem has been treated using marginal structural models relying on the counterfactual/potential response formalism. Another approach to causality is based on dynamical models, and causal influence has been formalized in the framework of the Doob-Meyer decomposition of stochastic processes. Causal inference however needs assumptions that we detail in this paper and we call this approach to causality the "stochastic system" approach. First we treat this problem in discrete time, then in continuous time. This approach allows incorporating biological knowledge naturally. When working in continuous time, the mechanistic approach involves distinguishing the model for the system and the model for the observations. Indeed, biological systems live in continuous time, and mechanisms can be expressed in the form of a system of differential equations, while observations are taken at discrete times. Inference in mechanistic models is challenging, particularly from a numerical point of view, but these models can yield much richer and reliable results.

  1. The threshold of a stochastic delayed SIR epidemic model with vaccination

    Science.gov (United States)

    Liu, Qun; Jiang, Daqing

    2016-11-01

    In this paper, we study the threshold dynamics of a stochastic delayed SIR epidemic model with vaccination. We obtain sufficient conditions for extinction and persistence in the mean of the epidemic. The threshold between persistence in the mean and extinction of the stochastic system is also obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number Rbar0 of the deterministic system. Results show that time delay has important effects on the persistence and extinction of the epidemic.

  2. A Non-linear Stochastic Model for an Office Building with Air Infiltration

    DEFF Research Database (Denmark)

    Thavlov, Anders; Madsen, Henrik

    2015-01-01

    This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model...

  3. Stochastic dynamical model of a growing citation network based on a self-exciting point process.

    Science.gov (United States)

    Golosovsky, Michael; Solomon, Sorin

    2012-08-31

    We put under experimental scrutiny the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose a citation network of physics papers and traced the citation history of 40,195 papers published in one year. Contrary to common belief, we find that the citation dynamics of the individual papers follows the superlinear preferential attachment, with the exponent α=1.25-1.3. Moreover, we show that the citation process cannot be described as a memoryless Markov chain since there is a substantial correlation between the present and recent citation rates of a paper. Based on our findings we construct a stochastic growth model of the citation network, perform numerical simulations based on this model and achieve an excellent agreement with the measured citation distributions.

  4. Stochasticity Modeling in Memristors

    KAUST Repository

    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.

  5. Stochasticity Modeling in Memristors

    KAUST Repository

    Naous, Rawan; Al-Shedivat, Maruan; Salama, Khaled N.

    2015-01-01

    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.

  6. Markov stochasticity coordinates

    International Nuclear Information System (INIS)

    Eliazar, Iddo

    2017-01-01

    Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

  7. Markov stochasticity coordinates

    Energy Technology Data Exchange (ETDEWEB)

    Eliazar, Iddo, E-mail: iddo.eliazar@intel.com

    2017-01-15

    Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

  8. Modelling Evolutionary Algorithms with Stochastic Differential Equations.

    Science.gov (United States)

    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.

  9. Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

    Science.gov (United States)

    Cotter, C J; Gottwald, G A; Holm, D D

    2017-09-01

    In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

  10. Spatial effect on stochastic dynamics of bistable evolutionary games

    International Nuclear Information System (INIS)

    So, Kohaku H Z; Ohtsuki, Hisashi; Kato, Takeo

    2014-01-01

    We consider the lifetimes of metastable states in bistable evolutionary games (coordination games), and examine how they are affected by spatial structure. A semiclassical approximation based on a path integral method is applied to stochastic evolutionary game dynamics with and without spatial structure, and the lifetimes of the metastable states are evaluated. It is shown that the population dependence of the lifetimes is qualitatively different in these two models. Our result indicates that spatial structure can accelerate the transitions between metastable states. (paper)

  11. Nonperturbative stochastic dynamics driven by strongly correlated colored noise

    Science.gov (United States)

    Jing, Jun; Li, Rui; You, J. Q.; Yu, Ting

    2015-02-01

    We propose a quantum model consisting of two remote qubits interacting with two correlated colored noises and establish an exact stochastic Schrödinger equation for this open quantum system. It is shown that the quantum dynamics of the qubit system is profoundly modulated by the mutual correlation between baths and the bath memory capability through dissipation and fluctuation. We report a physical effect on generating inner correlation and entanglement of two distant qubits arising from the strong bath-bath correlation.

  12. Backward-stochastic-differential-equation approach to modeling of gene expression.

    Science.gov (United States)

    Shamarova, Evelina; Chertovskih, Roman; Ramos, Alexandre F; Aguiar, Paulo

    2017-03-01

    In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of end-point ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein-level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time-reversed simulations, allowing, for example, the assessment of the biological conditions (e.g., protein concentrations) that preceded an experimentally measured event of interest (e.g., mitosis, apoptosis, etc.).

  13. Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods

    Directory of Open Access Journals (Sweden)

    Tetsuya Misawa

    2010-01-01

    Full Text Available “Symplectic” schemes for stochastic Hamiltonian dynamical systems are formulated through “composition methods (or operator splitting methods” proposed by Misawa (2001. In the proposed methods, a symplectic map, which is given by the solution of a stochastic Hamiltonian system, is approximated by composition of the stochastic flows derived from simpler Hamiltonian vector fields. The global error orders of the numerical schemes derived from the stochastic composition methods are provided. To examine the superiority of the new schemes, some illustrative numerical simulations on the basis of the proposed schemes are carried out for a stochastic harmonic oscillator system.

  14. A stochastic model of nanoparticle self-assembly on Cayley trees

    International Nuclear Information System (INIS)

    Mazilu, I; Schwen, E M; Banks, W E; Pope, B K; Mazilu, D A

    2015-01-01

    Nanomedicine is an emerging area of medical research that uses innovative nanotechnologies to improve the delivery of therapeutic and diagnostic agents with maximum clinical benefit. We present a versatile stochastic model that can be used to capture the basic features of drug encapsulation of nanoparticles on tree-like synthetic polymers called dendrimers. The geometry of a dendrimer is described mathematically as a Cayley tree. We use our stochastic model to study the dynamics of deposition and release of monomers (simulating the drug molecules) on Cayley trees (simulating dendrimers). We present analytical and Monte Carlo simulation results for the particle density on Cayley trees of coordination number three and four

  15. Discrete-State Stochastic Models of Calcium-Regulated Calcium Influx and Subspace Dynamics Are Not Well-Approximated by ODEs That Neglect Concentration Fluctuations

    Science.gov (United States)

    Weinberg, Seth H.; Smith, Gregory D.

    2012-01-01

    Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers. PMID:23509597

  16. Nonlinear and Stochastic Dynamics in the Heart

    Science.gov (United States)

    Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.

    2014-01-01

    In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems. PMID:25267872

  17. Nonlinear and stochastic dynamics in the heart

    Energy Technology Data Exchange (ETDEWEB)

    Qu, Zhilin, E-mail: zqu@mednet.ucla.edu [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Hu, Gang [Department of Physics, Beijing Normal University, Beijing 100875 (China); Garfinkel, Alan [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Integrative Biology and Physiology, University of California, Los Angeles, CA 90095 (United States); Weiss, James N. [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States)

    2014-10-10

    In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

  18. Nonlinear and stochastic dynamics in the heart

    International Nuclear Information System (INIS)

    Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.

    2014-01-01

    In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems

  19. 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.

  20. Information Dynamics of a Nonlinear Stochastic Nanopore System

    Directory of Open Access Journals (Sweden)

    Claire Gilpin

    2018-03-01

    Full Text Available Nanopores have become a subject of interest in the scientific community due to their potential uses in nanometer-scale laboratory and research applications, including infectious disease diagnostics and DNA sequencing. Additionally, they display behavioral similarity to molecular and cellular scale physiological processes. Recent advances in information theory have made it possible to probe the information dynamics of nonlinear stochastic dynamical systems, such as autonomously fluctuating nanopore systems, which has enhanced our understanding of the physical systems they model. We present the results of local (LER and specific entropy rate (SER computations from a simulation study of an autonomously fluctuating nanopore system. We learn that both metrics show increases that correspond to fluctuations in the nanopore current, indicating fundamental changes in information generation surrounding these fluctuations.

  1. Quantifying the contribution of chromatin dynamics to stochastic gene expression reveals long, locus-dependent periods between transcriptional bursts.

    Science.gov (United States)

    Viñuelas, José; Kaneko, Gaël; Coulon, Antoine; Vallin, Elodie; Morin, Valérie; Mejia-Pous, Camila; Kupiec, Jean-Jacques; Beslon, Guillaume; Gandrillon, Olivier

    2013-02-25

    A number of studies have established that stochasticity in gene expression may play an important role in many biological phenomena. This therefore calls for further investigations to identify the molecular mechanisms at stake, in order to understand and manipulate cell-to-cell variability. In this work, we explored the role played by chromatin dynamics in the regulation of stochastic gene expression in higher eukaryotic cells. For this purpose, we generated isogenic chicken-cell populations expressing a fluorescent reporter integrated in one copy per clone. Although the clones differed only in the genetic locus at which the reporter was inserted, they showed markedly different fluorescence distributions, revealing different levels of stochastic gene expression. Use of chromatin-modifying agents showed that direct manipulation of chromatin dynamics had a marked effect on the extent of stochastic gene expression. To better understand the molecular mechanism involved in these phenomena, we fitted these data to a two-state model describing the opening/closing process of the chromatin. We found that the differences between clones seemed to be due mainly to the duration of the closed state, and that the agents we used mainly seem to act on the opening probability. In this study, we report biological experiments combined with computational modeling, highlighting the importance of chromatin dynamics in stochastic gene expression. This work sheds a new light on the mechanisms of gene expression in higher eukaryotic cells, and argues in favor of relatively slow dynamics with long (hours to days) periods of quiet state.

  2. Quantization of dynamical systems and stochastic control theory

    International Nuclear Information System (INIS)

    Guerra, F.; Morato, L.M.

    1982-09-01

    In the general framework of stochastic control theory we introduce a suitable form of stochastic action associated to the controlled process. Then a variational principle gives all main features of Nelson's stochastic mechanics. In particular we derive the expression of the current velocity field as the gradient of the phase action. Moreover the stochastic corrections to the Hamilton-Jacobi equation are in agreement with the quantum mechanical form of the Madelung fluid (equivalent to the Schroedinger equation). Therefore stochastic control theory can provide a very simple model simulating quantum mechanical behavior

  3. 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.

  4. Levy-Student processes for a stochastic model of beam halos

    Energy Technology Data Exchange (ETDEWEB)

    Petroni, N. Cufaro [Department of Mathematics, University of Bari, and INFN Sezione di Bari, via E. Orabona 4, 70125 Bari (Italy)]. E-mail: cufaro@ba.infn.it; De Martino, S. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy); De Siena, S. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy); Illuminati, F. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy)

    2006-06-01

    We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the stochastic mechanics which produces time reversal invariant diffusion processes. In this paper we analyze the consequences of introducing the generalized Student laws, namely non-Gaussian, Levy infinitely divisible (but not stable) distributions. We will analyze this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) stochastic model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Levy process whose increments are Student distributed. In the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the Levy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.

  5. Levy-Student processes for a stochastic model of beam halos

    International Nuclear Information System (INIS)

    Petroni, N. Cufaro; De Martino, S.; De Siena, S.; Illuminati, F.

    2006-01-01

    We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the stochastic mechanics which produces time reversal invariant diffusion processes. In this paper we analyze the consequences of introducing the generalized Student laws, namely non-Gaussian, Levy infinitely divisible (but not stable) distributions. We will analyze this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) stochastic model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Levy process whose increments are Student distributed. In the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the Levy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams

  6. An introduction to continuous-time stochastic processes theory, models, and applications to finance, biology, and medicine

    CERN Document Server

    Capasso, Vincenzo

    2015-01-01

    This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: * Markov processes * Stochastic differential equations * Arbitrage-free markets and financial derivatives * Insurance risk * Population dynamics, and epidemics * Agent-based models New to the Third Edition: * Infinitely divisible distributions * Random measures * Levy processes * Fractional Brownian motion * Ergodic theory * Karhunen-Loeve expansion * Additional applications * Additional  exercises * Smoluchowski  approximation of  Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Editio...

  7. Stochastic linear hybrid systems: Modeling, estimation, and application

    Science.gov (United States)

    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

  8. Bayesian estimation and entropy for economic dynamic stochastic models: An exploration of overconsumption

    International Nuclear Information System (INIS)

    Argentiero, Amedeo; Bovi, Maurizio; Cerqueti, Roy

    2016-01-01

    This paper examines psycho-induced overconsumption in a dynamic stochastic context. As emphasized by well-established psychological results, these psycho-distortions derive from a decision making based on simple rules-of-thumb, not on analytically sounded optimizations. To our end, we therefore compare two New Keynesian models. The first is populated by optimizing Muth-rational agents and acts as the normative benchmark. The other is a “psycho-perturbed” version of the benchmark that allows for the potential presence of overoptimism and, hence, of overconsumption. The parameters of these models are estimated through a Bayesian-type procedure, and performances are evaluated by employing an entropy measure. Such methodologies are particularly appropriate here since they take in full consideration the complexity generated by the randomness of the considered systems. In particular, they let to derive a not negligible information on the size and on the cyclical properties of the biases. In line with cognitive psychology suggestions our evidence shows that the overoptimism/overconsumption is: widespread—it is detected in nation-wide data; persistent—it emerges in full-sample estimations; it moves according to the expected cyclical behavior—larger in booms, and it disappears in crises. Moreover, by taking into account the effect of these psycho-biases, the model fits actual data better than the benchmark. All considered, then, enhancing the existing literature our findings: i) sustain the importance of inserting psychological distortions in macroeconomic models and ii) underline that system dynamics and psycho biases have statistically significant and economically important connections.

  9. Stochastic dynamics of genetic broadcasting networks

    Science.gov (United States)

    Potoyan, Davit A.; Wolynes, Peter G.

    2017-11-01

    The complex genetic programs of eukaryotic cells are often regulated by key transcription factors occupying or clearing out of a large number of genomic locations. Orchestrating the residence times of these factors is therefore important for the well organized functioning of a large network. The classic models of genetic switches sidestep this timing issue by assuming the binding of transcription factors to be governed entirely by thermodynamic protein-DNA affinities. Here we show that relying on passive thermodynamics and random release times can lead to a "time-scale crisis" for master genes that broadcast their signals to a large number of binding sites. We demonstrate that this time-scale crisis for clearance in a large broadcasting network can be resolved by actively regulating residence times through molecular stripping. We illustrate these ideas by studying a model of the stochastic dynamics of the genetic network of the central eukaryotic master regulator NFκ B which broadcasts its signals to many downstream genes that regulate immune response, apoptosis, etc.

  10. Measures of thermodynamic irreversibility in deterministic and stochastic dynamics

    International Nuclear Information System (INIS)

    Ford, Ian J

    2015-01-01

    It is generally observed that if a dynamical system is sufficiently complex, then as time progresses it will share out energy and other properties amongst its component parts to eliminate any initial imbalances, retaining only fluctuations. This is known as energy dissipation and it is closely associated with the concept of thermodynamic irreversibility, measured by the increase in entropy according to the second law. It is of interest to quantify such behaviour from a dynamical rather than a thermodynamic perspective and to this end stochastic entropy production and the time-integrated dissipation function have been introduced as analogous measures of irreversibility, principally for stochastic and deterministic dynamics, respectively. We seek to compare these measures. First we modify the dissipation function to allow it to measure irreversibility in situations where the initial probability density function (pdf) of the system is asymmetric as well as symmetric in velocity. We propose that it tests for failure of what we call the obversibility of the system, to be contrasted with reversibility, the failure of which is assessed by stochastic entropy production. We note that the essential difference between stochastic entropy production and the time-integrated modified dissipation function lies in the sequence of procedures undertaken in the associated tests of irreversibility. We argue that an assumed symmetry of the initial pdf with respect to velocity inversion (within a framework of deterministic dynamics) can be incompatible with the Past Hypothesis, according to which there should be a statistical distinction between the behaviour of certain properties of an isolated system as it evolves into the far future and the remote past. Imposing symmetry on a velocity distribution is acceptable for many applications of statistical physics, but can introduce difficulties when discussing irreversible behaviour. (paper)

  11. Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model

    Energy Technology Data Exchange (ETDEWEB)

    Donnelly, Catherine, E-mail: C.Donnelly@hw.ac.uk [Heriot-Watt University, Department of Actuarial Mathematics and Statistics (United Kingdom)

    2011-10-15

    We prove a sufficient stochastic maximum principle for the optimal control of a regime-switching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be used to solve a mean-variance portfolio selection problem.

  12. Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model

    International Nuclear Information System (INIS)

    Donnelly, Catherine

    2011-01-01

    We prove a sufficient stochastic maximum principle for the optimal control of a regime-switching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be used to solve a mean-variance portfolio selection problem.

  13. 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...

  14. Improved ensemble-mean forecast skills of ENSO events by a zero-mean stochastic model-error model of an intermediate coupled model

    Science.gov (United States)

    Zheng, F.; Zhu, J.

    2015-12-01

    To perform an ensemble-based ENSO probabilistic forecast, the crucial issue is to design a reliable ensemble prediction strategy that should include the major uncertainties of a forecast system. In this study, we developed a new general ensemble perturbation technique to improve the ensemble-mean predictive skill of forecasting ENSO using an intermediate coupled model (ICM). The model uncertainties are first estimated and analyzed from EnKF analysis results through assimilating observed SST. Then, based on the pre-analyzed properties of the model errors, a zero-mean stochastic model-error model is developed to mainly represent the model uncertainties induced by some important physical processes missed in the coupled model (i.e., stochastic atmospheric forcing/MJO, extra-tropical cooling and warming, Indian Ocean Dipole mode, etc.). Each member of an ensemble forecast is perturbed by the stochastic model-error model at each step during the 12-month forecast process, and the stochastical perturbations are added into the modeled physical fields to mimic the presence of these high-frequency stochastic noises and model biases and their effect on the predictability of the coupled system. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr retrospective forecast experiments. The two forecast schemes are differentiated by whether they considered the model stochastic perturbations, with both initialized by the ensemble-mean analysis states from EnKF. The comparison results suggest that the stochastic model-error perturbations have significant and positive impacts on improving the ensemble-mean prediction skills during the entire 12-month forecast process. Because the nonlinear feature of the coupled model can induce the nonlinear growth of the added stochastic model errors with model integration, especially through the nonlinear heating mechanism with the vertical advection term of the model, the

  15. Stochastic dynamics for reinfection by transmitted diseases

    Science.gov (United States)

    Barros, Alessandro S.; Pinho, Suani T. R.

