Fast stochastic algorithm for simulating evolutionary population dynamics
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.
Stochastic Simulation of Cardiac Ventricular Myocyte Calcium Dynamics and Waves
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 ...
Parallel Stochastic discrete event simulation of calcium dynamics in neuron.
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.
Advanced Dynamically Adaptive Algorithms for Stochastic Simulations on Extreme Scales
Energy Technology Data Exchange (ETDEWEB)
Xiu, Dongbin [Univ. of Utah, Salt Lake City, UT (United States)
2017-03-03
The focus of the project is the development of mathematical methods and high-performance computational tools for stochastic simulations, with a particular emphasis on computations on extreme scales. The core of the project revolves around the design of highly efficient and scalable numerical algorithms that can adaptively and accurately, in high dimensional spaces, resolve stochastic problems with limited smoothness, even containing discontinuities.
Stabilizing simulations of complex stochastic representations for quantum dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Perret, C; Petersen, W P, E-mail: wpp@math.ethz.ch [Seminar for Applied Mathematics, ETH, Zurich (Switzerland)
2011-03-04
Path integral representations of quantum dynamics can often be formulated as stochastic differential equations (SDEs). In a series of papers, Corney and Drummond (2004 Phys. Rev. Lett. 93 260401), Deuar and Drummond (2001 Comput. Phys. Commun. 142 442-5), Drummond and Gardnier (1980 J. Phys. A: Math. Gen. 13 2353-68), Gardiner and Zoller (2004 Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer Series in Synergetics) 3rd edn (Berlin: Springer)) and Gilchrist et al (1997 Phys. Rev. A 55 3014-32) and their collaborators have derived SDEs from coherent states representations for density matrices. Computationally, these SDEs are attractive because they seem simple to simulate. They can be quite unstable, however. In this paper, we consider some of the instabilities and propose a few remedies. Particularly, because the variances of the simulated paths typically grow exponentially, the processes become de-localized in relatively short times. Hence, the issues of boundary conditions and stable integration methods become important. We use the Bose-Einstein Hamiltonian as an example. Our results reveal that it is possible to significantly extend integration times and show the periodic structure of certain functionals.
Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics
Directory of Open Access Journals (Sweden)
Nicolas Wieder
2011-01-01
pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.
Stochastic Rotation Dynamics simulations of wetting multi-phase flows
Hiller, Thomas; Sanchez de La Lama, Marta; Brinkmann, Martin
2016-06-01
Multi-color Stochastic Rotation Dynamics (SRDmc) has been introduced by Inoue et al. [1,2] as a particle based simulation method to study the flow of emulsion droplets in non-wetting microchannels. In this work, we extend the multi-color method to also account for different wetting conditions. This is achieved by assigning the color information not only to fluid particles but also to virtual wall particles that are required to enforce proper no-slip boundary conditions. To extend the scope of the original SRDmc algorithm to e.g. immiscible two-phase flow with viscosity contrast we implement an angular momentum conserving scheme (SRD+mc). We perform extensive benchmark simulations to show that a mono-phase SRDmc fluid exhibits bulk properties identical to a standard SRD fluid and that SRDmc fluids are applicable to a wide range of immiscible two-phase flows. To quantify the adhesion of a SRD+mc fluid in contact to the walls we measure the apparent contact angle from sessile droplets in mechanical equilibrium. For a further verification of our wettability implementation we compare the dewetting of a liquid film from a wetting stripe to experimental and numerical studies of interfacial morphologies on chemically structured surfaces.
Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process
Turner, Douglas C.; Ladde, Gangaram S.
2018-03-01
Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.
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...
Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.
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.
Simulation of quantum dynamics based on the quantum stochastic differential equation.
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.
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.
Variance decomposition in stochastic simulators.
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.
Variance decomposition in stochastic simulators
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.
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.
Variance decomposition in stochastic simulators
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.
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.
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.
Schilstra, Maria J; Martin, Stephen R
2009-01-01
Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.
Fiore, Andrew M.; Swan, James W.
2018-01-01
equations of motion leads to a stochastic differential algebraic equation (SDAE) of index 1, which is integrated forward in time using a mid-point integration scheme that implicitly produces stochastic displacements consistent with the fluctuation-dissipation theorem for the constrained system. Calculations for hard sphere dispersions are illustrated and used to explore the performance of the algorithm. An open source, high-performance implementation on graphics processing units capable of dynamic simulations of millions of particles and integrated with the software package HOOMD-blue is used for benchmarking and made freely available in the supplementary material (ftp://ftp.aip.org/epaps/journ_chem_phys/E-JCPSA6-148-012805)
Stochastic dynamics and irreversibility
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 ...
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.
Energy Technology Data Exchange (ETDEWEB)
Dunn, Aaron [Sandia National Laboratories, Albuquerque, 87185 NM (United States); George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, 30332 GA (United States); Muntifering, Brittany [Sandia National Laboratories, Albuquerque, 87185 NM (United States); Northwestern University, Chicago, 60208 IL (United States); Dingreville, Rémi; Hattar, Khalid [Sandia National Laboratories, Albuquerque, 87185 NM (United States); Capolungo, Laurent, E-mail: laurent@lanl.gov [George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, 30332 GA (United States); Material Science and Technology Division, MST-8, Los Alamos National Laboratory, Los Alamos, 87545 NM (United States)
2016-11-15
Charged particle irradiation is a frequently used experimental tool to study damage accumulation in metals expected during neutron irradiation. Understanding the correspondence between displacement rate and temperature during such studies is one of several factors that must be taken into account in order to design experiments that produce equivalent damage accumulation to neutron damage conditions. In this study, spatially resolved stochastic cluster dynamics (SRSCD) is used to simulate damage evolution in α-Fe and find displacement rate/temperature pairs under ‘target’ and ‘proxy’ conditions for which the local distribution of vacancies and vacancy clusters is the same as a function of displacement damage. The SRSCD methodology is chosen for this study due to its computational efficiency and ability to simulate damage accumulation in spatially inhomogeneous materials such as thin films. Results are presented for Frenkel pair irradiation and displacement cascade damage in thin films and bulk α-Fe. Holding all other material and irradiation conditions constant, temperature adjustments are shown to successfully make up for changes in displacement rate such that defect concentrations and cluster sizes remain relatively constant. The methodology presented in this study allows for a first-order prediction of the temperature at which ion irradiation experiments (‘proxy’ conditions) should take place in order to approximate neutron irradiation (‘target’ conditions).
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...
Geometric integrators for stochastic rigid body dynamics
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.
Geometric integrators for stochastic rigid body dynamics
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.
Stochastic modeling analysis and simulation
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
Stochastic ice stream dynamics.
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.
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.
Mostert, P F; Bokkers, E A M; van Middelaar, C E; Hogeveen, H; de Boer, I J M
2018-01-01
The objective of this study was to estimate the economic impact of subclinical ketosis (SCK) in dairy cows. This metabolic disorder occurs in the period around calving and is associated with an increased risk of other diseases. Therefore, SCK affects farm productivity and profitability. Estimating the economic impact of SCK may make farmers more aware of this problem, and can improve their decision-making regarding interventions to reduce SCK. We developed a dynamic stochastic simulation model that enables estimating the economic impact of SCK and related diseases (i.e. mastitis, metritis, displaced abomasum, lameness and clinical ketosis) occurring during the first 30 days after calving. This model, which was applied to a typical Dutch dairy herd, groups cows according to their parity (1 to 5+), and simulates the dynamics of SCK and related diseases, and milk production per cow during one lactation. The economic impact of SCK and related diseases resulted from a reduced milk production, discarded milk, treatment costs, costs from a prolonged calving interval and removal (culling or dying) of cows. The total costs of SCK were €130 per case per year, with a range between €39 and €348 (5 to 95 percentiles). The total costs of SCK per case per year, moreover, increased from €83 per year in parity 1 to €175 in parity 3. Most cows with SCK, however, had SCK only (61%), and costs were €58 per case per year. Total costs of SCK per case per year resulted for 36% from a prolonged calving interval, 24% from reduced milk production, 19% from treatment, 14% from discarded milk and 6% from removal. Results of the sensitivity analysis showed that the disease incidence, removal risk, relations of SCK with other diseases and prices of milk resulted in a high variation of costs of SCK. The costs of SCK, therefore, might differ per farm because of farm-specific circumstances. Improving data collection on the incidence of SCK and related diseases, and on consequences of
GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: Dynamics and stochastic simulations
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.
Dynamics of stochastic systems
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 ...
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...
A retrodictive stochastic simulation algorithm
International Nuclear Information System (INIS)
Vaughan, T.G.; Drummond, P.D.; Drummond, A.J.
2010-01-01
In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.
Stochastic dynamics of dengue epidemics.
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.
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.
Serva, Federico; Cagnazzo, Chiara; Riccio, Angelo
2016-04-01
version of the model, the default and a new stochastic version, in which the value of the perturbation field at launching level is not constant and uniform, but extracted at each time-step and grid-point from a given PDF. With this approach we are trying to add further variability to the effects given by the deterministic NOGW parameterization: the impact on the simulated climate will be assessed focusing on the Quasi-Biennial Oscillation of the equatorial stratosphere (known to be driven also by gravity waves) and on the variability of the mid-to-high latitudes atmosphere. The different characteristics of the circulation will be compared with recent reanalysis products in order to determine the advantages of the stochastic approach over the traditional deterministic scheme.
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...
Introduction to stochastic dynamic programming
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
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.)
Dynamic and stochastic multi-project planning
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.
Kanjilal, Oindrila; Manohar, C. S.
2017-07-01
The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.
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.