    2017-06-01

    The use of stochastic models to study the dynamics of infectious diseases is an important tool to understand the epidemiological process. For several directly transmitted diseases, reinfection is a relevant process, which can be expressed by endogenous reactivation of the pathogen or by exogenous reinfection due to direct contact with an infected individual (with smaller reinfection rate σ β than infection rate β ). In this paper, we examine the stochastic susceptible, infected, recovered, infected (SIRI) model simulating the endogenous reactivation by a spontaneous reaction, while exogenous reinfection by a catalytic reaction. Analyzing the mean-field approximations of a site and pairs of sites, and Monte Carlo (MC) simulations for the particular case of exogenous reinfection, we obtained continuous phase transitions involving endemic, epidemic, and no transmission phases for the simple approach; the approach of pairs is better to describe the phase transition from endemic phase (susceptible, infected, susceptible (SIS)-like model) to epidemic phase (susceptible, infected, and removed or recovered (SIR)-like model) considering the comparison with MC results; the reinfection increases the peaks of outbreaks until the system reaches endemic phase. For the particular case of endogenous reactivation, the approach of pairs leads to a continuous phase transition from endemic phase (SIS-like model) to no transmission phase. Finally, there is no phase transition when both effects are taken into account. We hope the results of this study can be generalized for the susceptible, exposed, infected, and removed or recovered (SEIRIE) model, for which the state exposed (infected but not infectious), describing more realistically transmitted diseases such as tuberculosis. In future work, we also intend to investigate the effect of network topology on phase transitions when the SIRI model describes both transmitted diseases (σ social contagions (σ >1 ).

  16. Dynamics of a stochastic delayed SIR epidemic model with vaccination and double diseases driven by Lévy jumps

    Science.gov (United States)

    Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar

    2018-02-01

    In this paper, we study the dynamics of a stochastic delayed SIR epidemic model with vaccination and double diseases which make the research more complex. The environment variability in this paper is characterized by white noise and Lévy noise. We establish sufficient conditions for extinction and persistence in the mean of the two epidemic diseases. It is shown that: (i) time delay and Lévy noise have important effects on the persistence and extinction of epidemic diseases; (ii) two diseases can coexist under certain conditions.

  17. The stochastic resonance for the incidence function model of metapopulation

    Science.gov (United States)

    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.

  18. Stochastic diffusion models for substitutable technological innovations

    NARCIS (Netherlands)

    Wang, L.; Hu, B.; Yu, X.

    2004-01-01

    Based on the analysis of firms' stochastic adoption behaviour, this paper first points out the necessity to build more practical stochastic models. And then, stochastic evolutionary models are built for substitutable innovation diffusion system. Finally, through the computer simulation of the

  19. 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...

  20. The Stochastic Dynamics for Ecological Tourism System with Visitor Educational Intervention

    Directory of Open Access Journals (Sweden)

    Dongping Wei

    2013-01-01

    Full Text Available The ever-increasing visitation in parks and protected areas continues to present a considerable challenge for worldwide land managers with allowing recreational use while preserving natural conditions. In China, the fast expanding visitation in protected areas is quickly damaging the natural resources and precious culture without effective visitor education, while regulation and site management are also gaining very limited efficacy. We propose a differential equation to describe the ecological tourism system. Shown by the theoretical proof and numerical simulation, the ecological tourism system is unstable without any perturbed factors, especially visitor educational intervention, because the solution of the dynamic system explodes in a finite time given any initial value. Supposing that the intrinsic increasing rate of stakeholders in the systems stochastically perturbed by the visitor educational intervention, we discover that the stochastic dynamic model can effectively suppress the explosion of the solution. As such, we demonstrate that the tourism system can develop steadily and safely even under a large amount of visitors in public vacation, when employing continuous visitor education intervention programmes.

  1. Intimate Partner Violence: A Stochastic Model.

    Science.gov (United States)

    Guidi, Elisa; Meringolo, Patrizia; Guazzini, Andrea; Bagnoli, Franco

    2017-01-01

    Intimate partner violence (IPV) has been a well-studied problem in the past psychological literature, especially through its classical methodology such as qualitative, quantitative and mixed methods. This article introduces two basic stochastic models as an alternative approach to simulate the short and long-term dynamics of a couple at risk of IPV. In both models, the members of the couple may assume a finite number of states, updating them in a probabilistic way at discrete time steps. After defining the transition probabilities, we first analyze the evolution of the couple in isolation and then we consider the case in which the individuals modify their behavior depending on the perceived violence from other couples in their environment or based on the perceived informal social support. While high perceived violence in other couples may converge toward the own presence of IPV by means a gender-specific transmission, the gender differences fade-out in the case of received informal social support. Despite the simplicity of the two stochastic models, they generate results which compare well with past experimental studies about IPV and they give important practical implications for prevention intervention in this field. Copyright: © 2016 by Fabrizio Serra editore, Pisa · Roma.

  2. Stochastic Effects; Application in Nuclear Physics

    International Nuclear Information System (INIS)

    Mazonka, O.

    2000-04-01

    Stochastic effects in nuclear physics refer to the study of the dynamics of nuclear systems evolving under stochastic equations of motion. In this dissertation we restrict our attention to classical scattering models. We begin with introduction of the model of nuclear dynamics and deterministic equations of evolution. We apply a Langevin approach - an additional property of the model, which reflect the statistical nature of low energy nuclear behaviour. We than concentrate our attention on the problem of calculating tails of distribution functions, which actually is the problem of calculating probabilities of rare outcomes. Two general strategies are proposed. Result and discussion follow. Finally in the appendix we consider stochastic effects in nonequilibrium systems. A few exactly solvable models are presented. For one model we show explicitly that stochastic behaviour in a microscopic description can lead to ordered collective effects on the macroscopic scale. Two others are solved to confirm the predictions of the fluctuation theorem. (author)

  3. Interactive macroeconomics stochastic aggregate dynamics with heterogeneous and interacting agents

    CERN Document Server

    Di Guilmi, Corrado

    2017-01-01

    One of the major problems of macroeconomic theory is the way in which the people exchange goods in decentralized market economies. There are major disagreements among macroeconomists regarding tools to influence required outcomes. Since the mainstream efficient market theory fails to provide an internal coherent framework, there is a need for an alternative theory. The book provides an innovative approach for the analysis of agent based models, populated by the heterogeneous and interacting agents in the field of financial fragility. The text is divided in two parts; the first presents analytical developments of stochastic aggregation and macro-dynamics inference methods. The second part introduces macroeconomic models of financial fragility for complex systems populated by heterogeneous and interacting agents. The concepts of financial fragility and macroeconomic dynamics are explained in detail in separate chapters. The statistical physics approach is applied to explain theories of macroeconomic modelling a...

  4. 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.

  5. Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

    Science.gov (United States)

    Zhang, Wei; Wang, Jun

    2018-05-01

    A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.

  6. Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics

    Science.gov (United States)

    Barthel, Thomas; De Bacco, Caterina; Franz, Silvio

    2018-01-01

    We introduce and apply an efficient method for the precise simulation of stochastic dynamical processes on locally treelike graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, our approach is based on a matrix product approximation of the so-called edge messages—conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both single instances as well as the thermodynamic limit. We employ it to examine prototypical nonequilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

  7. Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture

    Science.gov (United States)

    Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong

    The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.

  8. Stochastic Models of Plant Diversity: Application to White Sands Missile Range

    Science.gov (United States)

    2000-02-01

    decades and its models have been well developed. These models fall in the categories: dynamic models and stochastic models. In their book , Modeling...Gelb 1974), and dendro- climatology (Visser and Molenaar 1988). Optimal Estimation An optimal estimator is a computational algorithm that...Evaluation, M.B. Usher, ed., Chapman and Hall, London. Visser, H., and J. Molenaar . 1990. "Estimating Trends in Tree-ring Data." For. Sei. 36(1): 87

  9. Toward Development of a Stochastic Wake Model: Validation Using LES and Turbine Loads

    Directory of Open Access Journals (Sweden)

    Jae Sang Moon

    2017-12-01

    Full Text Available Wind turbines within an array do not experience free-stream undisturbed flow fields. Rather, the flow fields on internal turbines are influenced by wakes generated by upwind unit and exhibit different dynamic characteristics relative to the free stream. The International Electrotechnical Commission (IEC standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the development of a stochastic model for waked wind fields. First, high-fidelity physics-based waked wind velocity fields are generated using Large-Eddy Simulation (LES. Stochastic characteristics of these LES waked wind velocity field, including mean and turbulence components, are analyzed. Wake-related mean and turbulence field-related parameters are then estimated for use with a stochastic model, using Multivariate Multiple Linear Regression (MMLR with the LES data. To validate the simulated wind fields based on the stochastic model, wind turbine tower and blade loads are generated using aeroelastic simulation for utility-scale wind turbine models and compared with those based directly on the LES inflow. The study’s overall objective is to offer efficient and validated stochastic approaches that are computationally tractable for assessing the performance and loads of turbines operating in wakes.

  10. Stochastic Parametrisations and Regime Behaviour of Atmospheric Models

    Science.gov (United States)

    Arnold, Hannah; Moroz, Irene; Palmer, Tim

    2013-04-01

    -18, Shinfield Park, Reading, 1996. ECMWF. E. N. Lorenz. Regimes in simple systems. J. Atmos. Sci., 63(8):2056-2073, 2006. T. N Palmer. A nonlinear dynamical perspective on model error: A proposal for non-local stochastic-dynamic parametrisation in weather and climate prediction models. Q. J. Roy. Meteor. Soc., 127(572):279-304, 2001. T. N. Palmer, R. Buizza, F. Doblas-Reyes, T. Jung, M. Leutbecher, G. J. Shutts, M. Steinheimer, and A. Weisheimer. Stochastic parametrization and model uncertainty. Technical Report 598, European Centre for Medium-Range Weather Forecasts, 2009. J. Rougier, D. M. H. Sexton, J. M. Murphy, and D. Stainforth. Analyzing the climate sensitivity of the HadSM3 climate model using ensembles from different but related experiments. J. Climate, 22:3540-3557, 2009. S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, Tignor M., and H. L. Miller. Climate models and their evaluation. In Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge, United Kingdom and New York, NY, USA, 2007. Cambridge University Press. D. A Stainforth, T. Aina, C. Christensen, M. Collins, N. Faull, D. J. Frame, J. A. Kettleborough, S. Knight, A. Martin, J. M. Murphy, C. Piani, D. Sexton, L. A. Smith, R. A Spicer, A. J. Thorpe, and M. R Allen. Uncertainty in predictions of the climate response to rising levels of greenhouse gases. Nature, 433(7024):403-406, 2005.

  11. Emergent user behavior on Twitter modelled by a stochastic differential equation.

    Science.gov (United States)

    Mollgaard, Anders; Mathiesen, Joachim

    2015-01-01

    Data from the social-media site, Twitter, is used to study the fluctuations in tweet rates of brand names. The tweet rates are the result of a strongly correlated user behavior, which leads to bursty collective dynamics with a characteristic 1/f noise. Here we use the aggregated "user interest" in a brand name to model collective human dynamics by a stochastic differential equation with multiplicative noise. The model is supported by a detailed analysis of the tweet rate fluctuations and it reproduces both the exact bursty dynamics found in the data and the 1/f noise.

  12. An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

    NARCIS (Netherlands)

    Tarim, S.A.; Ozen, U.; Dogru, M.K.; Rossi, R.

    2011-01-01

    We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static–dynamic uncertainty strategy. The effectiveness of the proposed method

  13. Transport properties of stochastic Lorentz models

    NARCIS (Netherlands)

    Beijeren, H. van

    Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed

  14. Modeling and analysis of stochastic systems

    CERN Document Server

    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

  15. Maximum likelihood approach for several stochastic volatility models

    International Nuclear Information System (INIS)

    Camprodon, Jordi; Perelló, Josep

    2012-01-01

    Volatility measures the amplitude of price fluctuations. Despite it being one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility follow a two-dimensional diffusion process where volatility is the stochastic diffusion coefficient of the log-price dynamics. We apply this method to the simplest versions of the expOU, the OU and the Heston stochastic volatility models and we study their performance in terms of the log-price probability, the volatility probability, and its Mean First-Passage Time. The approach has some predictive power on the future returns amplitude by only knowing the current volatility. The assumed models do not consider long-range volatility autocorrelation and the asymmetric return-volatility cross-correlation but the method still yields very naturally these two important stylized facts. We apply the method to different market indices and with a good performance in all cases. (paper)

  16. 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...

  17. Discrete stochastic analogs of Erlang epidemic models.

    Science.gov (United States)

    Getz, Wayne M; Dougherty, Eric R

    2018-12-01

    Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

  18. Stochastic modeling of soil salinity

    Science.gov (United States)

    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.

  19. Can a microscopic stochastic model explain the emergence of pain cycles in patients?

    International Nuclear Information System (INIS)

    Di Patti, Francesca; Fanelli, Duccio

    2009-01-01

    A stochastic model is introduced here to investigate the molecular mechanisms which trigger the perception of pain. The action of analgesic drug compounds is discussed in a dynamical context, where the competition with inactive species is explicitly accounted for. Finite size effects inevitably perturb the mean-field dynamics: oscillations in the amount of bound receptors are spontaneously manifested, driven by the noise which is intrinsic to the system under scrutiny. These effects are investigated both numerically, via stochastic simulations, and analytically, through a large size expansion. The claim that our findings could provide a consistent interpretative framework for explaining the emergence of cyclic behaviors in response to analgesic treatments is substantiated

  20. Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling

    KAUST Repository

    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.

  1. Electricity price modeling with stochastic time change

    International Nuclear Information System (INIS)

    Borovkova, Svetlana; Schmeck, Maren Diane

    2017-01-01

    In this paper, we develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. This technique allows us to incorporate the characteristic features of electricity prices (such as seasonal volatility, time varying mean reversion and seasonally occurring price spikes) into the model in an elegant and economically justifiable way. The stochastic time change introduces stochastic as well as deterministic (e.g., seasonal) features in the price process' volatility and in the jump component. We specify the base process as a mean reverting jump diffusion and the time change as an absolutely continuous stochastic process with seasonal component. The activity rate of the stochastic time change can be related to the factors that influence supply and demand. Here we use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change, and show that this choice leads to realistic price paths. We derive properties of the resulting price process and develop the model calibration procedure. We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths by Monte Carlo simulations. We show that the simulated price process matches the distributional characteristics of the observed electricity prices in periods of both high and low demand. - Highlights: • We develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. • We incorporate the characteristic features of electricity prices, such as seasonal volatility and spikes into the model. • We use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change • We derive properties of the resulting price process and develop the model calibration procedure. • We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths.

  2. 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...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... 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...

  3. Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

    International Nuclear Information System (INIS)

    Pham, H.

    2002-01-01

    This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature

  4. Convergence of Sample Path Optimal Policies for Stochastic Dynamic Programming

    National Research Council Canada - National Science Library

    Fu, Michael C; Jin, Xing

    2005-01-01

    .... These results have practical implications for Monte Carlo simulation-based solution approaches to stochastic dynamic programming problems where it is impractical to extract the explicit transition...

  5. 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...

  6. 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 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....

  7. Stochastic disk dynamo as a model of reversals of the Earth's magnetic field

    International Nuclear Information System (INIS)

    Ito, H.M.

    1988-01-01

    A stochastic model is given of a system composed of N similar disk dynamos interacting with one another. The time evolution of the system is governed by a master equation of the class introduced by van Kampen as relevant to stochastic macrosystems. In the model, reversals of the Earth's magnetic field are regarded as large deviations caused by a small random force of O(N/sup -1/2/) from one of the field polarities to the other. Reversal processes are studied by simulation, which shows that the model explains well the activities of the paleomagnetic field inclusive of statistical laws of the reversal sequence and the intensity distribution. Comparison are made between the model and dynamical disk dynamo models

  8. Extinction threshold of a population in spatial and stochastic model

    OpenAIRE

    Soroka, Yevheniia; Rublyov, Bogdan

    2016-01-01

    In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically, we studied how the critical values for the model parameters that separate the cases of extinction and persistence depend on the spatial scales of the competition and dispersal kernels. We compared the simulations and analytical results to examine if and how ...

  9. Using Stochastic Dynamic Programming to Support Water Resources Management in the Ziya River Basin, China

    DEFF Research Database (Denmark)

    Davidsen, Claus; Cardenal, Silvio Javier Pereira; Liu, Suxia

    2015-01-01

    of stochastic dynamic programming, to optimize water resources management in the Ziya River basin. Natural runoff from the upper basin was estimated with a rainfall-runoff model autocalibrated using in situ measured discharge. The runoff serial correlation was described by a Markov chain and used as input...

  10. Yield curve event tree construction for multi stage stochastic programming models

    DEFF Research Database (Denmark)

    Rasmussen, Kourosh Marjani; Poulsen, Rolf

    Dynamic stochastic programming (DSP) provides an intuitive framework for modelling of financial portfolio choice problems where market frictions are present and dynamic re--balancing has a significant effect on initial decisions. The application of these models in practice, however, is limited....... Indeed defining a universal and tractable framework for fully ``appropriate'' event trees is in our opinion an impossible task. A problem specific approach to designing such event trees is the way ahead. In this paper we propose a number of desirable properties which should be present in an event tree...

  11. Stochastic population dynamic models as probability networks

    Science.gov (United States)

    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...

  12. Stochastic Models of Polymer Systems

    Science.gov (United States)

    2016-01-01

    Distribution Unlimited Final Report: Stochastic Models of Polymer Systems The views, opinions and/or findings contained in this report are those of the...ADDRESS. Princeton University PO Box 0036 87 Prospect Avenue - 2nd floor Princeton, NJ 08544 -2020 14-Mar-2014 ABSTRACT Number of Papers published in...peer-reviewed journals: Number of Papers published in non peer-reviewed journals: Final Report: Stochastic Models of Polymer Systems Report Title

  13. 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.

  14. Corruption dynamics model

    Science.gov (United States)

    Malafeyev, O. A.; Nemnyugin, S. A.; Rylow, D.; Kolpak, E. P.; Awasthi, Achal

    2017-07-01

    The corruption dynamics is analyzed by means of the lattice model which is similar to the three-dimensional Ising model. Agents placed at nodes of the corrupt network periodically choose to perfom or not to perform the act of corruption at gain or loss while making decisions based on the process history. The gain value and its dynamics are defined by means of the Markov stochastic process modelling with parameters established in accordance with the influence of external and individual factors on the agent's gain. The model is formulated algorithmically and is studied by means of the computer simulation. Numerical results are obtained which demonstrate asymptotic behaviour of the corruption network under various conditions.

  15. Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations.

    Science.gov (United States)

    Bouzat, Sebastián

    2016-01-01

    One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

  16. Extension of Nelson's stochastic quantization to finite temperature using thermo field dynamics

    International Nuclear Information System (INIS)

    Kobayashi, K.; Yamanaka, Y.

    2011-01-01

    We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schroedinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature. -- Highlights: → Utilizing TFD, we extend Nelson's stochastic method to finite temperature. → We introduce stochastic equations for tilde and non-tilde particles. → Our stochastic equations can reproduce the TFD-type Schroedinger equation. → Our formalism satisfies the uncertainly relation at finite temperature.

  17. Stochastic resonance in a generalized Von Foerster population growth model

    Energy Technology Data Exchange (ETDEWEB)

    Lumi, N.; Mankin, R. [Institute of Mathematics and Natural Sciences, Tallinn University, 25 Narva Road, 10120 Tallinn (Estonia)

    2014-11-12

    The stochastic dynamics of a population growth model, similar to the Von Foerster model for human population, is studied. The influence of fluctuating environment on the carrying capacity is modeled as a multiplicative dichotomous noise. It is established that an interplay between nonlinearity and environmental fluctuations can cause single unidirectional discontinuous transitions of the mean population size versus the noise amplitude, i.e., an increase of noise amplitude can induce a jump from a state with a moderate number of individuals to that with a very large number, while by decreasing the noise amplitude an opposite transition cannot be effected. An analytical expression of the mean escape time for such transitions is found. Particularly, it is shown that the mean transition time exhibits a strong minimum at intermediate values of noise correlation time, i.e., the phenomenon of stochastic resonance occurs. Applications of the results in ecology are also discussed.

  18. Modeling stochasticity and robustness in gene regulatory networks.

    Science.gov (United States)

    Garg, Abhishek; Mohanram, Kartik; Di Cara, Alessandro; De Micheli, Giovanni; Xenarios, Ioannis

    2009-06-15

    Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.

  19. Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties

    Energy Technology Data Exchange (ETDEWEB)

    Craven, Galen T.; Popov, Alexander V.; Hernandez, Rigoberto, E-mail: hernandez@chemistry.gatech.edu [Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 (United States)

    2015-04-21

    The dynamical properties of a system of soft rods governed by stochastic hard collisions (SHCs) have been determined over a varying range of softness using molecular dynamics simulations in one dimension and analytic theory. The SHC model allows for interpenetration of the system’s constituent particles in the simulations, generating overlapping clustering behavior analogous to the spatial structures observed in systems governed by deterministic bounded potentials. Through variation of an assigned softness parameter δ, the limiting ranges of intermolecular softness are bridged, connecting the limiting ensemble behavior from hard to ideal (completely soft). Various dynamical and structural observables are measured from simulation and compared to developed theoretical values. The spatial properties are found to be well predicted by theories developed for the deterministic penetrable-sphere model with a transformation from energetic to probabilistic arguments. While the overlapping spatial structures are complex, the dynamical properties can be adequately approximated through a theory built on impulsive interactions with Enskog corrections. Our theory suggests that as the softness of interaction is varied toward the ideal limit, correlated collision processes are less important to the energy transfer mechanism, and Markovian processes dominate the evolution of the configuration space ensemble. For interaction softness close to hard limit, collision processes are highly correlated and overlapping spatial configurations give rise to entanglement of single-particle trajectories.

  20. Stochastic Mixed-Effects Parameters Bertalanffy Process, with Applications to Tree Crown Width Modeling

    Directory of Open Access Journals (Sweden)

    Petras Rupšys

    2015-01-01

    Full Text Available A stochastic modeling approach based on the Bertalanffy law gained interest due to its ability to produce more accurate results than the deterministic approaches. We examine tree crown width dynamic with the Bertalanffy type stochastic differential equation (SDE and mixed-effects parameters. In this study, we demonstrate how this simple model can be used to calculate predictions of crown width. We propose a parameter estimation method and computational guidelines. The primary goal of the study was to estimate the parameters by considering discrete sampling of the diameter at breast height and crown width and by using maximum likelihood procedure. Performance statistics for the crown width equation include statistical indexes and analysis of residuals. We use data provided by the Lithuanian National Forest Inventory from Scots pine trees to illustrate issues of our modeling technique. Comparison of the predicted crown width values of mixed-effects parameters model with those obtained using fixed-effects parameters model demonstrates the predictive power of the stochastic differential equations model with mixed-effects parameters. All results were implemented in a symbolic algebra system MAPLE.

  1. Front propagation and effect of memory in stochastic desertification models with an absorbing state

    Science.gov (United States)

    Herman, Dor; Shnerb, Nadav M.

    2017-08-01

    Desertification in dryland ecosystems is considered to be a major environmental threat that may lead to devastating consequences. The concern increases when the system admits two alternative steady states and the transition is abrupt and irreversible (catastrophic shift). However, recent studies show that the inherent stochasticity of the birth-death process, when superimposed on the presence of an absorbing state, may lead to a continuous (second order) transition even if the deterministic dynamics supports a catastrophic transition. Following these works we present here a numerical study of a one-dimensional stochastic desertification model, where the deterministic predictions are confronted with the observed dynamics. Our results suggest that a stochastic spatial system allows for a propagating front only when its active phase invades the inactive (desert) one. In the extinction phase one observes transient front propagation followed by a global collapse. In the presence of a seed bank the vegetation state is shown to be more robust against demographic stochasticity, but the transition in that case still belongs to the directed percolation equivalence class.

  2. Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations

    Science.gov (United States)

    Subramani, D. N.; Haley, P., Jr.; Lermusiaux, P. F. J.

    2017-12-01

    The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex and intermittent with unstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. For efficient and rigorous quantification and prediction of these uncertainities, the stochastic Dynamically Orthogonal (DO) PDEs for a primitive equation ocean modeling system with a nonlinear free-surface are derived and numerical schemes for their space-time integration are obtained. Detailed numerical studies with idealized-to-realistic regional ocean dynamics are completed. These include consistency checks for the numerical schemes and comparisons with ensemble realizations. As an illustrative example, we simulate the 4-d multiscale uncertainty in the Middle Atlantic/New York Bight region during the months of Jan to Mar 2017. To provide intitial conditions for the uncertainty subspace, uncertainties in the region were objectively analyzed using historical data. The DO primitive equations were subsequently integrated in space and time. The probability distribution function (pdf) of the ocean fields is compared to in-situ, remote sensing, and opportunity data collected during the coincident POSYDON experiment. Results show that our probabilistic predictions had skill and are 3- to 4- orders of magnitude faster than classic ensemble schemes.

  3. Stochastic models in reliability and maintenance

    CERN Document Server

    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...

  4. Stochastic population dynamics in populations of western terrestrial garter snakes with divergent life histories.

    Science.gov (United States)

    Miller, David A; Clark, William R; Arnold, Stevan J; Bronikowski, Anne M

    2011-08-01

    Comparative evaluations of population dynamics in species with temporal and spatial variation in life-history traits are rare because they require long-term demographic time series from multiple populations. We present such an analysis using demographic data collected during the interval 1978-1996 for six populations of western terrestrial garter snakes (Thamnophis elegans) from two evolutionarily divergent ecotypes. Three replicate populations from a slow-living ecotype, found in mountain meadows of northeastern California, were characterized by individuals that develop slowly, mature late, reproduce infrequently with small reproductive effort, and live longer than individuals of three populations of a fast-living ecotype found at lakeshore locales. We constructed matrix population models for each of the populations based on 8-13 years of data per population and analyzed both deterministic dynamics based on mean annual vital rates and stochastic dynamics incorporating annual variation in vital rates. (1) Contributions of highly variable vital rates to fitness (lambda(s)) were buffered against the negative effects of stochastic variation, and this relationship was consistent with differences between the meadow (M-slow) and lakeshore (L-fast) ecotypes. (2) Annual variation in the proportion of gravid females had the greatest negative effect among all vital rates on lambda(s). The magnitude of variation in the proportion of gravid females and its effect on lambda(s) was greater in M-slow than L-fast populations. (3) Variation in the proportion of gravid females, in turn, depended on annual variation in prey availability, and its effect on lambda(s) was 4 23 times greater in M-slow than L-fast populations. In addition to differences in stochastic dynamics between ecotypes, we also found higher mean mortality rates across all age classes in the L-fast populations. Our results suggest that both deterministic and stochastic selective forces have affected the evolution of

  5. Phenomenology of stochastic exponential growth

    Science.gov (United States)

    Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

    2017-06-01

    Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

  6. The multivariate supOU stochastic volatility model

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole; Stelzer, Robert

    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...... 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....... 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....

  7. Hybrid Differential Dynamic Programming with Stochastic Search

    Science.gov (United States)

    Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob

    2016-01-01

    Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

  8. A Fractionally Integrated Wishart Stochastic Volatility Model

    NARCIS (Netherlands)

    M. Asai (Manabu); M.J. McAleer (Michael)

    2013-01-01

    textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of

  9. Stochastic Nominal Wage Contacts in a Cash-in-Advance Model

    OpenAIRE

    Collard, Fabrice; Ertz, Guy

    1996-01-01

    We build a simple cash-in-advance model for the German economy, in which we introduce stochastic nominal wage contracts. This allows to weaken the negative effect of the inflation tax such that monetary shocks exert a positive effect on output dynamics. The nominal wage contract model is able to mimic the correlation of inflation and real balances with output. It also lowers the standard deviation of inflation relative to that of output. Further, the variance decomposition analysis indicates ...

  10. Stochastic modeling of wetland-groundwater systems

    Science.gov (United States)

    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.

  11. A stochastic SIS epidemic model with vaccination

    Science.gov (United States)

    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 disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while 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.

  12. Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes

    International Nuclear Information System (INIS)

    Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti

    2016-01-01

    Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.

  13. Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti, E-mail: arti@iitm.ac.in [Department of Chemistry, Indian Institute of Technology, Madras, Chennai 600036 (India)

    2016-08-28

    Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.

  14. Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes

    Science.gov (United States)

    Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti

    2016-08-01

    Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.

  15. Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

    Science.gov (United States)

    de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

    2017-12-01

    The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of

  16. Stochastic Evolution Dynamic of the Rock-Scissors-Paper Game Based on a Quasi Birth and Death Process.

    Science.gov (United States)

    Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu

    2016-06-27

    Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.

  17. Stochastic sensitivity analysis of periodic attractors in non-autonomous nonlinear dynamical systems based on stroboscopic map

    Energy Technology Data Exchange (ETDEWEB)

    Guo, Kong-Ming, E-mail: kmguo@xidian.edu.cn [School of Electromechanical Engineering, Xidian University, P.O. Box 187, Xi' an 710071 (China); Jiang, Jun, E-mail: jun.jiang@mail.xjtu.edu.cn [State Key Laboratory for Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China)

    2014-07-04

    To apply stochastic sensitivity function method, which can estimate the probabilistic distribution of stochastic attractors, to non-autonomous dynamical systems, a 1/N-period stroboscopic map for a periodic motion is constructed in order to discretize the continuous cycle into a discrete one. In this way, the sensitivity analysis of a cycle for discrete map can be utilized and a numerical algorithm for the stochastic sensitivity analysis of periodic solutions of non-autonomous nonlinear dynamical systems under stochastic disturbances is devised. An external excited Duffing oscillator and a parametric excited laser system are studied as examples to show the validity of the proposed method. - Highlights: • A method to analyze sensitivity of stochastic periodic attractors in non-autonomous dynamical systems is proposed. • Probabilistic distribution around periodic attractors in an external excited Φ{sup 6} Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined.

  18. Stochastic quasi-gradient based optimization algorithms for dynamic reliability applications

    International Nuclear Information System (INIS)

    Bourgeois, F.; Labeau, P.E.

    2001-01-01

    On one hand, PSA results are increasingly used in decision making, system management and optimization of system design. On the other hand, when severe accidental transients are considered, dynamic reliability appears appropriate to account for the complex interaction between the transitions between hardware configurations, the operator behavior and the dynamic evolution of the system. This paper presents an exploratory work in which the estimation of the system unreliability in a dynamic context is coupled with an optimization algorithm to determine the 'best' safety policy. Because some reliability parameters are likely to be distributed, the cost function to be minimized turns out to be a random variable. Stochastic programming techniques are therefore envisioned to determine an optimal strategy. Monte Carlo simulation is used at all stages of the computations, from the estimation of the system unreliability to that of the stochastic quasi-gradient. The optimization algorithm is illustrated on a HNO 3 supply system

  19. Elementary amplitudes from full QCD and the stochastic vacuum model

    International Nuclear Information System (INIS)

    Martini, A.F.; Menon, M.J.

    2002-01-01

    In a previous work, making use of the gluon gauge-invariant two-point correlation function determined from lattice QCD in the quenched approximation and the stochastic vacuum model, we determined the elementary (parton-parton) scattering amplitude in the momentum transfer space. In this communication we compute the elementary amplitude from new lattice QCD calculations that include the effects of dynamical fermions (full QCD). The main conclusion is that the inclusion of dynamical fermions leads to a normalized elementary amplitude that decreases more quickly with the momentum transfer than that in the quenched approximation. (author)

  20. Stochastic ferromagnetism analysis and numerics

    CERN Document Server

    Brzezniak, Zdzislaw; Neklyudov, Mikhail; Prohl, Andreas

    2013-01-01

    This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). Comparative computational studies with the stochastic model are included. Constructive tools such as e.g. finite element methods are used to derive the theoretical results, which are then used for computational studies.

  1. On the stochastic approach to marine population dynamics

    Directory of Open Access Journals (Sweden)

    Eduardo Ferrandis

    2007-03-01

    Full Text Available The purpose of this article is to deepen and structure the statistical basis of marine population dynamics. The starting point is the correspondence between the concepts of mortality, survival and lifetime distribution. This is the kernel of the possibilities that survival analysis techniques offer to marine population dynamics. A rigorous definition of survival and mortality based on their properties and their probabilistic versions is briefly presented. Some well established models for lifetime distribution, which generalise the usual simple exponential distribution, might be used with their corresponding survivals and mortalities. A critical review of some published models is also made, including original models proposed in the way opened by Caddy (1991 and Sparholt (1990, which allow for a continuously decreasing natural mortality. Considering these elements, the pure death process dealt with in the literature is used as a theoretical basis for the evolution of a marine cohort. The elaboration of this process is based on Chiang´s study of the probability distribution of the life table (Chiang, 1960 and provides specific structured models for stock evolution as a Markovian process. These models may introduce new ideas in the line of thinking developed by Gudmundsson (1987 and Sampson (1990 in order to model the evolution of a marine cohort by stochastic processes. The suitable approximation of these processes by means of Gaussian processes may allow theoretical and computational multivariate Gaussian analysis to be applied to the probabilistic treatment of fisheries issues. As a consequence, the necessary catch equation appears as a stochastic integral with respect to the mentioned Markovian process of the stock. The solution of this equation is available when the mortalities are proportional, hence the use of the proportional hazards model (Cox, 1959. The assumption of these proportional mortalities leads naturally to the construction of a

  2. A stochastic aerodynamic model for stationary blades in unsteady 3D wind fields

    International Nuclear Information System (INIS)

    Fluck, Manuel; Crawford, Curran

    2016-01-01

    Dynamic loads play an important roll in the design of wind turbines, but establishing the life-time aerodynamic loads (e.g. extreme and fatigue loads) is a computationally expensive task. Conventional (deterministic) methods to analyze long term loads, which rely on the repeated analysis of multiple different wind samples, are usually too expensive to be included in optimization routines. We present a new stochastic approach, which solves the aerodynamic system equations (Lagrangian vortex model) in the stochastic space, and thus arrive directly at a stochastic description of the coupled loads along a turbine blade. This new approach removes the requirement of analyzing multiple different realizations. Instead, long term loads can be extracted from a single stochastic solution, a procedure that is obviously significantly faster. Despite the reduced analysis time, results obtained from the stochastic approach match deterministic result well for a simple test-case (a stationary blade). In future work, the stochastic method will be extended to rotating blades, thus opening up new avenues to include long term loads into turbine optimization. (paper)

  3. Path integral methods for the dynamics of stochastic and disordered systems

    DEFF Research Database (Denmark)

    Hertz, John A.; Roudi, Yasser; Sollich, Peter

    2017-01-01

    We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey...

  4. Stochastic optimal control in infinite dimension dynamic programming and HJB equations

    CERN Document Server

    Fabbri, Giorgio; Święch, Andrzej

    2017-01-01

    Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite ...

  5. Stochastic-hydrodynamic model of halo formation in charged particle beams

    Directory of Open Access Journals (Sweden)

    Nicola Cufaro Petroni

    2003-03-01

    Full Text Available The formation of the beam halo in charged particle accelerators is studied in the framework of a stochastic-hydrodynamic model for the collective motion of the particle beam. In such a stochastic-hydrodynamic theory the density and the phase of the charged beam obey a set of coupled nonlinear hydrodynamic equations with explicit time-reversal invariance. This leads to a linearized theory that describes the collective dynamics of the beam in terms of a classical Schrödinger equation. Taking into account space-charge effects, we derive a set of coupled nonlinear hydrodynamic equations. These equations define a collective dynamics of self-interacting systems much in the same spirit as in the Gross-Pitaevskii and Landau-Ginzburg theories of the collective dynamics for interacting quantum many-body systems. Self-consistent solutions of the dynamical equations lead to quasistationary beam configurations with enhanced transverse dispersion and transverse emittance growth. In the limit of a frozen space-charge core it is then possible to determine and study the properties of stationary, stable core-plus-halo beam distributions. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution.

  6. Environmental versus demographic variability in stochastic predator–prey models

    International Nuclear Information System (INIS)

    Dobramysl, U; Täuber, U C

    2013-01-01

    In contrast to the neutral population cycles of the deterministic mean-field Lotka–Volterra rate equations, including spatial structure and stochastic noise in models for predator–prey interactions yields complex spatio-temporal structures associated with long-lived erratic population oscillations. Environmental variability in the form of quenched spatial randomness in the predation rates results in more localized activity patches. Our previous study showed that population fluctuations in rare favorable regions in turn cause a remarkable increase in the asymptotic densities of both predators and prey. Very intriguing features are found when variable interaction rates are affixed to individual particles rather than lattice sites. Stochastic dynamics with demographic variability in conjunction with inheritable predation efficiencies generate non-trivial time evolution for the predation rate distributions, yet with overall essentially neutral optimization. (paper)

  7. Variance decomposition in stochastic simulators.

    Science.gov (United States)

    Le Maître, O P; Knio, O M; Moraes, A

    2015-06-28

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  8. Variance decomposition in stochastic simulators

    Science.gov (United States)

    Le Maître, O. P.; Knio, O. M.; Moraes, A.