Stochastic dynamics and control
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
Gross, Markus
2018-03-01
A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards–Wilkinson equation with non-conserved noise and the Mullins–Herring equation with conserved noise. The profile is subject to either periodic or Dirichlet (no-flux) boundary conditions. We determine the noise-driven time-evolution of the profile between an initially flat configuration and the instant at which the profile reaches a given height M for the first time. The shape of the averaged profile agrees well with the prediction of weak-noise theory (WNT), which describes the most-likely trajectory to a fixed first-passage time. Furthermore, in agreement with WNT, on average the profile approaches the height M algebraically in time, with an exponent that is essentially independent of the boundary conditions. However, the actual value of the dynamic exponent turns out to be significantly smaller than predicted by WNT. This ‘renormalization’ of the exponent is explained in terms of the entropic repulsion exerted by the impenetrable boundary on the fluctuations of the profile around its most-likely path. The entropic repulsion mechanism is analyzed in detail for a single (fractional) Brownian walker, which describes the anomalous diffusion of a tagged monomer of the interface as it approaches the absorbing boundary. The present study sheds light on the accuracy and the limitations of the weak-noise approximation for the description of the full first-passage dynamics.
Dynamic stochastic optimization
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...
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)
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
International Nuclear Information System (INIS)
Kuhn, W.L.; Westsik, J.H. Jr.
1989-01-01
Processing steps during the conversion of high-level nuclear waste into borosilicate glass in the Hanford Waste Vitrification Plant are being simulated on a computer by addressing transient mass balances. The results are being used to address the US Department of Energy's Waste Form Qualification requirements. The simulated addresses discontinuous (batch) operations and perturbations in the transient behavior of the process caused by errors in measurements and control actions. A collection of tests, based on process measurements, is continually checked and used to halt the simulated process when specified conditions are met. An associated set of control actions is then implemented in the simulation. The results for an example simulation are shown. 8 refs
Stochastic ground motion simulation
Rezaeian, Sanaz; Xiaodan, Sun; Beer, Michael; Kougioumtzoglou, Ioannis A.; Patelli, Edoardo; Siu-Kui Au, Ivan
2014-01-01
Strong earthquake ground motion records are fundamental in engineering applications. Ground motion time series are used in response-history dynamic analysis of structural or geotechnical systems. In such analysis, the validity of predicted responses depends on the validity of the input excitations. Ground motion records are also used to develop ground motion prediction equations(GMPEs) for intensity measures such as spectral accelerations that are used in response-spectrum dynamic analysis. Despite the thousands of available strong ground motion records, there remains a shortage of records for large-magnitude earthquakes at short distances or in specific regions, as well as records that sample specific combinations of source, path, and site characteristics.
Sparse learning of stochastic dynamical equations
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.
Stochastic Simulation of Process Calculi for Biology
Directory of Open Access Journals (Sweden)
Andrew Phillips
2010-10-01
Full Text Available Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed, many of which are expressive enough to generate unbounded numbers of molecular species and reactions. As a result of this expressiveness, such calculi cannot rely on standard reaction-based simulation methods, which require fixed numbers of species and reactions. Rather than implementing custom stochastic simulation algorithms for each process calculus, we propose to use a generic abstract machine that can be instantiated to a range of process calculi and a range of reaction-based simulation algorithms. The abstract machine functions as a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. In this short paper we give a brief summary of the generic abstract machine, and show how it can be instantiated with the stochastic simulation algorithm known as Gillespie's Direct Method. We also discuss the wider implications of such an abstract machine, and outline how it can be used to simulate multiple calculi simultaneously within a common framework.
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)
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...
Dynamics of non-holonomic systems with stochastic transport
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.
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
Energy Technology Data Exchange (ETDEWEB)
Karakulov, Valerii V., E-mail: valery@ftf.tsu.ru [National Research Tomsk State University, Tomsk, 634050 (Russian Federation); Smolin, Igor Yu., E-mail: smolin@ispms.ru, E-mail: skrp@ftf.tsu.ru; Skripnyak, Vladimir A., E-mail: smolin@ispms.ru, E-mail: skrp@ftf.tsu.ru [National Research Tomsk State University, Tomsk, 634050, Russia and Institute of Strength Physics and Materials Science SB RAS, Tomsk, 634055 (Russian Federation)
2014-11-14
Mechanical behavior of stochastic metal-ceramic composites with the aluminum matrix under high-rate deformation at shock-wave loading is numerically simulated with consideration for structural evolution. Effective values of mechanical parameters of metal-ceramic composites Al
Yifat, Jonathan; Gannot, Israel
2015-03-01
Early detection of malignant tumors plays a crucial role in the survivability chances of the patient. Therefore, new and innovative tumor detection methods are constantly searched for. Tumor-specific magnetic-core nano-particles can be used with an alternating magnetic field to detect and treat tumors by hyperthermia. For the analysis of the method effectiveness, the bio-heat transfer between the nanoparticles and the tissue must be carefully studied. Heat diffusion in biological tissue is usually analyzed using the Pennes Bio-Heat Equation, where blood perfusion plays an important role. Malignant tumors are known to initiate an angiogenesis process, where endothelial cell migration from neighboring vasculature eventually leads to the formation of a thick blood capillary network around them. This process allows the tumor to receive its extensive nutrition demands and evolve into a more progressive and potentially fatal tumor. In order to assess the effect of angiogenesis on the bio-heat transfer problem, we have developed a discrete stochastic 3D model & simulation of tumor-induced angiogenesis. The model elaborates other angiogenesis models by providing high resolution 3D stochastic simulation, capturing of fine angiogenesis morphological features, effects of dynamic sprout thickness functions, and stochastic parent vessel generator. We show that the angiogenesis realizations produced are well suited for numerical bio-heat transfer analysis. Statistical study on the angiogenesis characteristics was derived using Monte Carlo simulations. According to the statistical analysis, we provide analytical expression for the blood perfusion coefficient in the Pennes equation, as a function of several parameters. This updated form of the Pennes equation could be used for numerical and analytical analyses of the proposed detection and treatment method. Copyright © 2014 Elsevier Inc. All rights reserved.
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)
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.
International Nuclear Information System (INIS)
Sadeghi, Mahmood; Kalantar, Mohsen
2014-01-01
Highlights: • Defining a DG dynamic planning problem. • Applying a new evolutionary algorithm called “CMAES” in planning process. • Considering electricity price and fuel price variation stochastic conditions. • Scenario generation and reduction with MCS and backward reduction programs. • Considering approximately all of the costs of the distribution system. - Abstract: This paper presents a dynamic DG planning problem considering uncertainties related to the intermittent nature of the DG technologies such as wind turbines and solar units in addition to the stochastic economic conditions. The stochastic economic situation includes the uncertainties related to the fuel and electricity price of each year. The Monte Carlo simulation is used to generate the possible scenarios of uncertain situations and the produced scenarios are reduced through backward reduction program. The aim of this paper is to maximize the revenue of the distribution system through the benefit cost analysis alongside the encouraging and punishment functions. In order to close to reality, the different growth rates for the planning period are selected. In this paper the Covariance Matrix Adaptation Evolutionary Strategy is introduced and is used to find the best planning scheme of the DG units. The different DG types are considered in the planning problem. The main assumption of this paper is that the DISCO is the owner of the distribution system and the DG units. The proposed method is tested on a 9 bus test distribution system and the results are compared with the known genetic algorithm and PSO methods to show the applicability of the CMAES method in this problem
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.
Stochastic Simulation Using @ Risk for Dairy Business Investment Decisions
A dynamic, stochastic, mechanistic simulation model of a dairy business was developed to evaluate the cost and benefit streams coinciding with technology investments. The model was constructed to embody the biological and economical complexities of a dairy farm system within a partial budgeting fram...
Stochastic simulation using @Risk for dairy business investment decisions
Bewley, J.D.; Boehlje, M.D.; Gray, A.W.; Hogeveen, H.; Kenyon, S.J.; Eicher, S.D.; Schutz, M.M.
2010-01-01
Purpose – The purpose of this paper is to develop a dynamic, stochastic, mechanistic simulation model of a dairy business to evaluate the cost and benefit streams coinciding with technology investments. The model was constructed to embody the biological and economical complexities of a dairy farm
Energy Technology Data Exchange (ETDEWEB)
Kanjilal, Oindrila, E-mail: oindrila@civil.iisc.ernet.in; Manohar, C.S., E-mail: manohar@civil.iisc.ernet.in
2017-07-15
The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations. - Highlights: • The distance minimizing control forces minimize a bound on the sampling variance. • Establishing Girsanov controls via solution of a two-point boundary value problem. • Girsanov controls via Volterra's series representation for the transfer functions.
Stochastic dynamic modeling of regular and slow earthquakes
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
Multiscale Hy3S: Hybrid stochastic simulation for supercomputers
Directory of Open Access Journals (Sweden)
Kaznessis Yiannis N
2006-02-01
Full Text Available Abstract Background Stochastic simulation has become a useful tool to both study natural biological systems and design new synthetic ones. By capturing the intrinsic molecular fluctuations of "small" systems, these simulations produce a more accurate picture of single cell dynamics, including interesting phenomena missed by deterministic methods, such as noise-induced oscillations and transitions between stable states. However, the computational cost of the original stochastic simulation algorithm can be high, motivating the use of hybrid stochastic methods. Hybrid stochastic methods partition the system into multiple subsets and describe each subset as a different representation, such as a jump Markov, Poisson, continuous Markov, or deterministic process. By applying valid approximations and self-consistently merging disparate descriptions, a method can be considerably faster, while retaining accuracy. In this paper, we describe Hy3S, a collection of multiscale simulation programs. Results Building on our previous work on developing novel hybrid stochastic algorithms, we have created the Hy3S software package to enable scientists and engineers to both study and design extremely large well-mixed biological systems with many thousands of reactions and chemical species. We have added adaptive stochastic numerical integrators to permit the robust simulation of dynamically stiff biological systems. In addition, Hy3S has many useful features, including embarrassingly parallelized simulations with MPI; special discrete events, such as transcriptional and translation elongation and cell division; mid-simulation perturbations in both the number of molecules of species and reaction kinetic parameters; combinatorial variation of both initial conditions and kinetic parameters to enable sensitivity analysis; use of NetCDF optimized binary format to quickly read and write large datasets; and a simple graphical user interface, written in Matlab, to help users
Stochastic analysis for finance with simulations
Choe, Geon Ho
2016-01-01
This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoret...