    2015-06-01

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  9. Variance decomposition in stochastic simulators

    Energy Technology Data Exchange (ETDEWEB)

    Le Maître, O. P., E-mail: olm@limsi.fr [LIMSI-CNRS, UPR 3251, Orsay (France); Knio, O. M., E-mail: knio@duke.edu [Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708 (United States); Moraes, A., E-mail: alvaro.moraesgutierrez@kaust.edu.sa [King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)

    2015-06-28

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  10. Variance decomposition in stochastic simulators

    KAUST Repository

    Le Maî tre, O. P.; Knio, O. M.; Moraes, Alvaro

    2015-01-01

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  11. 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...

  12. Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

    International Nuclear Information System (INIS)

    Cruz, Roberto de la; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

    2017-01-01

    The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction–diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction–diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge

  13. Regular and stochastic particle motion in plasma dynamics

    International Nuclear Information System (INIS)

    Kaufman, A.N.

    1979-08-01

    A Hamiltonian formalism is presented for the study of charged-particle trajectories in the self-consistent field of the particles. The intention is to develop a general approach to plasma dynamics. Transformations of phase-space variables are used to separate out the regular, adiabatic motion from the irregular, stochastic trajectories. Several new techniques are included in this presentation

  14. Stochastic linear programming models, theory, and computation

    CERN Document Server

    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...

  15. Effects of random noise in a dynamical model of love

    Energy Technology Data Exchange (ETDEWEB)

    Xu Yong, E-mail: hsux3@nwpu.edu.cn [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); Gu Rencai; Zhang Huiqing [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)

    2011-07-15

    Highlights: > We model the complexity and unpredictability of psychology as Gaussian white noise. > The stochastic system of love is considered including bifurcation and chaos. > We show that noise can both suppress and induce chaos in dynamical models of love. - Abstract: This paper aims to investigate the stochastic model of love and the effects of random noise. We first revisit the deterministic model of love and some basic properties are presented such as: symmetry, dissipation, fixed points (equilibrium), chaotic behaviors and chaotic attractors. Then we construct a stochastic love-triangle model with parametric random excitation due to the complexity and unpredictability of the psychological system, where the randomness is modeled as the standard Gaussian noise. Stochastic dynamics under different three cases of 'Romeo's romantic style', are examined and two kinds of bifurcations versus the noise intensity parameter are observed by the criteria of changes of top Lyapunov exponent and shape of stationary probability density function (PDF) respectively. The phase portraits and time history are carried out to verify the proposed results, and the good agreement can be found. And also the dual roles of the random noise, namely suppressing and inducing chaos are revealed.

  16. Effects of random noise in a dynamical model of love

    International Nuclear Information System (INIS)

    Xu Yong; Gu Rencai; Zhang Huiqing

    2011-01-01

    Highlights: → We model the complexity and unpredictability of psychology as Gaussian white noise. → The stochastic system of love is considered including bifurcation and chaos. → We show that noise can both suppress and induce chaos in dynamical models of love. - Abstract: This paper aims to investigate the stochastic model of love and the effects of random noise. We first revisit the deterministic model of love and some basic properties are presented such as: symmetry, dissipation, fixed points (equilibrium), chaotic behaviors and chaotic attractors. Then we construct a stochastic love-triangle model with parametric random excitation due to the complexity and unpredictability of the psychological system, where the randomness is modeled as the standard Gaussian noise. Stochastic dynamics under different three cases of 'Romeo's romantic style', are examined and two kinds of bifurcations versus the noise intensity parameter are observed by the criteria of changes of top Lyapunov exponent and shape of stationary probability density function (PDF) respectively. The phase portraits and time history are carried out to verify the proposed results, and the good agreement can be found. And also the dual roles of the random noise, namely suppressing and inducing chaos are revealed.

  17. Computational stochastic model of ions implantation

    Energy Technology Data Exchange (ETDEWEB)

    Zmievskaya, Galina I., E-mail: zmi@gmail.ru; Bondareva, Anna L., E-mail: bal310775@yandex.ru [M.V. Keldysh Institute of Applied Mathematics RAS, 4,Miusskaya sq., 125047 Moscow (Russian Federation); Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru [VNII Geosystem Russian Federal Center, Varshavskoye roadway, 8, Moscow (Russian Federation); Maino, Giuseppe, E-mail: giuseppe.maino@enea.it [Scuola di Lettere e BeniCulturali, University di Bologna, sede di Ravenna, via Mariani 5, 48100 Ravenna (Italy)

    2015-03-10

    Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.

  18. How Levins’ dynamics emerges from a Ricker metapopulation model

    KAUST Repository

    Elí as-Wolff, F.; Eriksson, Anders; Manica, A.; Mehlig, B.

    2015-01-01

    Understanding the dynamics of metapopulations close to extinction is of vital importance for management. Levins-like models, in which local patches are treated as either occupied or empty, have been used extensively to explore the extinction dynamics of metapopulations, but they ignore the important role of local population dynamics. In this paper, we consider a stochastic metapopulation model where local populations follow a stochastic, density-dependent dynamics (the Ricker model), and use this framework to investigate the behaviour of the metapopulation on the brink of extinction. We determine under which circumstances the metapopulation follows a time evolution consistent with Levins’ dynamics. We derive analytical expressions for the colonisation and extinction rates (c and e) in Levins-type models in terms of reproduction, survival and dispersal parameters of the local populations, providing an avenue to parameterising Levins-like models from the type of information on local demography that is available for a number of species. To facilitate applying our results, we provide a numerical algorithm for computing c and e.

  19. How Levins’ dynamics emerges from a Ricker metapopulation model

    KAUST Repository

    Elías-Wolff, F.

    2015-09-24

    Understanding the dynamics of metapopulations close to extinction is of vital importance for management. Levins-like models, in which local patches are treated as either occupied or empty, have been used extensively to explore the extinction dynamics of metapopulations, but they ignore the important role of local population dynamics. In this paper, we consider a stochastic metapopulation model where local populations follow a stochastic, density-dependent dynamics (the Ricker model), and use this framework to investigate the behaviour of the metapopulation on the brink of extinction. We determine under which circumstances the metapopulation follows a time evolution consistent with Levins’ dynamics. We derive analytical expressions for the colonisation and extinction rates (c and e) in Levins-type models in terms of reproduction, survival and dispersal parameters of the local populations, providing an avenue to parameterising Levins-like models from the type of information on local demography that is available for a number of species. To facilitate applying our results, we provide a numerical algorithm for computing c and e.

  20. 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

  1. Population stochastic modelling (PSM)-An R package for mixed-effects models based on stochastic differential equations

    DEFF Research Database (Denmark)

    Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode

    2009-01-01

    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 FOCE1 approximation......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(l)) (2005) 109-141; C.W. Tornoe, R.V Overgaard, H. Agerso, 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...

  2. Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics

    DEFF Research Database (Denmark)

    Iwankiewicz, R.; Nielsen, Søren R. K.

    Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically-numerical tec......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...

  3. GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: Dynamics and stochastic simulations

    Science.gov (United States)

    Antoine, Xavier; Duboscq, Romain

    2015-08-01

    GPELab is a free Matlab toolbox for modeling and numerically solving large classes of systems of Gross-Pitaevskii equations that arise in the physics of Bose-Einstein condensates. The aim of this second paper, which follows (Antoine and Duboscq, 2014), is to first present the various pseudospectral schemes available in GPELab for computing the deterministic and stochastic nonlinear dynamics of Gross-Pitaevskii equations (Antoine, et al., 2013). Next, the corresponding GPELab functions are explained in detail. Finally, some numerical examples are provided to show how the code works for the complex dynamics of BEC problems.

  4. Improving filtering and prediction of spatially extended turbulent systems with model errors through stochastic parameter estimation

    International Nuclear Information System (INIS)

    Gershgorin, B.; Harlim, J.; Majda, A.J.

    2010-01-01

    The filtering and predictive skill for turbulent signals is often limited by the lack of information about the true dynamics of the system and by our inability to resolve the assumed dynamics with sufficiently high resolution using the current computing power. The standard approach is to use a simple yet rich family of constant parameters to account for model errors through parameterization. This approach can have significant skill by fitting the parameters to some statistical feature of the true signal; however in the context of real-time prediction, such a strategy performs poorly when intermittent transitions to instability occur. Alternatively, we need a set of dynamic parameters. One strategy for estimating parameters on the fly is a stochastic parameter estimation through partial observations of the true signal. In this paper, we extend our newly developed stochastic parameter estimation strategy, the Stochastic Parameterization Extended Kalman Filter (SPEKF), to filtering sparsely observed spatially extended turbulent systems which exhibit abrupt stability transition from time to time despite a stable average behavior. For our primary numerical example, we consider a turbulent system of externally forced barotropic Rossby waves with instability introduced through intermittent negative damping. We find high filtering skill of SPEKF applied to this toy model even in the case of very sparse observations (with only 15 out of the 105 grid points observed) and with unspecified external forcing and damping. Additive and multiplicative bias corrections are used to learn the unknown features of the true dynamics from observations. We also present a comprehensive study of predictive skill in the one-mode context including the robustness toward variation of stochastic parameters, imperfect initial conditions and finite ensemble effect. Furthermore, the proposed stochastic parameter estimation scheme applied to the same spatially extended Rossby wave system demonstrates

  5. Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service

    Directory of Open Access Journals (Sweden)

    Junhai Ma

    2017-01-01

    Full Text Available Apart from the price fluctuation, the retailers’ service level becomes another key factor that affects the market demand. This paper depicts a modified price and demand game model based on the stochastic demand and the retailer’s service level which influences the market demand decided by customers’ preference, while the market demand is stochastic in this model. We explore how the price adjustment speed affects the stability of the supply chain system with respect to service level and stochastic demand. The dynamic behavior of the system is researched by simulation and the stability domain and the bifurcation phenomenon are shown clearly. The largest Lyapunov exponent and the chaotic attractor are also given to confirm the chaotic characteristic of the system. The simulation results indicate that relatively small price adjustment speed may maintain the system at stable state. With the price adjustment speed gradually increasing, the price system gets unstable and finally becomes chaotic. This chaotic phenomenon will perturb the product market and this phenomenon should be controlled to keep the system stay in the stable region. So the chaos control is done and the chaos can be controlled completely. The conclusion makes significant contribution to the system referring to the price fluctuation based on the service level and stochastic demand.

  6. Bias correction in the realized stochastic volatility model for daily volatility on the Tokyo Stock Exchange

    Science.gov (United States)

    Takaishi, Tetsuya

    2018-06-01

    The realized stochastic volatility model has been introduced to estimate more accurate volatility by using both daily returns and realized volatility. The main advantage of the model is that no special bias-correction factor for the realized volatility is required a priori. Instead, the model introduces a bias-correction parameter responsible for the bias hidden in realized volatility. We empirically investigate the bias-correction parameter for realized volatilities calculated at various sampling frequencies for six stocks on the Tokyo Stock Exchange, and then show that the dynamic behavior of the bias-correction parameter as a function of sampling frequency is qualitatively similar to that of the Hansen-Lunde bias-correction factor although their values are substantially different. Under the stochastic diffusion assumption of the return dynamics, we investigate the accuracy of estimated volatilities by examining the standardized returns. We find that while the moments of the standardized returns from low-frequency realized volatilities are consistent with the expectation from the Gaussian variables, the deviation from the expectation becomes considerably large at high frequencies. This indicates that the realized stochastic volatility model itself cannot completely remove bias at high frequencies.

  7. Sharp asymptotics for stochastic dynamics with parallel updating rule

    NARCIS (Netherlands)

    Nardi, F.R.; Spitoni, C.

    2012-01-01

    In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e., the

  8. Sharp Asymptotics for Stochastic Dynamics with Parallel Updating Rule

    NARCIS (Netherlands)

    Nardi, F.R.; Spitoni, C.

    2012-01-01

    In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e.,

  9. 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.

  10. Stochastic Dynamics of a Time-Delayed Ecosystem Driven by Poisson White Noise Excitation

    Directory of Open Access Journals (Sweden)

    Wantao Jia

    2018-02-01

    Full Text Available We investigate the stochastic dynamics of a prey-predator type ecosystem with time delay and the discrete random environmental fluctuations. In this model, the delay effect is represented by a time delay parameter and the effect of the environmental randomness is modeled as Poisson white noise. The stochastic averaging method and the perturbation method are applied to calculate the approximate stationary probability density functions for both predator and prey populations. The influences of system parameters and the Poisson white noises are investigated in detail based on the approximate stationary probability density functions. It is found that, increasing time delay parameter as well as the mean arrival rate and the variance of the amplitude of the Poisson white noise will enhance the fluctuations of the prey and predator population. While the larger value of self-competition parameter will reduce the fluctuation of the system. Furthermore, the results from Monte Carlo simulation are also obtained to show the effectiveness of the results from averaging method.

  11. Dynamic behaviors of spin-1/2 bilayer system within Glauber-type stochastic dynamics based on the effective-field theory

    International Nuclear Information System (INIS)

    Ertaş, Mehmet; Kantar, Ersin; Keskin, Mustafa

    2014-01-01

    The dynamic phase transitions (DPTs) and dynamic phase diagrams of the kinetic spin-1/2 bilayer system in the presence of a time-dependent oscillating external magnetic field are studied by using Glauber-type stochastic dynamics based on the effective-field theory with correlations for the ferromagnetic/ferromagnetic (FM/FM), antiferromagnetic/ferromagnetic (AFM/FM) and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams for the amplitude of the oscillating field versus temperature were presented. The results are compared with the results of the same system within Glauber-type stochastic dynamics based on the mean-field theory. - Highlights: • The Ising bilayer system is investigated within the Glauber dynamics based on EFT. • The time variations of average order parameters to find phases are studied. • The dynamic phase diagrams are found for the different interaction parameters. • The system displays the critical points as well as a re-entrant behavior

  12. Dynamic behaviors of spin-1/2 bilayer system within Glauber-type stochastic dynamics based on the effective-field theory

    Energy Technology Data Exchange (ETDEWEB)

    Ertaş, Mehmet; Kantar, Ersin, E-mail: ersinkantar@erciyes.edu.tr; Keskin, Mustafa

    2014-05-01

    The dynamic phase transitions (DPTs) and dynamic phase diagrams of the kinetic spin-1/2 bilayer system in the presence of a time-dependent oscillating external magnetic field are studied by using Glauber-type stochastic dynamics based on the effective-field theory with correlations for the ferromagnetic/ferromagnetic (FM/FM), antiferromagnetic/ferromagnetic (AFM/FM) and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams for the amplitude of the oscillating field versus temperature were presented. The results are compared with the results of the same system within Glauber-type stochastic dynamics based on the mean-field theory. - Highlights: • The Ising bilayer system is investigated within the Glauber dynamics based on EFT. • The time variations of average order parameters to find phases are studied. • The dynamic phase diagrams are found for the different interaction parameters. • The system displays the critical points as well as a re-entrant behavior.

  13. Model selection for integrated pest management with stochasticity.

    Science.gov (United States)

    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.

  14. Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction

    Science.gov (United States)

    Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.

    2005-03-01

    We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

  15. 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...

  16. Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem.

    Science.gov (United States)

    Schilde, M; Doerner, K F; Hartl, R F

    2014-10-01

    In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches.

  17. Sharp asymptotics for stochastic dynamics with parallel updating rule

    NARCIS (Netherlands)

    Nardi, F.R.; Spitoni, C.

    2012-01-01

    In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a ¿nite volume Probabilistic Cellular Automaton (PCA) in a small external ¿eld at low temperature regime. We are interested in the nucleation of the system, i.e., the

  18. Stochastic modeling and analysis of telecoms networks

    CERN Document Server

    Decreusefond, Laurent

    2012-01-01

    This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an

  19. Analysis of dispatching rules in a stochastic dynamic job shop manufacturing system with sequence-dependent setup times

    Science.gov (United States)

    Sharma, Pankaj; Jain, Ajai

    2014-12-01

    Stochastic dynamic job shop scheduling problem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatching rules in such shop from makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures viewpoint. A discrete event simulation model of a stochastic dynamic job shop manufacturing system is developed for investigation purpose. Nine dispatching rules identified from literature are incorporated in the simulation model. The simulation experiments are conducted under due date tightness factor of 3, shop utilization percentage of 90% and setup times less than processing times. Results indicate that shortest setup time (SIMSET) rule provides the best performance for mean flow time and number of tardy jobs measures. The job with similar setup and modified earliest due date (JMEDD) rule provides the best performance for makespan, maximum flow time, mean tardiness, maximum tardiness, total setups and mean setup time measures.

  20. 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.

  1. Application of users’ light-switch stochastic models to dynamic energy simulation

    DEFF Research Database (Denmark)

    Camisassi, V.; Fabi, V.; Andersen, Rune Korsholm

    2015-01-01

    deterministic inputs, due to the uncertain nature of human behaviour. In this paper, new stochastic models of users’ interaction with artificial lighting systems are developed and implemented in the energy simulation software IDA ICE. They were developed from field measurements in an office building in Prague......The design of an innovative building should include building overall energy flows estimation. They are principally related to main six influencing factors (IEA-ECB Annex 53): climate, building envelope and equipment, operation and maintenance, occupant behaviour and indoor environment conditions...

  2. Simulation of quantum dynamics based on the quantum stochastic differential equation.

    Science.gov (United States)

    Li, Ming

    2013-01-01

    The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

  3. Using genetic algorithm to solve a new multi-period stochastic optimization model

    Science.gov (United States)

    Zhang, Xin-Li; Zhang, Ke-Cun

    2009-09-01

    This paper presents a new asset allocation model based on the CVaR risk measure and transaction costs. Institutional investors manage their strategic asset mix over time to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. One may use a multi-period portfolio optimization model in order to determine an optimal asset mix. Recently, an alternative stochastic programming model with simulated paths was proposed by Hibiki [N. Hibiki, A hybrid simulation/tree multi-period stochastic programming model for optimal asset allocation, in: H. Takahashi, (Ed.) The Japanese Association of Financial Econometrics and Engineering, JAFFE Journal (2001) 89-119 (in Japanese); N. Hibiki A hybrid simulation/tree stochastic optimization model for dynamic asset allocation, in: B. Scherer (Ed.), Asset and Liability Management Tools: A Handbook for Best Practice, Risk Books, 2003, pp. 269-294], which was called a hybrid model. However, the transaction costs weren't considered in that paper. In this paper, we improve Hibiki's model in the following aspects: (1) The risk measure CVaR is introduced to control the wealth loss risk while maximizing the expected utility; (2) Typical market imperfections such as short sale constraints, proportional transaction costs are considered simultaneously. (3) Applying a genetic algorithm to solve the resulting model is discussed in detail. Numerical results show the suitability and feasibility of our methodology.