Stochastic simulations of the tetracycline operon
Directory of Open Access Journals (Sweden)
Kaznessis Yiannis N
2011-01-01
Full Text Available Abstract Background The tetracycline operon is a self-regulated system. It is found naturally in bacteria where it confers resistance to antibiotic tetracycline. Because of the performance of the molecular elements of the tetracycline operon, these elements are widely used as parts of synthetic gene networks where the protein production can be efficiently turned on and off in response to the presence or the absence of tetracycline. In this paper, we investigate the dynamics of the tetracycline operon. To this end, we develop a mathematical model guided by experimental findings. Our model consists of biochemical reactions that capture the biomolecular interactions of this intriguing system. Having in mind that small biological systems are subjects to stochasticity, we use a stochastic algorithm to simulate the tetracycline operon behavior. A sensitivity analysis of two critical parameters embodied this system is also performed providing a useful understanding of the function of this system. Results Simulations generate a timeline of biomolecular events that confer resistance to bacteria against tetracycline. We monitor the amounts of intracellular TetR2 and TetA proteins, the two important regulatory and resistance molecules, as a function of intrecellular tetracycline. We find that lack of one of the promoters of the tetracycline operon has no influence on the total behavior of this system inferring that this promoter is not essential for Escherichia coli. Sensitivity analysis with respect to the binding strength of tetracycline to repressor and of repressor to operators suggests that these two parameters play a predominant role in the behavior of the system. The results of the simulations agree well with experimental observations such as tight repression, fast gene expression, induction with tetracycline, and small intracellular TetR2 amounts. Conclusions Computer simulations of the tetracycline operon afford augmented insight into the
Stochastic simulations of the tetracycline operon
2011-01-01
Background The tetracycline operon is a self-regulated system. It is found naturally in bacteria where it confers resistance to antibiotic tetracycline. Because of the performance of the molecular elements of the tetracycline operon, these elements are widely used as parts of synthetic gene networks where the protein production can be efficiently turned on and off in response to the presence or the absence of tetracycline. In this paper, we investigate the dynamics of the tetracycline operon. To this end, we develop a mathematical model guided by experimental findings. Our model consists of biochemical reactions that capture the biomolecular interactions of this intriguing system. Having in mind that small biological systems are subjects to stochasticity, we use a stochastic algorithm to simulate the tetracycline operon behavior. A sensitivity analysis of two critical parameters embodied this system is also performed providing a useful understanding of the function of this system. Results Simulations generate a timeline of biomolecular events that confer resistance to bacteria against tetracycline. We monitor the amounts of intracellular TetR2 and TetA proteins, the two important regulatory and resistance molecules, as a function of intrecellular tetracycline. We find that lack of one of the promoters of the tetracycline operon has no influence on the total behavior of this system inferring that this promoter is not essential for Escherichia coli. Sensitivity analysis with respect to the binding strength of tetracycline to repressor and of repressor to operators suggests that these two parameters play a predominant role in the behavior of the system. The results of the simulations agree well with experimental observations such as tight repression, fast gene expression, induction with tetracycline, and small intracellular TetR2 amounts. Conclusions Computer simulations of the tetracycline operon afford augmented insight into the interplay between its molecular
SELANSI: a toolbox for simulation of stochastic gene regulatory networks.
Pájaro, Manuel; Otero-Muras, Irene; Vázquez, Carlos; Alonso, Antonio A
2018-03-01
Gene regulation is inherently stochastic. In many applications concerning Systems and Synthetic Biology such as the reverse engineering and the de novo design of genetic circuits, stochastic effects (yet potentially crucial) are often neglected due to the high computational cost of stochastic simulations. With advances in these fields there is an increasing need of tools providing accurate approximations of the stochastic dynamics of gene regulatory networks (GRNs) with reduced computational effort. This work presents SELANSI (SEmi-LAgrangian SImulation of GRNs), a software toolbox for the simulation of stochastic multidimensional gene regulatory networks. SELANSI exploits intrinsic structural properties of gene regulatory networks to accurately approximate the corresponding Chemical Master Equation with a partial integral differential equation that is solved by a semi-lagrangian method with high efficiency. Networks under consideration might involve multiple genes with self and cross regulations, in which genes can be regulated by different transcription factors. Moreover, the validity of the method is not restricted to a particular type of kinetics. The tool offers total flexibility regarding network topology, kinetics and parameterization, as well as simulation options. SELANSI runs under the MATLAB environment, and is available under GPLv3 license at https://sites.google.com/view/selansi. antonio@iim.csic.es. © The Author(s) 2017. Published by Oxford University Press.
Stochastic dynamics for reinfection by transmitted diseases
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 ).
Automated Flight Routing Using Stochastic Dynamic Programming
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.
Simulation of Stochastic Loads for Fatigue Experiments
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Brincker, Rune
1989-01-01
process by a Markov process. Two different spectra from two tubular joints in an offshore structure (one narrow banded and one wide banded) are considered in an example. The results show that the simple direct method is quite efficient and results in a simulation speed of about 3000 load cycles per second......A simple direct simulation method for stochastic fatigue-load generation is described in this paper. The simulation method is based on the assumption that only the peaks of the load process significantly affect the fatigue life. The method requires the conditional distribution functions of load...... ranges given the last peak values. Analytical estimates of these distribution functions are presented in the paper and compared with estimates based on a more accurate simulation method. In the more accurate simulation method samples at equidistant times are generated by approximating the stochastic load...
Simulation of Stochastic Loads for Fatigue Experiments
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Brincker, Rune
process by a Markov process. Two different spectra from two tubular joints in an offshore structure (one narrow banded and one wide banded) are considered in an example. The results show that the simple direct method is quite efficient and is results in a simulation speed at about 3000 load cycles per......A simple direct simulation method for stochastic fatigue load generation is described in this paper. The simulation method is based on the assumption that only the peaks of the load process significantly affect the fatigue life. The method requires the conditional distribution functions of load...... ranges given the last peak values. Analytical estimates of these distribution functions are presented in the paper and compared with estimates based on a more accurate simulation method. In the more accurate simulation method samples at equidistant times are generated by approximating the stochastic load...
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.
Stochastic airspace simulation tool development
2009-10-01
Modeling and simulation is often used to study : the physical world when observation may not be : practical. The overall goal of a recent and ongoing : simulation tool project has been to provide a : documented, lifecycle-managed, multi-processor : c...
Stochastic integer programming by dynamic programming
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
DEFF Research Database (Denmark)
Morales Rodriguez, Ricardo; Meyer, Anne S.; Gernaey, Krist
of cellulose, co-fermentation of sugars and downstream processes for purification and recovery of most value-added products. The dynamic model involves both the mass and energy balances coupled with constitutive dynamic equations to assess the process yield and energy efficiency of different bioethanol...
Directory of Open Access Journals (Sweden)
Akke Kok
Full Text Available Shortening or omitting the dry period of dairy cows improves metabolic health in early lactation and reduces management transitions for dairy cows. The success of implementation of these strategies depends on their impact on milk yield and farm profitability. Insight in these impacts is valuable for informed decision-making by farmers. The aim of this study was to investigate how shortening or omitting the dry period of dairy cows affects production and cash flows at the herd level, and greenhouse gas emissions per unit of milk, using a dynamic stochastic simulation model. The effects of dry period length on milk yield and calving interval assumed in this model were derived from actual performance of commercial dairy cows over multiple lactations. The model simulated lactations, and calving and culling events of individual cows for herds of 100 cows. Herds were simulated for 5 years with a dry period of 56 (conventional, 28 or 0 days (n = 50 herds each. Partial cash flows were computed from revenues from sold milk, calves, and culled cows, and costs from feed and rearing youngstock. Greenhouse gas emissions were computed using a life cycle approach. A dry period of 28 days reduced milk production of the herd by 3.0% in years 2 through 5, compared with a dry period of 56 days. A dry period of 0 days reduced milk production by 3.5% in years 3 through 5, after a dip in milk production of 6.9% in year 2. On average, dry periods of 28 and 0 days reduced partial cash flows by €1,249 and €1,632 per herd per year, and increased greenhouse gas emissions by 0.7% and 0.5%, respectively. Considering the potential for enhancing cow welfare, these negative impacts of shortening or omitting the dry period seem justifiable, and they might even be offset by improved health.
Precharattana, Monamorn; Nokkeaw, Arthorn; Triampo, Wannapong; Triampo, Darapond; Lenbury, Yongwimon
2011-07-01
Acquired Immunodeficiency Syndrome (AIDS) is responsible for millions of deaths worldwide. To date, many drug treatment regimens have been applied to AIDS patients but none has resulted in a successful cure. This is mainly due to the fact that free HIV particles are frequently in mutation, and infected CD4(+) T cells normally reside in the lymphoid tissue where they cannot (so far) be eradicated. We present a stochastic cellular automaton (CA) model to computationally study what could be an alternative treatment, namely Leukapheresis (LCAP), to remove HIV infected leukocytes in the lymphoid tissue. We base our investigations on Monte Carlo computer simulations. Our major objective is to investigate how the number of infected CD4(+) T cells changes in response to LCAP during the short-time (weeks) and long-time (years) scales of HIV/AIDS progression in an infected individual. To achieve our goal, we analyze the time evolution of the CD4(+) T cell population in the lymphoid tissue (i.e., the lymph node) for HIV dynamics in treatment situations with various starting times and frequencies and under a no treatment condition. Our findings suggest that the effectiveness of the treatment depends mainly on the treatment starting time and the frequency of the LCAP. Other factors (e.g., the removal proportion, the treatment duration, and the state of removed cells) that likely influence disease progression are subjects for further investigation. Copyright © 2011 Elsevier Ltd. All rights reserved.
Molecular dynamics with deterministic and stochastic numerical methods
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...
A Stochastic Model for Malaria Transmission Dynamics
Directory of Open Access Journals (Sweden)
Rachel Waema Mbogo
2018-01-01
Full Text Available Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis. In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp. The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.
Stochastic control theory dynamic programming principle
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...
Dynamic optimization deterministic and stochastic models
Hinderer, Karl; Stieglitz, Michael
2016-01-01
This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.
Software Tools for Stochastic Simulations of Turbulence
2015-08-28
40] R. D. Richtmyer. Taylor instability in shock acceleration of compressible fluids. Comm. pure Appl. Math , 13(297-319), 1960. 76 [41] R. Samulyak, J...Research Triangle Park, NC 27709-2211 Pure sciences, Applied sciences, Front tracking, Large eddy simulations, Mesh convergence, Stochastic convergence, Weak...Illustration of a component grid with a front crossing solution stencil. Cells in the pure yellow and pure blue regions are assigned different components
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.
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.
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.
Computational Methods in Stochastic Dynamics Volume 2
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...
Computing Optimal Stochastic Portfolio Execution Strategies: A Parametric Approach Using Simulations
Moazeni, Somayeh; Coleman, Thomas F.; Li, Yuying
2010-09-01
Computing optimal stochastic portfolio execution strategies under appropriate risk consideration presents great computational challenge. We investigate a parametric approach for computing optimal stochastic strategies using Monte Carlo simulations. This approach allows reduction in computational complexity by computing coefficients for a parametric representation of a stochastic dynamic strategy based on static optimization. Using this technique, constraints can be similarly handled using appropriate penalty functions. We illustrate the proposed approach to minimize the expected execution cost and Conditional Value-at-Risk (CVaR).
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.)
Hoang, Tuan L.; Nazarov, Roman; Kang, Changwoo; Fan, Jiangyuan
2018-07-01
Under the multi-ion irradiation conditions present in accelerated material-testing facilities or fission/fusion nuclear reactors, the combined effects of atomic displacements with radiation products may induce complex synergies in the structural materials. However, limited access to multi-ion irradiation facilities and the lack of computational models capable of simulating the evolution of complex defects and their synergies make it difficult to understand the actual physical processes taking place in the materials under these extreme conditions. In this paper, we propose the application of pulsed single/dual-beam irradiation as replacements for the expensive steady triple-beam irradiation to study radiation damages in materials under multi-ion irradiation.
Simulation of Stochastic Processes by Coupled ODE-PDE
Zak, Michail
2008-01-01
A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.
Stochastic simulation of enzyme-catalyzed reactions with disparate timescales.
Barik, Debashis; Paul, Mark R; Baumann, William T; Cao, Yang; Tyson, John J
2008-10-01
Many physiological characteristics of living cells are regulated by protein interaction networks. Because the total numbers of these protein species can be small, molecular noise can have significant effects on the dynamical properties of a regulatory network. Computing these stochastic effects is made difficult by the large timescale separations typical of protein interactions (e.g., complex formation may occur in fractions of a second, whereas catalytic conversions may take minutes). Exact stochastic simulation may be very inefficient under these circumstances, and methods for speeding up the simulation without sacrificing accuracy have been widely studied. We show that the "total quasi-steady-state approximation" for enzyme-catalyzed reactions provides a useful framework for efficient and accurate stochastic simulations. The method is applied to three examples: a simple enzyme-catalyzed reaction where enzyme and substrate have comparable abundances, a Goldbeter-Koshland switch, where a kinase and phosphatase regulate the phosphorylation state of a common substrate, and coupled Goldbeter-Koshland switches that exhibit bistability. Simulations based on the total quasi-steady-state approximation accurately capture the steady-state probability distributions of all components of these reaction networks. In many respects, the approximation also faithfully reproduces time-dependent aspects of the fluctuations. The method is accurate even under conditions of poor timescale separation.
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.
Stochastic dynamic analysis of marine risers considering Gaussian system uncertainties
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.
Hybrid Differential Dynamic Programming with Stochastic Search
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.
Stochastic simulation of ecohydrological interactions between vegetation and groundwater
Dwelle, M. C.; Ivanov, V. Y.; Sargsyan, K.
2017-12-01
The complex interactions between groundwater and vegetation in the Amazon rainforest may yield vital ecophysiological interactions in specific landscape niches such as buffering plant water stress during dry season or suppression of water uptake due to anoxic conditions. Representation of such processes is greatly impacted by both external and internal sources of uncertainty: inaccurate data and subjective choice of model representation. The models that can simulate these processes are complex and computationally expensive, and therefore make it difficult to address uncertainty using traditional methods. We use the ecohydrologic model tRIBS+VEGGIE and a novel uncertainty quantification framework applied to the ZF2 watershed near Manaus, Brazil. We showcase the capability of this framework for stochastic simulation of vegetation-hydrology dynamics. This framework is useful for simulation with internal and external stochasticity, but this work will focus on internal variability of groundwater depth distribution and model parameterizations. We demonstrate the capability of this framework to make inferences on uncertain states of groundwater depth from limited in situ data, and how the realizations of these inferences affect the ecohydrological interactions between groundwater dynamics and vegetation function. We place an emphasis on the probabilistic representation of quantities of interest and how this impacts the understanding and interpretation of the dynamics at the groundwater-vegetation interface.
Some simulation aspects, from molecular systems to stochastic geometries of pebble bed reactors
International Nuclear Information System (INIS)
Mazzolo, A.
2009-06-01
After a brief presentation of his teaching and supervising activities, the author gives an overview of his research activities: investigation of atoms under high intensity magnetic field (investigation of the electronic structure under these fields), studies of theoretical and numerical electrochemistry (simulation coupling molecular dynamics and quantum calculations, comprehensive simulations of molecular dynamics), and studies relating stochastic geometry and neutron science
Stochastic Dynamics through Hierarchically Embedded Markov Chains.
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.
Lectures on Dynamics of Stochastic Systems
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
Stochastic population dynamics under resource constraints
Energy Technology Data Exchange (ETDEWEB)
Gavane, Ajinkya S., E-mail: ajinkyagavane@gmail.com; Nigam, Rahul, E-mail: rahul.nigam@hyderabad.bits-pilani.ac.in [BITS Pilani Hyderabad Campus, Shameerpet, Hyd - 500078 (India)
2016-06-02
This paper investigates the population growth of a certain species in which every generation reproduces thrice over a period of predefined time, under certain constraints of resources needed for survival of population. We study the survival period of a species by randomizing the reproduction probabilities within a window at same predefined ages and the resources are being produced by the working force of the population at a variable rate. This randomness in the reproduction rate makes the population growth stochastic in nature and one cannot predict the exact form of evolution. Hence we study the growth by running simulations for such a population and taking an ensemble averaged over 500 to 5000 such simulations as per the need. While the population reproduces in a stochastic manner, we have implemented a constraint on the amount of resources available for the population. This is important to make the simulations more realistic. The rate of resource production then is tuned to find the rate which suits the survival of the species. We also compute the mean life time of the species corresponding to different resource production rate. Study for these outcomes in the parameter space defined by the reproduction probabilities and rate of resource production is carried out.
Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games
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
Deterministic modelling and stochastic simulation of biochemical pathways using MATLAB.
Ullah, M; Schmidt, H; Cho, K H; Wolkenhauer, O
2006-03-01
The analysis of complex biochemical networks is conducted in two popular conceptual frameworks for modelling. The deterministic approach requires the solution of ordinary differential equations (ODEs, reaction rate equations) with concentrations as continuous state variables. The stochastic approach involves the simulation of differential-difference equations (chemical master equations, CMEs) with probabilities as variables. This is to generate counts of molecules for chemical species as realisations of random variables drawn from the probability distribution described by the CMEs. Although there are numerous tools available, many of them free, the modelling and simulation environment MATLAB is widely used in the physical and engineering sciences. We describe a collection of MATLAB functions to construct and solve ODEs for deterministic simulation and to implement realisations of CMEs for stochastic simulation using advanced MATLAB coding (Release 14). The program was successfully applied to pathway models from the literature for both cases. The results were compared to implementations using alternative tools for dynamic modelling and simulation of biochemical networks. The aim is to provide a concise set of MATLAB functions that encourage the experimentation with systems biology models. All the script files are available from www.sbi.uni-rostock.de/ publications_matlab-paper.html.
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...
Hybrid framework for the simulation of stochastic chemical kinetics
International Nuclear Information System (INIS)
Duncan, Andrew; Erban, Radek; Zygalakis, Konstantinos
2016-01-01
Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.
Hybrid framework for the simulation of stochastic chemical kinetics
Duncan, Andrew; Erban, Radek; Zygalakis, Konstantinos
2016-12-01
Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the "fast" reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.
Hybrid framework for the simulation of stochastic chemical kinetics
Energy Technology Data Exchange (ETDEWEB)
Duncan, Andrew, E-mail: a.duncan@imperial.ac.uk [Department of Mathematics, Imperial College, South Kensington Campus, London, SW7 2AZ (United Kingdom); Erban, Radek, E-mail: erban@maths.ox.ac.uk [Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Zygalakis, Konstantinos, E-mail: k.zygalakis@ed.ac.uk [School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD (United Kingdom)
2016-12-01
Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.