  4. Stochastic evolution of the Universe: A possible dynamical process ...

    Indian Academy of Sciences (India)

    C Sivakumar

    2017-12-11

    Dec 11, 2017 ... https://doi.org/10.1007/s12043-017-1491-z. Stochastic evolution of the Universe: A possible dynamical process leading to fractal structures. C SIVAKUMAR. Department of Physics, Maharaja's College, Ernakulam 682 011, India. E-mail: thrisivc@yahoo.com. MS received 6 July 2016; revised 26 June 2017; ...

  5. The dynamic behaviour of a non-stationary elevator compensating rope system under harmonic and stochastic excitations

    Energy Technology Data Exchange (ETDEWEB)

    Kaczmarczyk, S [School of Applied Sciences, University of Northampton, St. George' s Avenue, Northampton NN2 6JD (United Kingdom); Iwankiewicz, R [Institute of Mechanics and Ocean Engineering, Hamburg University of Technology, Eissendorfer Strasse 42 D-21073, Hamburg (Germany); Terumichi, Y, E-mail: stefan.kaczmarczyk@northampton.ac.u [Faculty of Science and Technology, Sophia University, 7-1 KIOI-CHO, CHIYODAKU, Tokyo, 102-8554 Japan (Japan)

    2009-08-01

    Moving slender elastic elements such as ropes, cables and belts are pivotal components of vertical transportation systems such as traction elevators. Their lengths vary within the host building structure during the elevator operation which results in the change of the mass and stiffness characteristics of the system. The structure of modern high-rise buildings is flexible and when subjected to loads due to strong winds and earthquakes it vibrates at low frequencies. The inertial load induced by the building motion excites the flexible components of the elevator system. The compensating ropes due to their lower tension are particularly affected and undergo large dynamic deformations. The paper focuses on the presentation of the non-stationary model of a building-compensating rope system and on the analysis to predict its dynamic response. The excitation mechanism is represented by a harmonic process and the results of computer simulations to predict transient resonance response are presented. The analysis of the simulation results leads to recommendations concerning the selection of the weight of the compensation assembly to minimize the effects of an adverse dynamic response of the system. The scenario when the excitation is represented as a narrow-band stochastic process with the state vector governed by stochastic equations is then discussed and the stochastic differential equations governing the second-order statistical moments of the state vector are developed.

  6. Integral projection models for finite populations in a stochastic environment.

    Science.gov (United States)

    Vindenes, Yngvild; Engen, Steinar; Saether, Bernt-Erik

    2011-05-01

    Continuous types of population structure occur when continuous variables such as body size or habitat quality affect the vital parameters of individuals. These structures can give rise to complex population dynamics and interact with environmental conditions. Here we present a model for continuously structured populations with finite size, including both demographic and environmental stochasticity in the dynamics. Using recent methods developed for discrete age-structured models we derive the demographic and environmental variance of the population growth as functions of a continuous state variable. These two parameters, together with the expected population growth rate, are used to define a one-dimensional diffusion approximation of the population dynamics. Thus, a substantial reduction in complexity is achieved as the dynamics of the complex structured model can be described by only three population parameters. We provide methods for numerical calculation of the model parameters and demonstrate the accuracy of the diffusion approximation by computer simulation of specific examples. The general modeling framework makes it possible to analyze and predict future dynamics and extinction risk of populations with various types of structure, and to explore consequences of changes in demography caused by, e.g., climate change or different management decisions. Our results are especially relevant for small populations that are often of conservation concern.

  7. 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.

  8. 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.

  9. Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras

    Science.gov (United States)

    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.

  10. Stochastic Alternating Dynamics for Synchronous EAD-Like Beating Rhythms in Cultured Cardiac Myocytes

    Institute of Scientific and Technical Information of China (English)

    ZHANG Ning; ZHANG Hui-Min; LIU Zhi-Qiang; DING Xue-Li; YANG Ming-Hao; GU Hua-Guang; REN Wei

    2009-01-01

    Dissolved cardiac myocytes can couple together and generate synchronous beatings in culture. We observed a synchronized early after-depolarization(EAD)-like rhythm in cultured cardiac myocytes and reproduced the experimental observation in a network mathematical model whose dynamics are close to a Hopf bifurcation. The mechanism for this EAD-like rhythm is attributed to noised-induced stochastic alternatings between the focus and the limit cycle. These results provide novel understandings for pathological heart rhythms like the early immature beatings.

  11. Stochastic Watershed Models for Risk Based Decision Making

    Science.gov (United States)

    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

  12. e-Dairy: a dynamic and stochastic whole-farm model that predicts biophysical and economic performance of grazing dairy systems.

    Science.gov (United States)

    Baudracco, J; Lopez-Villalobos, N; Holmes, C W; Comeron, E A; Macdonald, K A; Barry, T N

    2013-05-01

    A whole-farm, stochastic and dynamic simulation model was developed to predict biophysical and economic performance of grazing dairy systems. Several whole-farm models simulate grazing dairy systems, but most of them work at a herd level. This model, named e-Dairy, differs from the few models that work at an animal level, because it allows stochastic behaviour of the genetic merit of individual cows for several traits, namely, yields of milk, fat and protein, live weight (LW) and body condition score (BCS) within a whole-farm model. This model accounts for genetic differences between cows, is sensitive to genotype × environment interactions at an animal level and allows pasture growth, milk and supplements price to behave stochastically. The model includes an energy-based animal module that predicts intake at grazing, mammary gland functioning and body lipid change. This whole-farm model simulates a 365-day period for individual cows within a herd, with cow parameters randomly generated on the basis of the mean parameter values, defined as input and variance and co-variances from experimental data sets. The main inputs of e-Dairy are farm area, use of land, type of pasture, type of crops, monthly pasture growth rate, supplements offered, nutritional quality of feeds, herd description including herd size, age structure, calving pattern, BCS and LW at calving, probabilities of pregnancy, average genetic merit and economic values for items of income and costs. The model allows to set management policies to define: dry-off cows (ceasing of lactation), target pre- and post-grazing herbage mass and feed supplementation. The main outputs are herbage dry matter intake, annual pasture utilisation, milk yield, changes in BCS and LW, economic farm profit and return on assets. The model showed satisfactory accuracy of prediction when validated against two data sets from farmlet system experiments. Relative prediction errors were <10% for all variables, and concordance

  13. Kinetic theory of age-structured stochastic birth-death processes

    Science.gov (United States)

    Greenman, Chris D.; Chou, Tom

    2016-01-01

    Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

  14. Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.

    Science.gov (United States)

    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.

  15. 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......Stochastic processes and their rst passage times have been widely used to describe the membrane potential dynamics of single neurons and to reproduce neuronal spikes, respectively.However, cerebral cortex in human brains is estimated to contain 10-20 billions of neurons and each of them...... 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...

  16. 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...

  17. On the precision of quasi steady state assumptions in stochastic dynamics

    Science.gov (United States)

    Agarwal, Animesh; Adams, Rhys; Castellani, Gastone C.; Shouval, Harel Z.

    2012-07-01

    Many biochemical networks have complex multidimensional dynamics and there is a long history of methods that have been used for dimensionality reduction for such reaction networks. Usually a deterministic mass action approach is used; however, in small volumes, there are significant fluctuations from the mean which the mass action approach cannot capture. In such cases stochastic simulation methods should be used. In this paper, we evaluate the applicability of one such dimensionality reduction method, the quasi-steady state approximation (QSSA) [L. Menten and M. Michaelis, "Die kinetik der invertinwirkung," Biochem. Z 49, 333369 (1913)] for dimensionality reduction in case of stochastic dynamics. First, the applicability of QSSA approach is evaluated for a canonical system of enzyme reactions. Application of QSSA to such a reaction system in a deterministic setting leads to Michaelis-Menten reduced kinetics which can be used to derive the equilibrium concentrations of the reaction species. In the case of stochastic simulations, however, the steady state is characterized by fluctuations around the mean equilibrium concentration. Our analysis shows that a QSSA based approach for dimensionality reduction captures well the mean of the distribution as obtained from a full dimensional simulation but fails to accurately capture the distribution around that mean. Moreover, the QSSA approximation is not unique. We have then extended the analysis to a simple bistable biochemical network model proposed to account for the stability of synaptic efficacies; the substrate of learning and memory [J. E. Lisman, "A mechanism of memory storage insensitive to molecular turnover: A bistable autophosphorylating kinase," Proc. Natl. Acad. Sci. U.S.A. 82, 3055-3057 (1985)], 10.1073/pnas.82.9.3055. Our analysis shows that a QSSA based dimensionality reduction method results in errors as big as two orders of magnitude in predicting the residence times in the two stable states.

  18. Development of a generalized stochastic model for the analysis of monoenergetic space-time nuclear factor Kinetics

    International Nuclear Information System (INIS)

    Pham, Nhu Viet Ha

    2011-02-01

    To predict the space-time dependent behavior of a nuclear reactor, the conventional space-dependent kinetics equations are widely used for treating the spatial variables. However, the solutions of such deterministic space-dependent kinetics equations, which give only the mean values of the neutron population and the delayed neutron precursor concentrations, do not offer sufficient insight into the actual dynamic processes within a reactor, where the interacting populations vary randomly with space and time. It is also noted that at high power levels, the random behavior of a reactor is negligible but at low power levels, such as at start-up, random fluctuations in population dynamics can be significant. To mathematically describe the evolution of the state of a nuclear reactor using a set of stochastic kinetics equations, the forward stochastic model (FSM) in stochastic kinetics theory is devised through the concept of reactor transition probability and its probability generating function as the spatial domain of a reactor is partitioned into a number of space cells. Nevertheless, the FSM equations for the mean value of neutron and precursor distribution are deterministic-like. Furthermore, the numerical treatment of the FSM equations for the means, variances, and covariances is quite complicated and time-consuming. In the present study, a generalized stochastic model (called the stochastic space-dependent kinetics model or SSKM) based on the FSM and the Its stochastic differential equations was newly developed for the analysis of monoenergetic spacetime nuclear reactor kinetics in one dimension. First, the FSM equations for determining the mean values of neutron and delayed-neutron precursor populations were considered as the deterministic ones without taking into account their variances and covariances. Second, the system of interest was randomized again in the light of the Its stochastic differential equations in order to derive the SSKM. The proposed model

  19. Stochastic Dynamics through Hierarchically Embedded Markov Chains.

    Science.gov (United States)

    Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M

    2017-02-03

    Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.

  20. Consentaneous agent-based and stochastic model of the financial markets.

    Science.gov (United States)

    Gontis, Vygintas; Kononovicius, Aleksejus

    2014-01-01

    We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes the exceptional value of well defined analytically tractable agent systems. Herding as one of the behavior peculiarities considered in the behavioral finance is the main property of the agent interactions we deal with in this contribution. Looking for the consentaneous agent-based and macroscopic approach we combine two origins of the noise: exogenous one, related to the information flow, and endogenous one, arising form the complex stochastic dynamics of agents. As a result we propose a three state agent-based herding model of the financial markets. From this agent-based model we derive a set of stochastic differential equations, which describes underlying macroscopic dynamics of agent population and log price in the financial markets. The obtained solution is then subjected to the exogenous noise, which shapes instantaneous return fluctuations. We test both Gaussian and q-Gaussian noise as a source of the short term fluctuations. The resulting model of the return in the financial markets with the same set of parameters reproduces empirical probability and spectral densities of absolute return observed in New York, Warsaw and NASDAQ OMX Vilnius Stock Exchanges. Our result confirms the prevalent idea in behavioral finance that herding interactions may be dominant over agent rationality and contribute towards bubble formation.

  1. On an aggregation in birth-and-death stochastic dynamics

    Science.gov (United States)

    Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr; Zhizhina, Elena

    2014-06-01

    We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation.

  2. On an aggregation in birth-and-death stochastic dynamics

    International Nuclear Information System (INIS)

    Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr; Zhizhina, Elena

    2014-01-01

    We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation. (paper)

  3. Development of dynamic Bayesian models for web application test management

    Science.gov (United States)

    Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

    2018-03-01

    The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

  4. A model based on stochastic dynamic programming for determining China's optimal strategic petroleum reserve policy

    International Nuclear Information System (INIS)

    Zhang Xiaobing; Fan Ying; Wei Yiming

    2009-01-01

    China's Strategic Petroleum Reserve (SPR) is currently being prepared. But how large the optimal stockpile size for China should be, what the best acquisition strategies are, how to release the reserve if a disruption occurs, and other related issues still need to be studied in detail. In this paper, we develop a stochastic dynamic programming model based on a total potential cost function of establishing SPRs to evaluate the optimal SPR policy for China. Using this model, empirical results are presented for the optimal size of China's SPR and the best acquisition and drawdown strategies for a few specific cases. The results show that with comprehensive consideration, the optimal SPR size for China is around 320 million barrels. This size is equivalent to about 90 days of net oil import amount in 2006 and should be reached in the year 2017, three years earlier than the national goal, which implies that the need for China to fill the SPR is probably more pressing; the best stockpile release action in a disruption is related to the disruption levels and expected continuation probabilities. The information provided by the results will be useful for decision makers.

  5. 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

  6. 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...... 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...

  7. Test models for improving filtering with model errors through stochastic parameter estimation

    International Nuclear Information System (INIS)

    Gershgorin, B.; Harlim, J.; Majda, A.J.

    2010-01-01

    The filtering skill for turbulent signals from nature is often limited by model errors created by utilizing an imperfect model for filtering. Updating the parameters in the imperfect model through stochastic parameter estimation is one way to increase filtering skill and model performance. Here a suite of stringent test models for filtering with stochastic parameter estimation is developed based on the Stochastic Parameterization Extended Kalman Filter (SPEKF). These new SPEKF-algorithms systematically correct both multiplicative and additive biases and involve exact formulas for propagating the mean and covariance including the parameters in the test model. A comprehensive study is presented of robust parameter regimes for increasing filtering skill through stochastic parameter estimation for turbulent signals as the observation time and observation noise are varied and even when the forcing is incorrectly specified. The results here provide useful guidelines for filtering turbulent signals in more complex systems with significant model errors.

  8. Modelling and application of stochastic processes

    CERN Document Server

    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,...

  9. 100 years after Smoluchowski: stochastic processes in cell biology

    International Nuclear Information System (INIS)

    Holcman, D; Schuss, Z

    2017-01-01

    100 years after Smoluchowski introduced his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from a large number (tens of thousands) of single molecular trajectories or to study the diffusive motion of molecules, proteins or receptors. Stochastic modeling is a new step in large data analysis that serves extracting cell biology concepts. We review here Smoluchowski’s approach to stochastic processes and provide several applications for coarse-graining diffusion, studying polymer models for understanding nuclear organization and finally, we discuss the stochastic jump dynamics of telomeres across cell division and stochastic gene regulation. (topical review)

  10. 12th Workshop on Stochastic Models, Statistics and Their Applications

    CERN Document Server

    Rafajłowicz, Ewaryst; Szajowski, Krzysztof

    2015-01-01

    This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.

  11. Lévy stable noise-induced transitions: stochastic resonance, resonant activation and dynamic hysteresis

    International Nuclear Information System (INIS)

    Dybiec, Bartłomiej; Gudowska-Nowak, Ewa

    2009-01-01

    A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the existence of timescale separation between the dynamics of the measured observable and the typical timescale of the noise allows external fluctuations to be modeled as temporally uncorrelated and therefore white. However, in many natural phenomena the assumptions concerning the above mentioned properties of 'Gaussianity' and 'whiteness' of the noise can be violated. In this context, in contrast to the spatiotemporal coupling characterizing general forms of non-Markovian or semi-Markovian Lévy walks, so called Lévy flights correspond to the class of Markov processes which can still be interpreted as white, but distributed according to a more general, infinitely divisible, stable and non-Gaussian law. Lévy noise-driven non-equilibrium systems are known to manifest interesting physical properties and have been addressed in various scenarios of physical transport exhibiting a superdiffusive behavior. Here we present a brief overview of our recent investigations aimed at understanding features of stochastic dynamics under the influence of Lévy white noise perturbations. We find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by memoryless, non-Gaussian, heavy-tailed fluctuations with infinite variance

  12. Toward an innovative stochastic modeling of electric charges loss through dielectric

    Directory of Open Access Journals (Sweden)

    Micolau G.

    2016-01-01

    Full Text Available This paper deals with new stochastic modeling of very low tunneling currents in Non-Volatile Memories. For this purpose, we first develop current measurement method based on Floating Gate technique. In order to reach the long time behavior of electrical dynamic, we aim at using very basic tools (power supply, multimeter... but still having a very good current resolution. Also, our measurement is led in a very particular low-noise environment (underground laboratory allowing to keep the electrical contacts on the device under test as long as possible. After showing the feasibility of such measurements, we present a modeling approach of the charge loss process inside the Non-volatile Memories by using mathematical tool involving long memory effect. The model is based on stochastic counting process with memory effect yielding to a fractional relaxation equation for the charge loss over time. The main interest of the present model lies in the fact that the corresponding inversion problem involves only two parameters that can be carried out efficiently.

  13. Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations

    Science.gov (United States)

    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.

  14. Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical Networks

    Directory of Open Access Journals (Sweden)

    Simon Rosenfeld

    2009-01-01

    Full Text Available The question of dynamical stability and stochastic behavior of large biochemical networks is discussed. It is argued that stringent conditions of asymptotic stability have very little chance to materialize in a multidimensional system described by the differential equations of chemical kinetics. The reason is that the criteria of asymptotic stability (Routh- Hurwitz, Lyapunov criteria, Feinberg’s Deficiency Zero theorem would impose the limitations of very high algebraic order on the kinetic rates and stoichiometric coefficients, and there are no natural laws that would guarantee their unconditional validity. Highly nonlinear, dynamically unstable systems, however, are not necessarily doomed to collapse, as a simple Jacobian analysis would suggest. It is possible that their dynamics may assume the form of pseudo-random fluctuations quite similar to a shot noise, and, therefore, their behavior may be described in terms of Langevin and Fokker-Plank equations. We have shown by simulation that the resulting pseudo-stochastic processes obey the heavy-tailed Generalized Pareto Distribution with temporal sequence of pulses forming the set of constituent-specific Poisson processes. Being applied to intracellular dynamics, these properties are naturally associated with burstiness, a well documented phenomenon in the biology of gene expression.