Stochastic simulation of karst conduit networks
Pardo-Igúzquiza, Eulogio; Dowd, Peter A.; Xu, Chaoshui; Durán-Valsero, Juan José
2012-01-01
Karst aquifers have very high spatial heterogeneity. Essentially, they comprise a system of pipes (i.e., the network of conduits) superimposed on rock porosity and on a network of stratigraphic surfaces and fractures. This heterogeneity strongly influences the hydraulic behavior of the karst and it must be reproduced in any realistic numerical model of the karst system that is used as input to flow and transport modeling. However, the directly observed karst conduits are only a small part of the complete karst conduit system and knowledge of the complete conduit geometry and topology remains spatially limited and uncertain. Thus, there is a special interest in the stochastic simulation of networks of conduits that can be combined with fracture and rock porosity models to provide a realistic numerical model of the karst system. Furthermore, the simulated model may be of interest per se and other uses could be envisaged. The purpose of this paper is to present an efficient method for conditional and non-conditional stochastic simulation of karst conduit networks. The method comprises two stages: generation of conduit geometry and generation of topology. The approach adopted is a combination of a resampling method for generating conduit geometries from templates and a modified diffusion-limited aggregation method for generating the network topology. The authors show that the 3D karst conduit networks generated by the proposed method are statistically similar to observed karst conduit networks or to a hypothesized network model. The statistical similarity is in the sense of reproducing the tortuosity index of conduits, the fractal dimension of the network, the direction rose of directions, the Z-histogram and Ripley's K-function of the bifurcation points (which differs from a random allocation of those bifurcation points). The proposed method (1) is very flexible, (2) incorporates any experimental data (conditioning information) and (3) can easily be modified when
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
Nonlinear and Stochastic Dynamics in the Heart
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
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.
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
An Exploration Algorithm for Stochastic Simulators Driven by Energy Gradients
Directory of Open Access Journals (Sweden)
Anastasia S. Georgiou
2017-06-01
Full Text Available In recent work, we have illustrated the construction of an exploration geometry on free energy surfaces: the adaptive computer-assisted discovery of an approximate low-dimensional manifold on which the effective dynamics of the system evolves. Constructing such an exploration geometry involves geometry-biased sampling (through both appropriately-initialized unbiased molecular dynamics and through restraining potentials and, machine learning techniques to organize the intrinsic geometry of the data resulting from the sampling (in particular, diffusion maps, possibly enhanced through the appropriate Mahalanobis-type metric. In this contribution, we detail a method for exploring the conformational space of a stochastic gradient system whose effective free energy surface depends on a smaller number of degrees of freedom than the dimension of the phase space. Our approach comprises two steps. First, we study the local geometry of the free energy landscape using diffusion maps on samples computed through stochastic dynamics. This allows us to automatically identify the relevant coarse variables. Next, we use the information garnered in the previous step to construct a new set of initial conditions for subsequent trajectories. These initial conditions are computed so as to explore the accessible conformational space more efficiently than by continuing the previous, unbiased simulations. We showcase this method on a representative test system.
Spreading dynamics on complex networks: a general stochastic approach.
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.
Quantum simulation of a quantum stochastic walk
Govia, Luke C. G.; Taketani, Bruno G.; Schuhmacher, Peter K.; Wilhelm, Frank K.
2017-03-01
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk (QSW), which allows for incoherent movement of the walker, and therefore, directionality, is a generalization on the fully coherent quantum walk. While a QSW can always be described in Lindblad formalism, this does not mean that it can be microscopically derived in the standard weak-coupling limit under the Born-Markov approximation. This restricts the class of QSWs that can be experimentally realized in a simple manner. To circumvent this restriction, we introduce a technique to simulate open system evolution on a fully coherent quantum computer, using a quantum trajectories style approach. We apply this technique to a broad class of QSWs, and show that they can be simulated with minimal experimental resources. Our work opens the path towards the experimental realization of QSWs on large graphs with existing quantum technologies.
MCdevelop - a universal framework for Stochastic Simulations
Slawinska, M.; Jadach, S.
2011-03-01
We present MCdevelop, a universal computer framework for developing and exploiting the wide class of Stochastic Simulations (SS) software. This powerful universal SS software development tool has been derived from a series of scientific projects for precision calculations in high energy physics (HEP), which feature a wide range of functionality in the SS software needed for advanced precision Quantum Field Theory calculations for the past LEP experiments and for the ongoing LHC experiments at CERN, Geneva. MCdevelop is a "spin-off" product of HEP to be exploited in other areas, while it will still serve to develop new SS software for HEP experiments. Typically SS involve independent generation of large sets of random "events", often requiring considerable CPU power. Since SS jobs usually do not share memory it makes them easy to parallelize. The efficient development, testing and running in parallel SS software requires a convenient framework to develop software source code, deploy and monitor batch jobs, merge and analyse results from multiple parallel jobs, even before the production runs are terminated. Throughout the years of development of stochastic simulations for HEP, a sophisticated framework featuring all the above mentioned functionality has been implemented. MCdevelop represents its latest version, written mostly in C++ (GNU compiler gcc). It uses Autotools to build binaries (optionally managed within the KDevelop 3.5.3 Integrated Development Environment (IDE)). It uses the open-source ROOT package for histogramming, graphics and the mechanism of persistency for the C++ objects. MCdevelop helps to run multiple parallel jobs on any computer cluster with NQS-type batch system. Program summaryProgram title:MCdevelop Catalogue identifier: AEHW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http
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
Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games
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.
International Nuclear Information System (INIS)
Marchetti, Luca; Priami, Corrado; Thanh, Vo Hong
2016-01-01
This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms.
Energy Technology Data Exchange (ETDEWEB)
Marchetti, Luca, E-mail: marchetti@cosbi.eu [The Microsoft Research – University of Trento Centre for Computational and Systems Biology (COSBI), Piazza Manifattura, 1, 38068 Rovereto (Italy); Priami, Corrado, E-mail: priami@cosbi.eu [The Microsoft Research – University of Trento Centre for Computational and Systems Biology (COSBI), Piazza Manifattura, 1, 38068 Rovereto (Italy); University of Trento, Department of Mathematics (Italy); Thanh, Vo Hong, E-mail: vo@cosbi.eu [The Microsoft Research – University of Trento Centre for Computational and Systems Biology (COSBI), Piazza Manifattura, 1, 38068 Rovereto (Italy)
2016-07-15
This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms.
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)
Extended Plefka expansion for stochastic dynamics
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.
Global sensitivity analysis in stochastic simulators of uncertain reaction networks
Navarro, Marí a; Le Maitre, Olivier; Knio, Omar
2016-01-01
sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity
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...
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
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.
Reliability-based Dynamic Network Design with Stochastic Networks
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
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.
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.
Dynamics of the stochastic low concentration trimolecular oscillatory chemical system with jumps
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.
Safety Analysis of Stochastic Dynamical Systems
DEFF Research Database (Denmark)
Sloth, Christoffer; Wisniewski, Rafael
2015-01-01
This paper presents a method for verifying the safety of a stochastic system. In particular, we show how to compute the largest set of initial conditions such that a given stochastic system is safe with probability p. To compute the set of initial conditions we rely on the moment method that via...... that shows how the p-safe initial set is computed numerically....
Provably unbounded memory advantage in stochastic simulation using quantum mechanics
Garner, Andrew J. P.; Liu, Qing; Thompson, Jayne; Vedral, Vlatko; Gu, mile
2017-10-01
Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the simulation is thus generally limited by the internal memory available to the simulator. Here, using tools from computational mechanics, we show that quantum processors with a fixed finite memory can simulate stochastic processes of real variables to arbitrarily high precision. This demonstrates a provable, unbounded memory advantage that a quantum simulator can exhibit over its best possible classical counterpart.
Provably unbounded memory advantage in stochastic simulation using quantum mechanics
International Nuclear Information System (INIS)
Garner, Andrew J P; Thompson, Jayne; Vedral, Vlatko; Gu, Mile; Liu, Qing
2017-01-01
Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the simulation is thus generally limited by the internal memory available to the simulator. Here, using tools from computational mechanics, we show that quantum processors with a fixed finite memory can simulate stochastic processes of real variables to arbitrarily high precision. This demonstrates a provable, unbounded memory advantage that a quantum simulator can exhibit over its best possible classical counterpart. (paper)
Evaluation of Electric Power Procurement Strategies by Stochastic Dynamic Programming
Saisho, Yuichi; Hayashi, Taketo; Fujii, Yasumasa; Yamaji, Kenji
In deregulated electricity markets, the role of a distribution company is to purchase electricity from the wholesale electricity market at randomly fluctuating prices and to provide it to its customers at a given fixed price. Therefore the company has to take risk stemming from the uncertainties of electricity prices and/or demand fluctuation instead of the customers. The way to avoid the risk is to make a bilateral contact with generating companies or install its own power generation facility. This entails the necessity to develop a certain method to make an optimal strategy for electric power procurement. In such a circumstance, this research has the purpose for proposing a mathematical method based on stochastic dynamic programming and additionally considering the characteristics of the start-up cost of electric power generation facility to evaluate strategies of combination of the bilateral contract and power auto-generation with its own facility for procuring electric power in deregulated electricity market. In the beginning we proposed two approaches to solve the stochastic dynamic programming, and they are a Monte Carlo simulation method and a finite difference method to derive the solution of a partial differential equation of the total procurement cost of electric power. Finally we discussed the influences of the price uncertainty on optimal strategies of power procurement.
Stochastic dynamics of genetic broadcasting networks
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.
Constant-pH molecular dynamics using stochastic titration
Baptista, António M.; Teixeira, Vitor H.; Soares, Cláudio M.
2002-09-01
A new method is proposed for performing constant-pH molecular dynamics (MD) simulations, that is, MD simulations where pH is one of the external thermodynamic parameters, like the temperature or the pressure. The protonation state of each titrable site in the solute is allowed to change during a molecular mechanics (MM) MD simulation, the new states being obtained from a combination of continuum electrostatics (CE) calculations and Monte Carlo (MC) simulation of protonation equilibrium. The coupling between the MM/MD and CE/MC algorithms is done in a way that ensures a proper Markov chain, sampling from the intended semigrand canonical distribution. This stochastic titration method is applied to succinic acid, aimed at illustrating the method and examining the choice of its adjustable parameters. The complete titration of succinic acid, using constant-pH MD simulations at different pH values, gives a clear picture of the coupling between the trans/gauche isomerization and the protonation process, making it possible to reconcile some apparently contradictory results of previous studies. The present constant-pH MD method is shown to require a moderate increase of computational cost when compared to the usual MD method.
Stochastic Dynamics Underlying Cognitive Stability and Flexibility.
Directory of Open Access Journals (Sweden)
Kai Ueltzhöffer
2015-06-01
updating and dopaminergic modulation of cognitive flexibility. These results show that stochastic dynamical systems can implement the basic computations underlying cognitive stability and flexibility and explain neurobiological bases of individual differences.
National Research Council Canada - National Science Library
Frazier, John; Chusak, Yaroslav; Foy, Brent
2008-01-01
.... The software uses either exact or approximate stochastic simulation algorithms for generating Monte Carlo trajectories that describe the time evolution of the behavior of biomolecular reaction networks...
Monte Carlo simulation of fully Markovian stochastic geometries
International Nuclear Information System (INIS)
Lepage, Thibaut; Delaby, Lucie; Malvagi, Fausto; Mazzolo, Alain
2010-01-01
The interest in resolving the equation of transport in stochastic media has continued to increase these last years. For binary stochastic media it is often assumed that the geometry is Markovian, which is never the case in usual environments. In the present paper, based on rigorous mathematical theorems, we construct fully two-dimensional Markovian stochastic geometries and we study their main properties. In particular, we determine a percolation threshold p c , equal to 0.586 ± 0.0015 for such geometries. Finally, Monte Carlo simulations are performed through these geometries and the results compared to homogeneous geometries. (author)
The stochastic dynamics of tethered microcantilevers in a viscous fluid
Energy Technology Data Exchange (ETDEWEB)
Robbins, Brian A.; Paul, Mark R. [Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24061 (United States); Radiom, Milad; Ducker, William A. [Department of Chemical Engineering, Virginia Tech, Blacksburg, Virginia 24061 (United States); Walz, John Y. [Department of Chemical Engineering, University of Kentucky, Lexington, Kentucky 40506 (United States)
2014-10-28
We explore and quantify the coupled dynamics of a pair of micron scale cantilevers immersed in a viscous fluid that are also directly tethered to one another at their tips by a spring force. The spring force, for example, could represent the molecular stiffness or elasticity of a biomolecule or material tethered between the cantilevers. We use deterministic numerical simulations with the fluctuation-dissipation theorem to compute the stochastic dynamics of the cantilever pair for the conditions of experiment when driven only by Brownian motion. We validate our approach by comparing directly with experimental measurements in the absence of the tether which shows excellent agreement. Using numerical simulations, we quantify the correlated dynamics of the cantilever pair over a range of tether stiffness. Our results quantify the sensitivity of the auto- and cross-correlations of equilibrium fluctuations in cantilever displacement to the stiffness of the tether. We show that the tether affects the magnitude of the correlations which can be used in a measurement to probe the properties of an attached tethering substance. For the configurations of current interest using micron scale cantilevers in water, we show that the magnitude of the fluid coupling between the cantilevers is sufficiently small such that the influence of the tether can be significant. Our results show that the cross-correlation is more sensitive to tether stiffness than the auto-correlation indicating that a two-cantilever measurement has improved sensitivity when compared with a measurement using a single cantilever.
Bewley, J.M.; Boehlje, M.D.; Gray, A.W.; Hogeveen, H.; Kenyon, S.J.; Eicher, S.D.; Schutz, M.M.
2010-01-01
Purpose – The purpose of this paper is to develop a dynamic, stochastic, mechanistic simulation model of a dairy business to evaluate the cost and benefit streams coinciding with technology investments. The model was constructed to embody the biological and economical complexities of a dairy farm
Assessing predictability of a hydrological stochastic-dynamical system
Gelfan, Alexander
2014-05-01
to those of the corresponding series of the actual data measured at the station. Beginning from the initial conditions and being forced by Monte-Carlo generated synthetic meteorological series, the model simulated diverging trajectories of soil moisture characteristics (water content of soil column, moisture of different soil layers, etc.). Limit of predictability of the specific characteristic was determined through time of stabilization of variance of the characteristic between the trajectories, as they move away from the initial state. Numerical experiments were carried out with the stochastic-dynamical model to analyze sensitivity of the soil moisture predictability assessments to uncertainty in the initial conditions, to determine effects of the soil hydraulic properties and processes of soil freezing on the predictability. It was found, particularly, that soil water content predictability is sensitive to errors in the initial conditions and strongly depends on the hydraulic properties of soil under both unfrozen and frozen conditions. Even if the initial conditions are "well-established", the assessed predictability of water content of unfrozen soil does not exceed 30-40 days, while for frozen conditions it may be as long as 3-4 months. The latter creates opportunity for utilizing the autumn water content of soil as the predictor for spring snowmelt runoff in the region under consideration.
Efficient stochastic thermostatting of path integral molecular dynamics.
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E; Manolopoulos, David E
2010-09-28
The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.
International Nuclear Information System (INIS)
Xu, Zuwei; Zhao, Haibo; Zheng, Chuguang
2015-01-01
This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are
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...
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.
Ichikawa, Kazuhisa; Suzuki, Takashi; Murata, Noboru
2010-11-30
Molecular events in biological cells occur in local subregions, where the molecules tend to be small in number. The cytoskeleton, which is important for both the structural changes of cells and their functions, is also a countable entity because of its long fibrous shape. To simulate the local environment using a computer, stochastic simulations should be run. We herein report a new method of stochastic simulation based on random walk and reaction by the collision of all molecules. The microscopic reaction rate P(r) is calculated from the macroscopic rate constant k. The formula involves only local parameters embedded for each molecule. The results of the stochastic simulations of simple second-order, polymerization, Michaelis-Menten-type and other reactions agreed quite well with those of deterministic simulations when the number of molecules was sufficiently large. An analysis of the theory indicated a relationship between variance and the number of molecules in the system, and results of multiple stochastic simulation runs confirmed this relationship. We simulated Ca²(+) dynamics in a cell by inward flow from a point on the cell surface and the polymerization of G-actin forming F-actin. Our results showed that this theory and method can be used to simulate spatially inhomogeneous events.
International Nuclear Information System (INIS)
Ichikawa, Kazuhisa; Suzuki, Takashi; Murata, Noboru
2010-01-01
Molecular events in biological cells occur in local subregions, where the molecules tend to be small in number. The cytoskeleton, which is important for both the structural changes of cells and their functions, is also a countable entity because of its long fibrous shape. To simulate the local environment using a computer, stochastic simulations should be run. We herein report a new method of stochastic simulation based on random walk and reaction by the collision of all molecules. The microscopic reaction rate P r is calculated from the macroscopic rate constant k. The formula involves only local parameters embedded for each molecule. The results of the stochastic simulations of simple second-order, polymerization, Michaelis–Menten-type and other reactions agreed quite well with those of deterministic simulations when the number of molecules was sufficiently large. An analysis of the theory indicated a relationship between variance and the number of molecules in the system, and results of multiple stochastic simulation runs confirmed this relationship. We simulated Ca 2+ dynamics in a cell by inward flow from a point on the cell surface and the polymerization of G-actin forming F-actin. Our results showed that this theory and method can be used to simulate spatially inhomogeneous events
HSimulator: Hybrid Stochastic/Deterministic Simulation of Biochemical Reaction Networks
Directory of Open Access Journals (Sweden)
Luca Marchetti
2017-01-01
Full Text Available HSimulator is a multithread simulator for mass-action biochemical reaction systems placed in a well-mixed environment. HSimulator provides optimized implementation of a set of widespread state-of-the-art stochastic, deterministic, and hybrid simulation strategies including the first publicly available implementation of the Hybrid Rejection-based Stochastic Simulation Algorithm (HRSSA. HRSSA, the fastest hybrid algorithm to date, allows for an efficient simulation of the models while ensuring the exact simulation of a subset of the reaction network modeling slow reactions. Benchmarks show that HSimulator is often considerably faster than the other considered simulators. The software, running on Java v6.0 or higher, offers a simulation GUI for modeling and visually exploring biological processes and a Javadoc-documented Java library to support the development of custom applications. HSimulator is released under the COSBI Shared Source license agreement (COSBI-SSLA.
Parallel Monte Carlo simulation of aerosol dynamics
Zhou, K.; He, Z.; Xiao, M.; Zhang, Z.
2014-01-01
is simulated with a stochastic method (Marcus-Lushnikov stochastic process). Operator splitting techniques are used to synthesize the deterministic and stochastic parts in the algorithm. The algorithm is parallelized using the Message Passing Interface (MPI
Forecasting financial asset processes: stochastic dynamics via learning neural networks.
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.
MONTE CARLO SIMULATION OF MULTIFOCAL STOCHASTIC SCANNING SYSTEM
Directory of Open Access Journals (Sweden)
LIXIN LIU
2014-01-01
Full Text Available Multifocal multiphoton microscopy (MMM has greatly improved the utilization of excitation light and imaging speed due to parallel multiphoton excitation of the samples and simultaneous detection of the signals, which allows it to perform three-dimensional fast fluorescence imaging. Stochastic scanning can provide continuous, uniform and high-speed excitation of the sample, which makes it a suitable scanning scheme for MMM. In this paper, the graphical programming language — LabVIEW is used to achieve stochastic scanning of the two-dimensional galvo scanners by using white noise signals to control the x and y mirrors independently. Moreover, the stochastic scanning process is simulated by using Monte Carlo method. Our results show that MMM can avoid oversampling or subsampling in the scanning area and meet the requirements of uniform sampling by stochastically scanning the individual units of the N × N foci array. Therefore, continuous and uniform scanning in the whole field of view is implemented.
Stochastic Online Learning in Dynamic Networks under Unknown Models
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
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.
Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations
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.
Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator
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.