  15. A Dynamic Momentum Compaction Factor Lattice for Improvements to Stochastic Cooling in Storage Rings

    Energy Technology Data Exchange (ETDEWEB)

    Olivieri, David Nicholas [Massachusetts U., Amherst

    1996-01-01

    A dynamic momentum compaction factor, also referred to as a dynamic $\\Delta \\gamma \\tau$, lattice for the FNAL Antiproton Source Debuncher Storage Ring is studied, both theoretically and experimentally, for the purpose of improving stochastic precooling, and hence, improving the global antiproton production and stacking performance. A dynamic $\\Delta \\gamma \\tau$ lattice is proposed due to the competing requirements inherent within the Debuncher storage ring upon $\\gamma \\tau$· Specifically, the Debuncher storage ring performs two disparate functions, $(i)$ accepting and debunching a large number of $\\overline{p}$s/pulse at the outset of the production cycle, which would perform ideally with a large value of $\\gamma\\tau$, and $(ii)$ subsequently employing stochastic cooling throughout the remainder of the $\\overline{p}$ production cycle for improved transfer and stacking efficiency into the Accumulator, for which a small value $\\gamma \\tau$ is ideal in order to reduce the diffusive heating caused by the mixing factor. In the initial design of the Debuncher optical lattice, an intermediate value of $\\gamma \\tau$ was chosen as a compromise between the two functional requirements. The goal of the thesis is to improve stochastic precooling by changing $\\gamma \\tau$ between two desired values during each p production cycle. In particular, the dynamic $\\Delta \\gamma \\tau$ lattice accomplishes a reduction in $\\gamma \\tau$, and hence the mixing factor, through an uniform increase to the dispersion throughout the arc sections of the storage ring. Experimental measurements of cooling rates and system performance parameters, with the implementation of the dynamic $\\Delta \\gamma \\tau$ lattice, are in agreement with theoretical predictions based upon a detailed integration of the stochastic cooling Fokker Planck equations. Based upon the consistency between theory and experiment, predictions of cooling rates are presented for future operational

  16. Dynamical phase transitions in spin models and automata

    International Nuclear Information System (INIS)

    Derrida, B.

    1989-01-01

    Some of the models and methods developed in the study of the dynamics of spin models and automata are described. Special attention is given to the distance method which consists of comparing the time evolution of two configurations. The method is used to obtain the phase boundary between a frozen and a chaotic phase in the case of deterministic models. For stochastic systems the method is used to obtain dynamical phase transitions

  17. Trip-oriented stochastic optimal energy management strategy for plug-in hybrid electric bus

    International Nuclear Information System (INIS)

    Du, Yongchang; Zhao, Yue; Wang, Qinpu; Zhang, Yuanbo; Xia, Huaicheng

    2016-01-01

    A trip-oriented stochastic optimal energy management strategy for plug-in hybrid electric bus is presented in this paper, which includes the offline stochastic dynamic programming part and the online implementation part performed by equivalent consumption minimization strategy. In the offline part, historical driving cycles of the fixed route are divided into segments according to the position of bus stops, and then a segment-based stochastic driving condition model based on Markov chain is built. With the segment-based stochastic model obtained, the control set for real-time implemented equivalent consumption minimization strategy can be achieved by solving the offline stochastic dynamic programming problem. Results of stochastic dynamic programming are converted into a 3-dimensional lookup table of parameters for online implemented equivalent consumption minimization strategy. The proposed strategy is verified by both simulation and hardware-in-loop test of real-world driving cycle on an urban bus route. Simulation results show that the proposed method outperforms both the well-tuned equivalent consumption minimization strategy and the rule-based strategy in terms of fuel economy, and even proved to be close to the optimal result obtained by dynamic programming. Furthermore, the practical application potential of the proposed control method was proved by hardware-in-loop test. - Highlights: • A stochastic problem was formed based on a stochastic segment-based driving condition model. • Offline stochastic dynamic programming was employed to solve the stochastic problem. • The instant power split decision was made by the online equivalent consumption minimization strategy. • Good performance in fuel economy of the proposed method was verified by simulation results. • Practical application potential of the proposed method was verified by the hardware-in-loop test results.

  18. Dynamic Asset Allocation with Stochastic Income and Interest Rates

    DEFF Research Database (Denmark)

    Munk, Claus; Sørensen, Carsten

    2010-01-01

    We solve for optimal portfolios when interest rates and labor income are stochastic with the expected income growth being affine in the short-term interest rate in order to encompass business cycle variations in wages. Our calibration based on the Panel Study of Income Dynamics (PSID) data supports...

  19. 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.

  20. A Stochastic After-Taxes Optimisation Model to Support Distribution Network Strategies

    DEFF Research Database (Denmark)

    Fernandes, Rui; Hvolby, Hans-Henrik; Gouveia, Borges

    2012-01-01

    The paper proposes a stochastic model to integrate tax issues into strategic distribution network decisions. Specifically, this study will explore the role of distribution models in business profitability, and how to use the network design to deliver additional bottom-line results, using...... distribution centres located in different countries. The challenge is also to reveal how financial and tax knowledge can help logistic leaders improving the value to their companies under global solutions and sources of business net profitability in a dynamic environment. In particular, based on inventory...

  1. Stochastic linearization of turbulent dynamics of dispersive waves in equilibrium and non-equilibrium state

    International Nuclear Information System (INIS)

    Jiang, Shixiao W; Lu, Haihao; Zhou, Douglas; Cai, David

    2016-01-01

    Characterizing dispersive wave turbulence in the long time dynamics is central to understanding of many natural phenomena, e.g., in atmosphere ocean dynamics, nonlinear optics, and plasma physics. Using the β -Fermi–Pasta–Ulam nonlinear system as a prototypical example, we show that in thermal equilibrium and non-equilibrium steady state the turbulent state even in the strongly nonlinear regime possesses an effective linear stochastic structure in renormalized normal variables. In this framework, we can well characterize the spatiotemporal dynamics, which are dominated by long-wavelength renormalized waves. We further demonstrate that the energy flux is nearly saturated by the long-wavelength renormalized waves in non-equilibrium steady state. The scenario of such effective linear stochastic dynamics can be extended to study turbulent states in other nonlinear wave systems. (paper)

  2. Health safety nets can break cycles of poverty and disease: a stochastic ecological model.

    Science.gov (United States)

    Plucinski, Mateusz M; Ngonghala, Calistus N; Bonds, Matthew H

    2011-12-07

    The persistence of extreme poverty is increasingly attributed to dynamic interactions between biophysical processes and economics, though there remains a dearth of integrated theoretical frameworks that can inform policy. Here, we present a stochastic model of disease-driven poverty traps. Whereas deterministic models can result in poverty traps that can only be broken by substantial external changes to the initial conditions, in the stochastic model there is always some probability that a population will leave or enter a poverty trap. We show that a 'safety net', defined as an externally enforced minimum level of health or economic conditions, can guarantee ultimate escape from a poverty trap, even if the safety net is set within the basin of attraction of the poverty trap, and even if the safety net is only in the form of a public health measure. Whereas the deterministic model implies that small improvements in initial conditions near the poverty-trap equilibrium are futile, the stochastic model suggests that the impact of changes in the location of the safety net on the rate of development may be strongest near the poverty-trap equilibrium.

  3. A cavitation model based on Eulerian stochastic fields

    Science.gov (United States)

    Magagnato, F.; Dumond, J.

    2013-12-01

    Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

  4. Stochastic quantization for the axial model

    International Nuclear Information System (INIS)

    Farina, C.; Montani, H.; Albuquerque, L.C.

    1991-01-01

    We use bosonization ideas to solve the axial model in the stochastic quantization framework. We obtain the fermion propagator of the theory decoupling directly the Langevin equation, instead of the Fokker-Planck equation. In the Appendix we calculate explicitly the anomalous divergence of the axial-vector current by using a regularization that does not break the Markovian character of the stochastic process

  5. Stochastic model simulation using Kronecker product analysis and Zassenhaus formula approximation.

    Science.gov (United States)

    Caglar, Mehmet Umut; Pal, Ranadip

    2013-01-01

    Probabilistic Models are regularly applied in Genetic Regulatory Network modeling to capture the stochastic behavior observed in the generation of biological entities such as mRNA or proteins. Several approaches including Stochastic Master Equations and Probabilistic Boolean Networks have been proposed to model the stochastic behavior in genetic regulatory networks. It is generally accepted that Stochastic Master Equation is a fundamental model that can describe the system being investigated in fine detail, but the application of this model is computationally enormously expensive. On the other hand, Probabilistic Boolean Network captures only the coarse-scale stochastic properties of the system without modeling the detailed interactions. We propose a new approximation of the stochastic master equation model that is able to capture the finer details of the modeled system including bistabilities and oscillatory behavior, and yet has a significantly lower computational complexity. In this new method, we represent the system using tensors and derive an identity to exploit the sparse connectivity of regulatory targets for complexity reduction. The algorithm involves an approximation based on Zassenhaus formula to represent the exponential of a sum of matrices as product of matrices. We derive upper bounds on the expected error of the proposed model distribution as compared to the stochastic master equation model distribution. Simulation results of the application of the model to four different biological benchmark systems illustrate performance comparable to detailed stochastic master equation models but with considerably lower computational complexity. The results also demonstrate the reduced complexity of the new approach as compared to commonly used Stochastic Simulation Algorithm for equivalent accuracy.

  6. Analysis of stochastic effects in Kaldor-type business cycle discrete model

    Science.gov (United States)

    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.

  7. Economic analysis of energy system considering the uncertainties of crude oil, natural gas and nuclear utilization employing stochastic dynamic programming

    International Nuclear Information System (INIS)

    Hasegawa, Keita; Komiyama, Ryoichi; Fujii, Yasumasa

    2016-01-01

    The paper presents an economic rationality analysis of power generation mix by stochastic dynamic programming considering fuel price uncertainties and supply disruption risks such as import disruption and nuclear power plant shutdown risk. The situation revolving around Japan's energy security adopted the past statistics, it cannot be applied to a quantitative analysis of future uncertainties. Further objective and quantitative evaluation methods are required in order to analyze Japan's energy system and make it more resilient in sight of long time scale. In this paper, the authors firstly develop the cost minimization model considering oil and natural gas price respectively by stochastic dynamic programming. Then, the authors show several premises of model and an example of result with related to crude oil stockpile, liquefied natural gas stockpile and nuclear power plant capacity. (author)

  8. Stochastic fusion of dynamic hydrological and geophysical data for estimating hydraulic conductivities: insights and observations (Invited)

    Science.gov (United States)

    Irving, J. D.; Singha, K.

    2010-12-01

    Traditionally, hydrological measurements have been used to estimate subsurface properties controlling groundwater flow and contaminant transport. However, such measurements are limited by their support volume and expense. A considerable benefit of geophysical measurements is that they provide a degree of spatial coverage and resolution that are unattainable with other methods, and the data can be acquired in a cost-effective manner. In particular, dynamic geophysical data allow us to indirectly observe changes in hydrological state variables as flow and transport processes occur, and can thus provide a link to hydrological properties when coupled with a process-based model. Stochastic fusion of these two data types offers the potential to provide not only estimates of subsurface hydrological properties, but also a quantification of their uncertainty. This information is critical when considering the end use of the data, which may be for groundwater remediation and management decision making. Here, we examine a number of key issues in the stochastic fusion of dynamic hydrogeophysical data. We focus our attention on the specific problem of integrating time-lapse crosshole electrical resistivity measurements and saline tracer-test concentration data in order to estimate the spatial distribution of hydraulic conductivity (K). To assimilate the geophysical and hydrological measurements in a stochastic manner, we use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology. This provides multiple realizations of the subsurface K field that are consistent with the measured data and assumptions regarding model structure and data errors. To account for incomplete petrophysical knowledge, the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration following the general form of Archie’s law. To make the spatially distributed, fully stochastic inverse problem computationally tractable, we take

  9. Optimization of environmental management strategies through a dynamic stochastic possibilistic multiobjective program

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Xiaodong, E-mail: xiaodong.zhang@beg.utexas.edu [Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX 78713 (United States); Huang, Gordon [Institute of Energy, Environment and Sustainable Communities, University of Regina, Regina, Saskatchewan S4S 0A2 (Canada)

    2013-02-15

    Highlights: ► A dynamic stochastic possibilistic multiobjective programming model is developed. ► Greenhouse gas emission control is considered. ► Three planning scenarios are analyzed and compared. ► Optimal decision schemes under three scenarios and different p{sub i} levels are obtained. ► Tradeoffs between economics and environment are reflected. -- Abstract: Greenhouse gas (GHG) emissions from municipal solid waste (MSW) management facilities have become a serious environmental issue. In MSW management, not only economic objectives but also environmental objectives should be considered simultaneously. In this study, a dynamic stochastic possibilistic multiobjective programming (DSPMP) model is developed for supporting MSW management and associated GHG emission control. The DSPMP model improves upon the existing waste management optimization methods through incorporation of fuzzy possibilistic programming and chance-constrained programming into a general mixed-integer multiobjective linear programming (MOP) framework where various uncertainties expressed as fuzzy possibility distributions and probability distributions can be effectively reflected. Two conflicting objectives are integrally considered, including minimization of total system cost and minimization of total GHG emissions from waste management facilities. Three planning scenarios are analyzed and compared, representing different preferences of the decision makers for economic development and environmental-impact (i.e. GHG-emission) issues in integrated MSW management. Optimal decision schemes under three scenarios and different p{sub i} levels (representing the probability that the constraints would be violated) are generated for planning waste flow allocation and facility capacity expansions as well as GHG emission control. The results indicate that economic and environmental tradeoffs can be effectively reflected through the proposed DSPMP model. The generated decision variables can help

  10. 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.

  11. Collective, stochastic and nonequilibrium behavior of highly excited hadronic matter

    Energy Technology Data Exchange (ETDEWEB)

    Carruthers, P [Los Alamos National Lab., NM (USA). Theoretical Div.

    1984-04-23

    We discuss selected problems concerning the dynamics and stochastic behavior of highly excited matter, particularly the QCD plasma. For the latter we consider the equation of state, kinetics, quasiparticles, flow properties and possible chaos and turbulence. The promise of phase space distribution functions for covariant transport and kinetic theory is stressed. The possibility and implications of a stochastic bag are spelled out. A simplified space-time model of hadronic collisions is pursued, with applications to A-A collisions and other matters. The domain wall between hadronic and plasma phase is of potential importance: its thickness and relation to surface tension is noticed. Finally, we review the recently developed stochastic cell model of multiparticle distributions and KNO scaling. This topic leads to the notion that fractional dimensions are involved in a rather general dynamical context. We speculate that various scaling phenomena are independent of the full dynamical structure, depending only on a general stochastic framework having to do with simple maps and strange attractors. 42 refs.

  12. Tsunamis: stochastic models of occurrence and generation mechanisms

    Science.gov (United States)

    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.

  13. 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...

  14. 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...

  15. Dislocation climb models from atomistic scheme to dislocation dynamics

    OpenAIRE

    Niu, Xiaohua; Luo, Tao; Lu, Jianfeng; Xiang, Yang

    2016-01-01

    We develop a mesoscopic dislocation dynamics model for vacancy-assisted dislocation climb by upscalings from a stochastic model on the atomistic scale. Our models incorporate microscopic mechanisms of (i) bulk diffusion of vacancies, (ii) vacancy exchange dynamics between bulk and dislocation core, (iii) vacancy pipe diffusion along the dislocation core, and (iv) vacancy attachment-detachment kinetics at jogs leading to the motion of jogs. Our mesoscopic model consists of the vacancy bulk dif...

  16. Price dynamics of the financial markets using the stochastic differential equation for a potential double well

    Science.gov (United States)

    Lima, L. S.; Miranda, L. L. B.

    2018-01-01

    We have used the Itô's stochastic differential equation for the double well with additive white noise as a mathematical model for price dynamics of the financial market. We have presented a model which allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents, with respect to the facts of financial markets. We have obtained the mean price in terms of the β parameter that represents the force of the randomness term of the model.

  17. Dynamic analysis of stochastic bidirectional associative memory neural networks with delays

    International Nuclear Information System (INIS)

    Zhao Hongyong; Ding Nan

    2007-01-01

    In this paper, stochastic bidirectional associative memory neural networks model with delays is considered. By constructing Lyapunov functionals, and using stochastic analysis method and inequality technique, we give some sufficient criteria ensuring almost sure exponential stability, pth exponential stability and mean value exponential stability. The obtained criteria can be used as theoretic guidance to stabilize neural networks in practical applications when stochastic noise is taken into consideration

  18. Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

    Science.gov (United States)

    Manzione, Rodrigo L.; Wendland, Edson; Tanikawa, Diego H.

    2012-11-01

    Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.

  19. Renormalization group and instantons in stochastic nonlinear dynamics, from self-organized criticality to thermonuclear reactors

    International Nuclear Information System (INIS)

    Volchenkov, D.

    2009-01-01

    Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magnetohydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications. (author)

  20. Renormalization group and instantons in stochastic nonlinear dynamics, from self-organized criticality to thermonuclear reactors

    Energy Technology Data Exchange (ETDEWEB)

    Volchenkov, D. [Bielefeld Univ., Center of Excellence Cognitive Interaction Technology (CITEC) (Germany)

    2009-03-15

    Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magnetohydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications. (author)

  1. Modeling dynamic swarms

    KAUST Repository

    Ghanem, Bernard

    2013-01-01

    This paper proposes the problem of modeling video sequences of dynamic swarms (DSs). We define a DS as a large layout of stochastically repetitive spatial configurations of dynamic objects (swarm elements) whose motions exhibit local spatiotemporal interdependency and stationarity, i.e., the motions are similar in any small spatiotemporal neighborhood. Examples of DS abound in nature, e.g., herds of animals and flocks of birds. To capture the local spatiotemporal properties of the DS, we present a probabilistic model that learns both the spatial layout of swarm elements (based on low-level image segmentation) and their joint dynamics that are modeled as linear transformations. To this end, a spatiotemporal neighborhood is associated with each swarm element, in which local stationarity is enforced both spatially and temporally. We assume that the prior on the swarm dynamics is distributed according to an MRF in both space and time. Embedding this model in a MAP framework, we iterate between learning the spatial layout of the swarm and its dynamics. We learn the swarm transformations using ICM, which iterates between estimating these transformations and updating their distribution in the spatiotemporal neighborhoods. We demonstrate the validity of our method by conducting experiments on real and synthetic video sequences. Real sequences of birds, geese, robot swarms, and pedestrians evaluate the applicability of our model to real world data. © 2012 Elsevier Inc. All rights reserved.