Stochastic simulation of off-shore oil terminal systems
International Nuclear Information System (INIS)
Frankel, E.G.; Oberle, J.
1991-01-01
To cope with the problem of uncertainty and conditionality in the planning, design, and operation of offshore oil transshipment terminal systems, a conditional stochastic simulation approach is presented. Examples are shown, using SLAM II, a computer simulation language based on GERT, a conditional stochastic network analysis methodology in which use of resources such as time and money are expressed by the moment generating function of the statistics of the resource requirements. Similarly each activity has an associated conditional probability of being performed and/or of requiring some of the resources. The terminal system is realistically represented by modelling the statistics of arrivals, loading and unloading times, uncertainties in costs and availabilities, etc
The Theory of Dynamic Public Transit Priority with Dynamic Stochastic Park and Ride
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...
Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations
Christensen, H. M.; Dawson, A.; Palmer, T.
2017-12-01
Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.
Real option valuation of power transmission investments by stochastic simulation
International Nuclear Information System (INIS)
Pringles, Rolando; Olsina, Fernando; Garcés, Francisco
2015-01-01
Network expansions in power markets usually lead to investment decisions subject to substantial irreversibility and uncertainty. Hence, investors need valuing the flexibility to change decisions as uncertainty unfolds progressively. Real option analysis is an advanced valuation technique that enables planners to take advantage of market opportunities while preventing or mitigating losses if future conditions evolve unfavorably. In the past, many approaches for valuing real options have been developed. However, applying these methods to value transmission projects is often inappropriate as revenue cash flows are path-dependent and affected by a myriad of uncertain variables. In this work, a valuation technique based on stochastic simulation and recursive dynamic programming, called Least-Square Monte Carlo, is applied to properly value the deferral option in a transmission investment. The effect of option's maturity, the initial outlay and the capital cost upon the value of the postponement option is investigated. Finally, sensitivity analysis determines optimal decision regions to execute, postpone or reject the investment projects. - Highlights: • A modern investment appraisal method is applied to value power transmission projects. • The value of the option to postpone decision to invest in transmission projects is assessed. • Simulation methods are best suited for valuing real options in transmission investments
Improved operating strategies for uranium extraction: a stochastic simulation
International Nuclear Information System (INIS)
Broekman, B.R.
1986-01-01
Deterministic and stochastic simulations of a Western Transvaal uranium process are used in this research report to determine more profitable uranium plant operating strategies and to gauge the potential financial benefits of automatic process control. The deterministic simulation model was formulated using empirical and phenomenological process models. The model indicated that profitability increases significantly as the uranium leaching strategy becomes harsher. The stochastic simulation models use process variable distributions corresponding to manually and automatically controlled conditions to investigate the economic gains that may be obtained if a change is made from manual to automatic control of two important process variables. These lognormally distributed variables are the pachuca 1 sulphuric acid concentration and the ferric to ferrous ratio. The stochastic simulations show that automatic process control is justifiable in certain cases. Where the leaching strategy is relatively harsh, such as that in operation during January 1986, it is not possible to justify an automatic control system. Automatic control is, however, justifiable if a relatively mild leaching strategy is adopted. The stochastic and deterministic simulations represent two different approaches to uranium process modelling. This study has indicated the necessity for each approach to be applied in the correct context. It is contended that incorrect conclusions may have been drawn by other investigators in South Africa who failed to consider the two approaches separately
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....
A constrained approach to multiscale stochastic simulation of chemically reacting systems
Cotter, Simon L.
2011-01-01
Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems. © 2011 American Institute of Physics.
Simulating biological processes: stochastic physics from whole cells to colonies
Earnest, Tyler M.; Cole, John A.; Luthey-Schulten, Zaida
2018-05-01
The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a ‘minimal cell’. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.
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.
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.
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.
Analysing initial attack on wildland fires using stochastic simulation.
Jeremy S. Fried; J. Keith Gilless; James. Spero
2006-01-01
Stochastic simulation models of initial attack on wildland fire can be designed to reflect the complexity of the environmental, administrative, and institutional context in which wildland fire protection agencies operate, but such complexity may come at the cost of a considerable investment in data acquisition and management. This cost may be well justified when it...
Powering stochastic reliability models by discrete event simulation
DEFF Research Database (Denmark)
Kozine, Igor; Wang, Xiaoyun
2012-01-01
it difficult to find a solution to the problem. The power of modern computers and recent developments in discrete-event simulation (DES) software enable to diminish some of the drawbacks of stochastic models. In this paper we describe the insights we have gained based on using both Markov and DES models...
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.
Stochastic search in structural optimization - Genetic algorithms and simulated annealing
Hajela, Prabhat
1993-01-01
An account is given of illustrative applications of genetic algorithms and simulated annealing methods in structural optimization. The advantages of such stochastic search methods over traditional mathematical programming strategies are emphasized; it is noted that these methods offer a significantly higher probability of locating the global optimum in a multimodal design space. Both genetic-search and simulated annealing can be effectively used in problems with a mix of continuous, discrete, and integer design variables.
Dynamics and Physiological Roles of Stochastic Firing Patterns Near Bifurcation Points
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.
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.
Stochastic sensitivity analysis and Langevin simulation for neural network learning
International Nuclear Information System (INIS)
Koda, Masato
1997-01-01
A comprehensive theoretical framework is proposed for the learning of a class of gradient-type neural networks with an additive Gaussian white noise process. The study is based on stochastic sensitivity analysis techniques, and formal expressions are obtained for stochastic learning laws in terms of functional derivative sensitivity coefficients. The present method, based on Langevin simulation techniques, uses only the internal states of the network and ubiquitous noise to compute the learning information inherent in the stochastic correlation between noise signals and the performance functional. In particular, the method does not require the solution of adjoint equations of the back-propagation type. Thus, the present algorithm has the potential for efficiently learning network weights with significantly fewer computations. Application to an unfolded multi-layered network is described, and the results are compared with those obtained by using a back-propagation method
Pricing decisions in an experimental dynamic stochastic general equilibrium economy
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
Sharp asymptotics for stochastic dynamics with parallel updating rule
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
Sharp asymptotics for stochastic dynamics with parallel updating rule
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
Sharp Asymptotics for Stochastic Dynamics with Parallel Updating Rule
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.,
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
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...
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; ...
Stochastic simulation of nucleation in binary alloys
L’vov, P. E.; Svetukhin, V. V.
2018-06-01
In this study, we simulate nucleation in binary alloys with respect to thermal fluctuations of the alloy composition. The simulation is based on the Cahn–Hilliard–Cook equation. We have considered the influence of some fluctuation parameters (wave vector cutoff and noise amplitude) on the kinetics of nucleation and growth of minority phase precipitates. The obtained results are validated by the example of iron–chromium alloys.
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.
Qualitative and Quantitative Integrated Modeling for Stochastic Simulation and Optimization
Directory of Open Access Journals (Sweden)
Xuefeng Yan
2013-01-01
Full Text Available The simulation and optimization of an actual physics system are usually constructed based on the stochastic models, which have both qualitative and quantitative characteristics inherently. Most modeling specifications and frameworks find it difficult to describe the qualitative model directly. In order to deal with the expert knowledge, uncertain reasoning, and other qualitative information, a qualitative and quantitative combined modeling specification was proposed based on a hierarchical model structure framework. The new modeling approach is based on a hierarchical model structure which includes the meta-meta model, the meta-model and the high-level model. A description logic system is defined for formal definition and verification of the new modeling specification. A stochastic defense simulation was developed to illustrate how to model the system and optimize the result. The result shows that the proposed method can describe the complex system more comprehensively, and the survival probability of the target is higher by introducing qualitative models into quantitative simulation.
Stochastic stresses in granular matter simulated by dripping identical ellipses into plane silo
DEFF Research Database (Denmark)
Berntsen, Kasper Nikolaj; Ditlevsen, Ove Dalager
2000-01-01
A two-dimensional silo pressure model-problem is investigated by molecular dynamics simulations. A plane silo container is filled by a granular matter consisting of congruent elliptic particles dropped one by one into the silo. A suitable energy absorbing contact force mechanism is activatedduring...... the granular matter in the silo are compared to thesolution of a stochastic equilibrium differential equation. In this equation the stochasticity source is a homogeneouswhite noise gamma-distributed side pressure factor field along the walls. This is a generalization of the deterministic side pressure factor...... proposed by Janssen in 1895. The stochastic Janssen factor model is shown to be fairly consistentwith the observations from which the mean and the intensity of the white noise is estimated by the method of maximumlikelihood using the properties of the gamma-distribution. Two wall friction coefficients...
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.
A stochastic six-degree-of-freedom flight simulator for passively controlled high power rockets
Box, Simon; Bishop, Christopher M.; Hunt, Hugh
2011-01-01
This paper presents a method for simulating the flight of a passively controlled rocket in six degrees of freedom, and the descent under parachute in three degrees of freedom, Also presented is a method for modelling the uncertainty in both the rocket dynamics and the atmospheric conditions using stochastic parameters and the Monte-Carlo method. Included within this we present a method for quantifying the uncertainty in the atmospheric conditions using historical atmospheric data. The core si...
New "Tau-Leap" Strategy for Accelerated Stochastic Simulation.