  2. High-energy hadron dynamics based on a stochastic-field multieikonal theory

    International Nuclear Information System (INIS)

    Arnold, R.C.

    1977-01-01

    Multieikonal theory, using a stochastic-field representation for collective long-range rapidity correlations, is developed and applied to the calculation of Regge-pole parameters, high-transverse-momentum enhancements, and fluctuation patterns in rapidity densities. If a short-range-order model, such as the one-dimensional planar bootstrap, with only leading t-channel meson poles, is utilized as input to the multieikonal method, the pole spectrum is modified in three ways: promotion and renormalization of leading trajectories (suggesting an effective Pomeron above unity at intermediate energies), and a proliferation of dynamical secondary trajectories, reminiscent of dual models. When transverse dimensions are included, the collective effects produce a growth with energy of large-P/sub T/ inclusive cross sections. Typical-event rapidity distributions, at energies of a few TeV, can be estimated by suitable approximations; the fluctuations give rise to ''domain'' patterns, which have the appearance of clusters separated by rapidity gaps. The relations between this approach to strong-interaction dynamics and a possible unification of weak, electromagnetic, and strong interactions are outlined

  3. Modeling stochasticity in biochemical reaction networks

    International Nuclear Information System (INIS)

    Constantino, P H; Vlysidis, M; Smadbeck, P; Kaznessis, Y N

    2016-01-01

    Small biomolecular systems are inherently stochastic. Indeed, fluctuations of molecular species are substantial in living organisms and may result in significant variation in cellular phenotypes. The chemical master equation (CME) is the most detailed mathematical model that can describe stochastic behaviors. However, because of its complexity the CME has been solved for only few, very small reaction networks. As a result, the contribution of CME-based approaches to biology has been very limited. In this review we discuss the approach of solving CME by a set of differential equations of probability moments, called moment equations. We present different approaches to produce and to solve these equations, emphasizing the use of factorial moments and the zero information entropy closure scheme. We also provide information on the stability analysis of stochastic systems. Finally, we speculate on the utility of CME-based modeling formalisms, especially in the context of synthetic biology efforts. (topical review)

  4. Stochastic factor model for electricity spot price-the case of the Nordic market

    International Nuclear Information System (INIS)

    Vehvilaeinen, Iivo; Pyykkoenen, Tuomas

    2005-01-01

    This paper presents a stochastic factor based approach to mid-term modeling of spot prices in deregulated electricity markets. The fundamentals affecting the spot price are modeled independently and a market equilibrium model combines them to form spot price. Main advantage of the model is the transparency of the generated prices because each underlying factor and the dynamics between factors can be modeled and studied in detail. Paper shows realistic numerical examples on the forerunner Scandinavian electricity market. The model is used to price an exotic electricity derivative

  5. Stochastic factor model for electricity spot price - the case of the Nordic market

    International Nuclear Information System (INIS)

    Vehvilainen, I.; Pyykkoenen, T.

    2005-01-01

    This paper presents a stochastic factor based approach to mid-term modeling of spot prices in deregulated electricity markets. The fundamentals affecting the spot price are modeled independently and a market equilibrium model combines them to form spot price. Main advantage of the model is the transparency of the generated prices because each underlying factor and the dynamics between factors can be modeled and studied in detail. Paper shows realistic numerical examples on the forerunner Scandinavian electricity market. The model is used to price an exotic electricity derivative. (author)

  6. Applications of Nonlinear Dynamics Model and Design of Complex Systems

    CERN Document Server

    In, Visarath; Palacios, Antonio

    2009-01-01

    This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

  7. Dynamical reduction models with general gaussian noises

    International Nuclear Information System (INIS)

    Bassi, Angelo; Ghirardi, GianCarlo

    2002-02-01

    We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the statevector, white noise stochastic processes with non white ones. We prove that such a modification can be consistently performed without altering the most interesting features of the previous models. One of the reasons to discuss this matter derives from the desire of being allowed to deal with physical stochastic fields, such as the gravitational one, which cannot give rise to white noises. From our point of view the most relevant motivation for the approach we propose here derives from the fact that in relativistic models the occurrence of white noises is the main responsible for the appearance of untractable divergences. Therefore, one can hope that resorting to non white noises one can overcome such a difficulty. We investigate stochastic equations with non white noises, we discuss their reduction properties and their physical implications. Our analysis has a precise interest not only for the above mentioned subject but also for the general study of dissipative systems and decoherence. (author)

  8. Dynamical reduction models with general Gaussian noises

    International Nuclear Information System (INIS)

    Bassi, Angelo; Ghirardi, GianCarlo

    2002-01-01

    We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the state vector, white-noise stochastic processes with nonwhite ones. We prove that such a modification can be consistently performed without altering the most interesting features of the previous models. One of the reasons to discuss this matter derives from the desire of being allowed to deal with physical stochastic fields, such as the gravitational one, which cannot give rise to white noises. From our point of view, the most relevant motivation for the approach we propose here derives from the fact that in relativistic models intractable divergences appear as a consequence of the white nature of the noises. Therefore, one can hope that resorting to nonwhite noises, one can overcome such a difficulty. We investigate stochastic equations with nonwhite noises, we discuss their reduction properties and their physical implications. Our analysis has a precise interest not only for the above-mentioned subject but also for the general study of dissipative systems and decoherence

  9. Stochastic Dynamics of Clay Translocation and Formation of Argillic Horizons

    Science.gov (United States)

    Calabrese, S.; Richter, D. D., Jr.; Porporato, A. M.

    2017-12-01

    The formation of argillic horizons in vertical soil profiles is mainly attributed to lessivage, namely the transport of clay from an upper E horizon to a deeper illuviated horizon. Because of the long timescales involved in this phenomenon, quantitative modeling is useful to explore the role of clay lessivage on soil formation and sub-surface clay accumulation. The limitations of detailed models of colloidal transport to short timescales make it necessary to resort to simple models. Here, we present a parsimonious model of clay transport in which lessivage is interpreted stochastically. Clay particles approach the soil surface at a speed equal to the erosion rate and are intermittently transported to deeper soil layers when percolation events occur or removed by erosion. Along with the evolution of clay particles trajectories, the model predicts the vertical clay profile, the depth of the B horizon, and the mean time to erosion. Dimensional analysis reveals the two dimensionless parameters governing the dynamics, leading to a new classification of soil types based on erosion rates and intensity of lessivage.

  10. Distributed parallel computing in stochastic modeling of groundwater systems.

    Science.gov (United States)

    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.

  11. Comparison of stochastic resonance in static and dynamical nonlinearities

    International Nuclear Information System (INIS)

    Ma, Yumei; Duan, Fabing

    2014-01-01

    We compare the stochastic resonance (SR) effects in parallel arrays of static and dynamical nonlinearities via the measure of output signal-to-noise ratio (SNR). For a received noisy periodic signal, parallel arrays of both static and dynamical nonlinearities can enhance the output SNR by optimizing the internal noise level. The static nonlinearity is easily implementable, while the dynamical nonlinearity has more parameters to be tuned, at the risk of not exploiting the beneficial role of internal noise components. It is of interest to note that, for an input signal buried in the external Laplacian noise, we show that the dynamical nonlinearity is superior to the static nonlinearity in obtaining a better output SNR. This characteristic is assumed to be closely associated with the kurtosis of noise distribution. - Highlights: • Comparison of SR effects in arrays of both static and dynamical nonlinearities. • Static nonlinearity is easily implementable for the SNR enhancement. • Dynamical nonlinearity yields a better output SNR for external Laplacian noise

  12. Stochastic modeling of total suspended solids (TSS) in urban areas during rain events.

    Science.gov (United States)

    Rossi, Luca; Krejci, Vladimir; Rauch, Wolfgang; Kreikenbaum, Simon; Fankhauser, Rolf; Gujer, Willi

    2005-10-01

    The load of total suspended solids (TSS) is one of the most important parameters for evaluating wet-weather pollution in urban sanitation systems. In fact, pollutants such as heavy metals, polycyclic aromatic hydrocarbons (PAHs), phosphorous and organic compounds are adsorbed onto these particles so that a high TSS load indicates the potential impact on the receiving waters. In this paper, a stochastic model is proposed to estimate the TSS load and its dynamics during rain events. Information on the various simulated processes was extracted from different studies of TSS in urban areas. The model thus predicts the probability of TSS loads arising from combined sewer overflows (CSOs) in combined sewer systems as well as from stormwater in separate sewer systems in addition to the amount of TSS retained in treatment devices in both sewer systems. The results of this TSS model illustrate the potential of the stochastic modeling approach for assessing environmental problems.

  13. Stochastic resonance and coherence resonance in groundwater-dependent plant ecosystems.

    Science.gov (United States)

    Borgogno, Fabio; D'Odorico, Paolo; Laio, Francesco; Ridolfi, Luca

    2012-01-21

    Several studies have shown that non-linear deterministic dynamical systems forced by external random components can give rise to unexpectedly regular temporal behaviors. Stochastic resonance and coherence resonance, the two best known processes of this type, have been studied in a number of physical and chemical systems. Here, we explore their possible occurrence in the dynamics of groundwater-dependent plant ecosystems. To this end, we develop two eco-hydrological models, which allow us to demonstrate that stochastic and coherence resonance may emerge in the dynamics of phreatophyte vegetation, depending on their deterministic properties and the intensity of external stochastic drivers. Copyright © 2011 Elsevier Ltd. All rights reserved.

  14. A Volterra series approach to the approximation of stochastic nonlinear dynamics

    NARCIS (Netherlands)

    Wouw, van de N.; Nijmeijer, H.; Campen, van D.H.

    2002-01-01

    A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system isapproximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this

  15. STOCHASTIC CHARACTERISTICS AND MODELING OF RELATIVE ...

    African Journals Online (AJOL)

    Test

    Results are highly accurate and promising for all models based on Lewis' criteria. ... hydrological cycle. Future increases in ... STOCHASTIC CHARACTERISTICS AND MODELING OF RELATIVE HUMIDITY OF OGUN BASIN, NIGERIA. 71 ...

  16. 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

  17. 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...... are needed for initial defects and damage accumulation. In this paper, stochastic models are formulated considering some of the failure modes observed in these components. The models are based on theoretical considerations, manufacturing uncertainties, size effects of different scales. It is illustrated how...

  18. Applied stochastic modelling

    CERN Document Server

    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...

  19. Evaluation of Stochastic Rainfall Models in Capturing Climate Variability for Future Drought and Flood Risk Assessment

    Science.gov (United States)

    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.

  20. A Markov model for the temporal dynamics of balanced random networks of finite size

    Science.gov (United States)

    Lagzi, Fereshteh; Rotter, Stefan

    2014-01-01

    The balanced state of recurrent networks of excitatory and inhibitory spiking neurons is characterized by fluctuations of population activity about an attractive fixed point. Numerical simulations show that these dynamics are essentially nonlinear, and the intrinsic noise (self-generated fluctuations) in networks of finite size is state-dependent. Therefore, stochastic differential equations with additive noise of fixed amplitude cannot provide an adequate description of the stochastic dynamics. The noise model should, rather, result from a self-consistent description of the network dynamics. Here, we consider a two-state Markovian neuron model, where spikes correspond to transitions from the active state to the refractory state. Excitatory and inhibitory input to this neuron affects the transition rates between the two states. The corresponding nonlinear dependencies can be identified directly from numerical simulations of networks of leaky integrate-and-fire neurons, discretized at a time resolution in the sub-millisecond range. Deterministic mean-field equations, and a noise component that depends on the dynamic state of the network, are obtained from this model. The resulting stochastic model reflects the behavior observed in numerical simulations quite well, irrespective of the size of the network. In particular, a strong temporal correlation between the two populations, a hallmark of the balanced state in random recurrent networks, are well represented by our model. Numerical simulations of such networks show that a log-normal distribution of short-term spike counts is a property of balanced random networks with fixed in-degree that has not been considered before, and our model shares this statistical property. Furthermore, the reconstruction of the flow from simulated time series suggests that the mean-field dynamics of finite-size networks are essentially of Wilson-Cowan type. We expect that this novel nonlinear stochastic model of the interaction between

  1. 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.

  2. 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

  3. 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.

  4. Theory on the Coupled Stochastic Dynamics of Transcription and Splice-Site Recognition

    Science.gov (United States)

    Murugan, Rajamanickam; Kreiman, Gabriel

    2012-01-01

    Eukaryotic genes are typically split into exons that need to be spliced together to form the mature mRNA. The splicing process depends on the dynamics and interactions among transcription by the RNA polymerase II complex (RNAPII) and the spliceosomal complex consisting of multiple small nuclear ribonucleo proteins (snRNPs). Here we propose a biophysically plausible initial theory of splicing that aims to explain the effects of the stochastic dynamics of snRNPs on the splicing patterns of eukaryotic genes. We consider two different ways to model the dynamics of snRNPs: pure three-dimensional diffusion and a combination of three- and one-dimensional diffusion along the emerging pre-mRNA. Our theoretical analysis shows that there exists an optimum position of the splice sites on the growing pre-mRNA at which the time required for snRNPs to find the 5′ donor site is minimized. The minimization of the overall search time is achieved mainly via the increase in non-specific interactions between the snRNPs and the growing pre-mRNA. The theory further predicts that there exists an optimum transcript length that maximizes the probabilities for exons to interact with the snRNPs. We evaluate these theoretical predictions by considering human and mouse exon microarray data as well as RNAseq data from multiple different tissues. We observe that there is a broad optimum position of splice sites on the growing pre-mRNA and an optimum transcript length, which are roughly consistent with the theoretical predictions. The theoretical and experimental analyses suggest that there is a strong interaction between the dynamics of RNAPII and the stochastic nature of snRNP search for 5′ donor splicing sites. PMID:23133354

  5. Theory on the coupled stochastic dynamics of transcription and splice-site recognition.

    Directory of Open Access Journals (Sweden)

    Rajamanickam Murugan

    Full Text Available Eukaryotic genes are typically split into exons that need to be spliced together to form the mature mRNA. The splicing process depends on the dynamics and interactions among transcription by the RNA polymerase II complex (RNAPII and the spliceosomal complex consisting of multiple small nuclear ribonucleo proteins (snRNPs. Here we propose a biophysically plausible initial theory of splicing that aims to explain the effects of the stochastic dynamics of snRNPs on the splicing patterns of eukaryotic genes. We consider two different ways to model the dynamics of snRNPs: pure three-dimensional diffusion and a combination of three- and one-dimensional diffusion along the emerging pre-mRNA. Our theoretical analysis shows that there exists an optimum position of the splice sites on the growing pre-mRNA at which the time required for snRNPs to find the 5' donor site is minimized. The minimization of the overall search time is achieved mainly via the increase in non-specific interactions between the snRNPs and the growing pre-mRNA. The theory further predicts that there exists an optimum transcript length that maximizes the probabilities for exons to interact with the snRNPs. We evaluate these theoretical predictions by considering human and mouse exon microarray data as well as RNAseq data from multiple different tissues. We observe that there is a broad optimum position of splice sites on the growing pre-mRNA and an optimum transcript length, which are roughly consistent with the theoretical predictions. The theoretical and experimental analyses suggest that there is a strong interaction between the dynamics of RNAPII and the stochastic nature of snRNP search for 5' donor splicing sites.

  6. Stochastic models of the Social Security trust funds.

    Science.gov (United States)

    Burdick, Clark; Manchester, Joyce

    Each year in March, the Board of Trustees of the Social Security trust funds reports on the current and projected financial condition of the Social Security programs. Those programs, which pay monthly benefits to retired workers and their families, to the survivors of deceased workers, and to disabled workers and their families, are financed through the Old-Age, Survivors, and Disability Insurance (OASDI) Trust Funds. In their 2003 report, the Trustees present, for the first time, results from a stochastic model of the combined OASDI trust funds. Stochastic modeling is an important new tool for Social Security policy analysis and offers the promise of valuable new insights into the financial status of the OASDI trust funds and the effects of policy changes. The results presented in this article demonstrate that several stochastic models deliver broadly consistent results even though they use very different approaches and assumptions. However, they also show that the variation in trust fund outcomes differs as the approach and assumptions are varied. Which approach and assumptions are best suited for Social Security policy analysis remains an open question. Further research is needed before the promise of stochastic modeling is fully realized. For example, neither parameter uncertainty nor variability in ultimate assumption values is recognized explicitly in the analyses. Despite this caveat, stochastic modeling results are already shedding new light on the range and distribution of trust fund outcomes that might occur in the future.

  7. Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film-shape memory alloy composite cantilever plate subjected to in-plane harmonic and stochastic excitation

    International Nuclear Information System (INIS)

    Zhu, Zhiwen; Zhang, Qingxin; Xu, Jia

    2014-01-01

    Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased

  8. Stochastic dynamics and control

    CERN Document Server

    Sun, Jian-Qiao; Zaslavsky, George

    2006-01-01

    This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress proc

  9. Exact solutions to chaotic and stochastic systems

    Science.gov (United States)

    González, J. A.; Reyes, L. I.; Guerrero, L. E.

    2001-03-01

    We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.

  10. Microbial and Organic Fine Particle Transport Dynamics in Streams - a Combined Experimental and Stochastic Modeling Approach

    Science.gov (United States)

    Drummond, Jen; Davies-Colley, Rob; Stott, Rebecca; Sukias, James; Nagels, John; Sharp, Alice; Packman, Aaron

    2014-05-01

    Transport dynamics of microbial cells and organic fine particles are important to stream ecology and biogeochemistry. Cells and particles continuously deposit and resuspend during downstream transport owing to a variety of processes including gravitational settling, interactions with in-stream structures or biofilms at the sediment-water interface, and hyporheic exchange and filtration within underlying sediments. Deposited cells and particles are also resuspended following increases in streamflow. Fine particle retention influences biogeochemical processing of substrates and nutrients (C, N, P), while remobilization of pathogenic microbes during flood events presents a hazard to downstream uses such as water supplies and recreation. We are conducting studies to gain insights into the dynamics of fine particles and microbes in streams, with a campaign of experiments and modeling. The results improve understanding of fine sediment transport, carbon cycling, nutrient spiraling, and microbial hazards in streams. We developed a stochastic model to describe the transport and retention of fine particles and microbes in rivers that accounts for hyporheic exchange and transport through porewaters, reversible filtration within the streambed, and microbial inactivation in the water column and subsurface. This model framework is an advance over previous work in that it incorporates detailed transport and retention processes that are amenable to measurement. Solute, particle, and microbial transport were observed both locally within sediment and at the whole-stream scale. A multi-tracer whole-stream injection experiment compared the transport and retention of a conservative solute, fluorescent fine particles, and the fecal indicator bacterium Escherichia coli. Retention occurred within both the underlying sediment bed and stands of submerged macrophytes. The results demonstrate that the combination of local measurements, whole-stream tracer experiments, and advanced modeling

  11. 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...... 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...

  12. Aspects if stochastic models for short-term hydropower scheduling and bidding

    Energy Technology Data Exchange (ETDEWEB)

    Belsnes, Michael Martin [Sintef Energy, Trondheim (Norway); Follestad, Turid [Sintef Energy, Trondheim (Norway); Wolfgang, Ove [Sintef Energy, Trondheim (Norway); Fosso, Olav B. [Dep. of electric power engineering NTNU, Trondheim (Norway)

    2012-07-01

    This report discusses challenges met when turning from deterministic to stochastic decision support models for short-term hydropower scheduling and bidding. The report describes characteristics of the short-term scheduling and bidding problem, different market and bidding strategies, and how a stochastic optimization model can be formulated. A review of approaches for stochastic short-term modelling and stochastic modelling for the input variables inflow and market prices is given. The report discusses methods for approximating the predictive distribution of uncertain variables by scenario trees. Benefits of using a stochastic over a deterministic model are illustrated by a case study, where increased profit is obtained to a varying degree depending on the reservoir filling and price structure. Finally, an approach for assessing the effect of using a size restricted scenario tree to approximate the predictive distribution for stochastic input variables is described. The report is a summary of the findings of Work package 1 of the research project #Left Double Quotation Mark#Optimal short-term scheduling of wind and hydro resources#Right Double Quotation Mark#. The project aims at developing a prototype for an operational stochastic short-term scheduling model. Based on the investigations summarized in the report, it is concluded that using a deterministic equivalent formulation of the stochastic optimization problem is convenient and sufficient for obtaining a working prototype. (author)

  13. Stochastic resonance and noise delayed extinction in a model of two competing species

    Science.gov (United States)

    Valenti, D.; Fiasconaro, A.; Spagnolo, B.

    2004-01-01

    We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka-Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term, which accounts for the environment temperature variation. We find noise-induced periodic oscillations of the species concentrations and stochastic resonance phenomenon. We find also a nonmonotonic behavior of the mean extinction time of one of the two competing species as a function of the additive noise intensity.

  14. Characterizing economic trends by Bayesian stochastic model specifi cation search

    OpenAIRE

    Grassi, Stefano; Proietti, Tommaso

    2010-01-01

    We apply a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. We illustrate that the methodology can be quite successfully applied to discriminate between stochastic and deterministic trends. In particular, we formulate autoregressive models with stochastic trends components and decide on whether a specific feature of the series, i.e. the underlying level and/or the rate...

  15. Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

    NARCIS (Netherlands)

    Jiang, G.J.; van der Sluis, P.J.

    2000-01-01

    This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the

  16. Stochastic Reachability Analysis of Hybrid Systems

    CERN Document Server

    Bujorianu, Luminita Manuela

    2012-01-01

    Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then...

  17. A stochastic dynamic model to assess land use change scenarios on the ecological status of fluvial water bodies under the Water Framework Directive

    Energy Technology Data Exchange (ETDEWEB)

    Hughes, Samantha Jane, E-mail: shughes@utad.pt [Fluvial Ecology Laboratory, CITAB – Centre for the Research and Technology of Agro-Environment and Biological Sciences, University of Trás-os-Montes e Alto Douro, Vila Real (Portugal); Cabral, João Alexandre, E-mail: jcabral@utad.pt [Laboratory of Applied Ecology, CITAB – Centre for the Research and Technology of Agro-Environment and Biological Sciences, University of Trás-os-Montes e Alto Douro, Vila Real (Portugal); Bastos, Rita, E-mail: ritabastos@utad.pt [Laboratory of Applied Ecology, CITAB – Centre for the Research and Technology of Agro-Environment and Biological Sciences, University of Trás-os-Montes e Alto Douro, Vila Real (Portugal); Cortes, Rui, E-mail: rcortes@utad.pt [Fluvial Ecology Laboratory, CITAB – Centre for the Research and Technology of Agro-Environment and Biological Sciences, University of Trás-os-Montes e Alto Douro, Vila Real (Portugal); Vicente, Joana, E-mail: jsvicente@fc.up.pt [Centro de Investigacão em Biodiversidade e Recursos Genéticos (CIBIO), Faculdade de Ciências, Universidade do Porto, Porto (Portugal); Eitelberg, David, E-mail: d.a.eitelberg@vu.nl [Faculty of Earth and Life Sciences, VU University Amsterdam, De Boelelaan 1087, 1081 HV Amsterdam (Netherlands); Yu, Huirong, E-mail: h.yu@vu.nl [Faculty of Earth and Life Sciences, VU University Amsterdam, De Boelelaan 1087, 1081 HV Amsterdam (Netherlands); College of Resources and Environmental Sciences, China Agricultural University, 2 Yuanmingyuan W. Road, Haidian District, Beijing 100193 (China); and others

    2016-09-15

    This method development paper outlines an integrative stochastic dynamic methodology (StDM) framework to anticipate land use (LU) change effects on the ecological status of monitored and non-monitored lotic surface waters under the Water Framework Directive (WFD). Tested in the Alto Minho River Basin District in North West Portugal, the model is an innovative step towards developing a decision-making and planning tool to assess the influence impacts such as LU change and climate change on these complex systems. Comprising a series of sequential steps, a Generalized Linear Model based, competing model Multi Model Inference (MMI) approach was used for parameter estimation to identify principal land use types (distal factors) driving change in biological and physicochemical support elements (proximal factors) in monitored water bodies. The framework integrated MMI constants and coefficients of selected LU categories in the StDM simulations and spatial projections to simulate the ecological status of monitored and non-monitored lotic waterbodies in the test area under 2 scenarios of (1) LU intensification and (2) LU extensification. A total of 100 simulations were run for a 50 year period for each scenario. Spatially dynamic projections of WFD metrics were obtained, taking into account the occurrence of stochastic wildfire events which typically occur in the study region and are exacerbated by LU change. A marked projected decline to “Moderate” ecological status for most waterbodies was detected under intensification but little change under extensification; only a few waterbodies fell to “moderate” status. The latter scenario describes the actual regional socio-economic situation of agricultural abandonment due to rural poverty, partly explaining the projected lack of change in ecological status. Based on the WFD “one out all out” criterion, projected downward shifts in ecological status were due to physicochemical support elements, namely increased

  18. A stochastic dynamic model to assess land use change scenarios on the ecological status of fluvial water bodies under the Water Framework Directive

    International Nuclear Information System (INIS)

    Hughes, Samantha Jane; Cabral, João Alexandre; Bastos, Rita; Cortes, Rui; Vicente, Joana; Eitelberg, David; Yu, Huirong

    2016-01-01

    This method development paper outlines an integrative stochastic dynamic methodology (StDM) framework to anticipate land use (LU) change effects on the ecological status of monitored and non-monitored lotic surface waters under the Water Framework Directive (WFD). Tested in the Alto Minho River Basin District in North West Portugal, the model is an innovative step towards developing a decision-making and planning tool to assess the influence impacts such as LU change and climate change on these complex systems. Comprising a series of sequential steps, a Generalized Linear Model based, competing model Multi Model Inference (MMI) approach was used for parameter estimation to identify principal land use types (distal factors) driving change in biological and physicochemical support elements (proximal factors) in monitored water bodies. The framework integrated MMI constants and coefficients of selected LU categories in the StDM simulations and spatial projections to simulate the ecological status of monitored and non-monitored lotic waterbodies in the test area under 2 scenarios of (1) LU intensification and (2) LU extensification. A total of 100 simulations were run for a 50 year period for each scenario. Spatially dynamic projections of WFD metrics were obtained, taking into account the occurrence of stochastic wildfire events which typically occur in the study region and are exacerbated by LU change. A marked projected decline to “Moderate” ecological status for most waterbodies was detected under intensification but little change under extensification; only a few waterbodies fell to “moderate” status. The latter scenario describes the actual regional socio-economic situation of agricultural abandonment due to rural poverty, partly explaining the projected lack of change in ecological status. Based on the WFD “one out all out” criterion, projected downward shifts in ecological status were due to physicochemical support elements, namely increased

  19. Mellin Transform Method for European Option Pricing with Hull-White Stochastic Interest Rate

    Directory of Open Access Journals (Sweden)

    Ji-Hun Yoon

    2014-01-01

    Full Text Available Even though interest rates fluctuate randomly in the marketplace, many option-pricing models do not fully consider their stochastic nature owing to their generally limited impact on option prices. However, stochastic dynamics in stochastic interest rates may have a significant impact on option prices as we take account of issues of maturity, hedging, or stochastic volatility. In this paper, we derive a closed form solution for European options in Black-Scholes model with stochastic interest rate using Mellin transform techniques.

  20. 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...... velocity distributions that depend on height above the ground both with respect to standard deviation and skewness are substituted into the stationary Fokker/Planck equation. The particle position distribution is taken to be uniform *the well/mixed condition( and also a given dispersion coefficient...

  1. Model-based stochastic-deterministic State and Force Estimation using Kalman filtering with Application to Hanko-1 Channel Marker

    OpenAIRE

    Petersen, Øyvind Wiig

    2014-01-01

    Force identification in structural dynamics is an inverse problem concerned with finding loads from measured structural response. The main objective of this thesis is to perform and study state (displacement and velocity) and force estimation by Kalman filtering. Theory on optimal control and state-space models are presented, adapted to linear structural dynamics. Accommodation for measurement noise and model inaccuracies are attained by stochastic-deterministic coupling. Explicit requirem...

  2. Effects of demographic stochasticity on biological community assembly on evolutionary time scales

    KAUST Repository

    Murase, Yohsuke; Shimada, Takashi; Ito, Nobuyasu; Rikvold, Per Arne

    2010-01-01

    We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/ f2 fluctuations are found for the model without demographic noise. © 2010 The American Physical Society.

  3. Effects of demographic stochasticity on biological community assembly on evolutionary time scales

    KAUST Repository

    Murase, Yohsuke

    2010-04-13

    We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/ f2 fluctuations are found for the model without demographic noise. © 2010 The American Physical Society.

  4. 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

  5. Extended Plefka expansion for stochastic dynamics

    International Nuclear Information System (INIS)

    Bravi, B; Sollich, P; Opper, M

    2016-01-01

    We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is sufficiently general to allow application to e.g. biochemical networks involved in metabolism and regulation. The main feature of our approach is to constrain in the Plefka expansion not just first moments akin to magnetizations, but also second moments, specifically two-time correlations and responses for each degree of freedom. The end result is an effective equation of motion for each single degree of freedom, where couplings to other variables appear as a self-coupling to the past (i.e. memory term) and a coloured noise. This constitutes a new mean field approximation that should become exact in the thermodynamic limit of a large network, for suitably long-ranged couplings. For the analytically tractable case of linear dynamics we establish this exactness explicitly by appeal to spectral methods of random matrix theory, for Gaussian couplings with arbitrary degree of symmetry. (paper)

  6. Extended Plefka expansion for stochastic dynamics

    Science.gov (United States)

    Bravi, B.; Sollich, P.; Opper, M.

    2016-05-01

    We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is sufficiently general to allow application to e.g. biochemical networks involved in metabolism and regulation. The main feature of our approach is to constrain in the Plefka expansion not just first moments akin to magnetizations, but also second moments, specifically two-time correlations and responses for each degree of freedom. The end result is an effective equation of motion for each single degree of freedom, where couplings to other variables appear as a self-coupling to the past (i.e. memory term) and a coloured noise. This constitutes a new mean field approximation that should become exact in the thermodynamic limit of a large network, for suitably long-ranged couplings. For the analytically tractable case of linear dynamics we establish this exactness explicitly by appeal to spectral methods of random matrix theory, for Gaussian couplings with arbitrary degree of symmetry.

  7. 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

  8. Brain-inspired Stochastic Models and Implementations

    KAUST Repository

    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.

  9. Seasonal Synchronization of a Simple Stochastic Dynamical Model Capturing El Niño Diversity

    Science.gov (United States)

    Thual, S.; Majda, A.; Chen, N.

    2017-12-01

    The El Niño-Southern Oscillation (ENSO) has significant impact on global climate and seasonal prediction. Recently, a simple ENSO model was developed that automatically captures the ENSO diversity and intermittency in nature, where state-dependent stochastic wind bursts and nonlinear advection of sea surface temperature (SST) are coupled to simple ocean-atmosphere processes that are otherwise deterministic, linear and stable. In the present article, it is further shown that the model can reproduce qualitatively the ENSO synchronization (or phase-locking) to the seasonal cycle in nature. This goal is achieved by incorporating a cloud radiative feedback that is derived naturally from the model's atmosphere dynamics with no ad-hoc assumptions and accounts in simple fashion for the marked seasonal variations of convective activity and cloud cover in the eastern Pacific. In particular, the weak convective response to SSTs in boreal fall favors the eastern Pacific warming that triggers El Niño events while the increased convective activity and cloud cover during the following spring contributes to the shutdown of those events by blocking incoming shortwave solar radiations. In addition to simulating the ENSO diversity with realistic non-Gaussian statistics in different Niño regions, both the eastern Pacific moderate and super El Niño, the central Pacific El Niño as well as La Niña show a realistic chronology with a tendency to peak in boreal winter as well as decreased predictability in spring consistent with the persistence barrier in nature. The incorporation of other possible seasonal feedbacks in the model is also documented for completeness.

  10. 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...

  11. Stochastic population oscillations in spatial predator-prey models

    International Nuclear Information System (INIS)

    Taeuber, Uwe C

    2011-01-01

    It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield long-lived, but ultimately decaying erratic population oscillations, which can be understood through a resonant amplification mechanism for density fluctuations. In Monte Carlo simulations of spatial stochastic predator-prey systems, one observes striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey. In the presence of local particle density restrictions (finite prey carrying capacity), there exists an extinction threshold for the predator population. The accompanying continuous non-equilibrium phase transition is governed by the directed-percolation universality class. We employ field-theoretic methods based on the Doi-Peliti representation of the master equation for stochastic particle interaction models to (i) map the ensuing action in the vicinity of the absorbing state phase transition to Reggeon field theory, and (ii) to quantitatively address fluctuation-induced renormalizations of the population oscillation frequency, damping, and diffusion coefficients in the species coexistence phase.

  12. Linking agent-based models and stochastic models of financial markets.

    Science.gov (United States)

    Feng, Ling; Li, Baowen; Podobnik, Boris; Preis, Tobias; Stanley, H Eugene

    2012-05-29

    It is well-known that financial asset returns exhibit fat-tailed distributions and long-term memory. These empirical features are the main objectives of modeling efforts using (i) stochastic processes to quantitatively reproduce these features and (ii) agent-based simulations to understand the underlying microscopic interactions. After reviewing selected empirical and theoretical evidence documenting the behavior of traders, we construct an agent-based model to quantitatively demonstrate that "fat" tails in return distributions arise when traders share similar technical trading strategies and decisions. Extending our behavioral model to a stochastic model, we derive and explain a set of quantitative scaling relations of long-term memory from the empirical behavior of individual market participants. Our analysis provides a behavioral interpretation of the long-term memory of absolute and squared price returns: They are directly linked to the way investors evaluate their investments by applying technical strategies at different investment horizons, and this quantitative relationship is in agreement with empirical findings. Our approach provides a possible behavioral explanation for stochastic models for financial systems in general and provides a method to parameterize such models from market data rather than from statistical fitting.

  13. A combined stochastic programming and optimal control approach to personal finance and pensions

    DEFF Research Database (Denmark)

    Konicz, Agnieszka Karolina; Pisinger, David; Rasmussen, Kourosh Marjani

    2015-01-01

    The paper presents a model that combines a dynamic programming (stochastic optimal control) approach and a multi-stage stochastic linear programming approach (SLP), integrated into one SLP formulation. Stochastic optimal control produces an optimal policy that is easy to understand and implement....

  14. 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

  15. 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.

  16. Systematic parameter inference in stochastic mesoscopic modeling

    Energy Technology Data Exchange (ETDEWEB)

    Lei, Huan; Yang, Xiu [Pacific Northwest National Laboratory, Richland, WA 99352 (United States); Li, Zhen [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States); Karniadakis, George Em, E-mail: george_karniadakis@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)

    2017-02-01

    We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving dissipative particle dynamics (eDPD). The response surfaces of various target properties (viscosity, diffusivity, pressure, etc.) with respect to model parameters are constructed based on the generalized polynomial chaos (gPC) expansion using simulation results on sampling points (e.g., individual parameter sets). To alleviate the computational cost to evaluate the target properties, we employ the compressive sensing method to compute the coefficients of the dominant gPC terms given the prior knowledge that the coefficients are “sparse”. The proposed method shows comparable accuracy with the standard probabilistic collocation method (PCM) while it imposes a much weaker restriction on the number of the simulation samples especially for systems with high dimensional parametric space. Fully access to the response surfaces within the confidence range enables us to infer the optimal force parameters given the desirable values of target properties at the macroscopic scale. Moreover, it enables us to investigate the intrinsic relationship between the model parameters, identify possible degeneracies in the parameter space, and optimize the model by eliminating model redundancies. The proposed method provides an efficient alternative approach for constructing mesoscopic models by inferring model parameters to recover target properties of the physics systems (e.g., from experimental measurements), where those force field parameters and formulation cannot be derived from the microscopic level in a straight forward way.

  17. Dynamic stochastic optimization

    CERN Document Server

    Ermoliev, Yuri; Pflug, Georg

    2004-01-01

    Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic­ itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec­ tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci­ sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu­ tions. Objective an...

  18. 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.

  19. Stochastic growth logistic model with aftereffect for batch fermentation process

    Science.gov (United States)

    Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

    2014-06-01

    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.

  20. 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