Ramkrishna, Doraiswami; Shu, Che-Chi; Tran, Vu
2014-12-10
The "Tau-Leap" strategy for stochastic simulations of chemical reaction systems due to Gillespie and co-workers has had considerable impact on various applications. This strategy is reexamined with Chebyshev's inequality for random variables as it provides a rigorous probabilistic basis for a measured τ-leap thus adding significantly to simulation efficiency. It is also shown that existing strategies for simulation times have no probabilistic assurance that they satisfy the τ-leap criterion while the use of Chebyshev's inequality leads to a specified degree of certainty with which the τ-leap criterion is satisfied. This reduces the loss of sample paths which do not comply with the τ-leap criterion. The performance of the present algorithm is assessed, with respect to one discussed by Cao et al. ( J. Chem. Phys. 2006 , 124 , 044109), a second pertaining to binomial leap (Tian and Burrage J. Chem. Phys. 2004 , 121 , 10356; Chatterjee et al. J. Chem. Phys. 2005 , 122 , 024112; Peng et al. J. Chem. Phys. 2007 , 126 , 224109), and a third regarding the midpoint Poisson leap (Peng et al., 2007; Gillespie J. Chem. Phys. 2001 , 115 , 1716). The performance assessment is made by estimating the error in the histogram measured against that obtained with the so-called stochastic simulation algorithm. It is shown that the current algorithm displays notably less histogram error than its predecessor for a fixed computation time and, conversely, less computation time for a fixed accuracy. This computational advantage is an asset in repetitive calculations essential for modeling stochastic systems. The importance of stochastic simulations is derived from diverse areas of application in physical and biological sciences, process systems, and economics, etc. Computational improvements such as those reported herein are therefore of considerable significance.
Stochastic dynamic programming model for optimal resource ...
Indian Academy of Sciences (India)
M Bhuvaneswari
2018-04-11
Apr 11, 2018 ... handover in VANET; because of high dynamics in net- work topology, collaboration ... containers, doctors, nurses, cash and stocks. Similarly, ... GTBA does not take the resource types and availability into consideration.
HYDRASTAR - a code for stochastic simulation of groundwater flow
International Nuclear Information System (INIS)
Norman, S.
1992-05-01
The computer code HYDRASTAR was developed as a tool for groundwater flow and transport simulations in the SKB 91 safety analysis project. Its conceptual ideas can be traced back to a report by Shlomo Neuman in 1988, see the reference section. The main idea of the code is the treatment of the rock as a stochastic continuum which separates it from the deterministic methods previously employed by SKB and also from the discrete fracture models. The current report is a comprehensive description of HYDRASTAR including such topics as regularization or upscaling of a hydraulic conductivity field, unconditional and conditional simulation of stochastic processes, numerical solvers for the hydrology and streamline equations and finally some proposals for future developments
GillespieSSA: Implementing the Gillespie Stochastic Simulation Algorithm in R
Directory of Open Access Journals (Sweden)
Mario Pineda-Krch
2008-02-01
Full Text Available The deterministic dynamics of populations in continuous time are traditionally described using coupled, first-order ordinary differential equations. While this approach is accurate for large systems, it is often inadequate for small systems where key species may be present in small numbers or where key reactions occur at a low rate. The Gillespie stochastic simulation algorithm (SSA is a procedure for generating time-evolution trajectories of finite populations in continuous time and has become the standard algorithm for these types of stochastic models. This article presents a simple-to-use and flexible framework for implementing the SSA using the high-level statistical computing language R and the package GillespieSSA. Using three ecological models as examples (logistic growth, Rosenzweig-MacArthur predator-prey model, and Kermack-McKendrick SIRS metapopulation model, this paper shows how a deterministic model can be formulated as a finite-population stochastic model within the framework of SSA theory and how it can be implemented in R. Simulations of the stochastic models are performed using four different SSA Monte Carlo methods: one exact method (Gillespie's direct method; and three approximate methods (explicit, binomial, and optimized tau-leap methods. Comparison of simulation results confirms that while the time-evolution trajectories obtained from the different SSA methods are indistinguishable, the approximate methods are up to four orders of magnitude faster than the exact methods.
International Nuclear Information System (INIS)
Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying
2013-01-01
We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.
Stochastic and simulation models of maritime intercept operations capabilities
Sato, Hiroyuki
2005-01-01
The research formulates and exercises stochastic and simulation models to assess the Maritime Intercept Operations (MIO) capabilities. The models focus on the surveillance operations of the Maritime Patrol Aircraft (MPA). The analysis using the models estimates the probability with which a terrorist vessel (Red) is detected, correctly classified, and escorted for intensive investigation and neutralization before it leaves an area of interest (AOI). The difficulty of obtaining adequate int...
Dynamic option pricing with endogenous stochastic arbitrage
Contreras, Mauricio; Montalva, Rodrigo; Pellicer, Rely; Villena, Marcelo
2010-09-01
Only few efforts have been made in order to relax one of the key assumptions of the Black-Scholes model: the no-arbitrage assumption. This is despite the fact that arbitrage processes usually exist in the real world, even though they tend to be short-lived. The purpose of this paper is to develop an option pricing model with endogenous stochastic arbitrage, capable of modelling in a general fashion any future and underlying asset that deviate itself from its market equilibrium. Thus, this investigation calibrates empirically the arbitrage on the futures on the S&P 500 index using transaction data from September 1997 to June 2009, from here a specific type of arbitrage called “arbitrage bubble”, based on a t-step function, is identified and hence used in our model. The theoretical results obtained for Binary and European call options, for this kind of arbitrage, show that an investment strategy that takes advantage of the identified arbitrage possibility can be defined, whenever it is possible to anticipate in relative terms the amplitude and timespan of the process. Finally, the new trajectory of the stock price is analytically estimated for a specific case of arbitrage and some numerical illustrations are developed. We find that the consequences of a finite and small endogenous arbitrage not only change the trajectory of the asset price during the period when it started, but also after the arbitrage bubble has already gone. In this context, our model will allow us to calibrate the B-S model to that new trajectory even when the arbitrage already started.
Stochastic Simulation of the Exchange Rate
Directory of Open Access Journals (Sweden)
Anamaria ALDEA
2007-01-01
Full Text Available The rational expectations paradigm, that dominates macroeconomicsfails to take into account the complexity of the information, which is so vast that the individual brain cannot understand the full of it. The agents are boundedly rational,so they use simple forecasting rules that do not incorporate all available information, but they are willing to learn and will switch to other rules if it turns out that these rules are more profitable than the rule they have been using. Such trial and error learning strategies create the dynamics in the foreign exchange market, with two types of equilibria, a fundamental and a non-fundamental equilibrium to which the exchange rate is attracted.
Stochastic simulations of calcium contents in sugarcane area
Directory of Open Access Journals (Sweden)
Gener T. Pereira
2015-08-01
Full Text Available ABSTRACTThe aim of this study was to quantify and to map the spatial distribution and uncertainty of soil calcium (Ca content in a sugarcane area by sequential Gaussian and simulated-annealing simulation methods. The study was conducted in the municipality of Guariba, northeast of the São Paulo state. A sampling grid with 206 points separated by a distance of 50 m was established, totaling approximately 42 ha. The calcium contents were evaluated in layer of 0-0.20 m. Techniques of geostatistical estimation, ordinary kriging and stochastic simulations were used. The technique of ordinary kriging does not reproduce satisfactorily the global statistics of the Ca contents. The use of simulation techniques allows reproducing the spatial variability pattern of Ca contents. The techniques of sequential Gaussian simulation and simulated annealing showed significant variations in the contents of Ca in the small scale.
On an aggregation in birth-and-death stochastic dynamics
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.
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)
A data driven nonlinear stochastic model for blood glucose dynamics.
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.
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
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.
Stochastic GARCH dynamics describing correlations between stocks
Prat-Ortega, G.; Savel'ev, S. E.
2014-09-01
The ARCH and GARCH processes have been successfully used for modelling price dynamics such as stock returns or foreign exchange rates. Analysing the long range correlations between stocks, we propose a model, based on the GARCH process, which is able to describe the main characteristics of the stock price correlations, including the mean, variance, probability density distribution and the noise spectrum.
Stochastic population dynamic models as probability networks
M.E. and D.C. Lee. Borsuk
2009-01-01
The dynamics of a population and its response to environmental change depend on the balance of birth, death and age-at-maturity, and there have been many attempts to mathematically model populations based on these characteristics. Historically, most of these models were deterministic, meaning that the results were strictly determined by the equations of the model and...
Stochastic Computer Simulation of Cermet Coatings Formation
Directory of Open Access Journals (Sweden)
Oleg P. Solonenko
2015-01-01
Full Text Available An approach to the modeling of the process of the formation of thermal coatings lamellar structure, including plasma coatings, at the spraying of cermet powders is proposed. The approach based on the theoretical fundamentals developed which could be used for rapid and sufficiently accurate prediction of thickness and diameter of cermet splats as well as temperature at interface “flattening quasi-liquid cermet particle-substrate” depending on the key physical parameters (KPPs: temperature, velocity and size of particle, substrate temperature, and concentration of finely dispersed solid inclusions uniformly distributed in liquid metal binder. The results are presented, which concern the development of the computational algorithm and the program complex for modeling the process of laying the splats in the coating with regard to the topology of its surface, which varies dynamically at the spraying, as well as the formation of lamellar structure and porosity of the coating. The results of numerical experiments are presented through the example of thermal spraying the cermet TiC-30 vol.% NiCr powder, illustrating the performance of the developed computational technology.
STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB
Klingbeil, G.; Erban, R.; Giles, M.; Maini, P. K.
2011-01-01
Motivation: The importance of stochasticity in biological systems is becoming increasingly recognized and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new
Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C.
2010-01-01
The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when
Simulation of anaerobic digestion processes using stochastic algorithm.
Palanichamy, Jegathambal; Palani, Sundarambal
2014-01-01
The Anaerobic Digestion (AD) processes involve numerous complex biological and chemical reactions occurring simultaneously. Appropriate and efficient models are to be developed for simulation of anaerobic digestion systems. Although several models have been developed, mostly they suffer from lack of knowledge on constants, complexity and weak generalization. The basis of the deterministic approach for modelling the physico and bio-chemical reactions occurring in the AD system is the law of mass action, which gives the simple relationship between the reaction rates and the species concentrations. The assumptions made in the deterministic models are not hold true for the reactions involving chemical species of low concentration. The stochastic behaviour of the physicochemical processes can be modeled at mesoscopic level by application of the stochastic algorithms. In this paper a stochastic algorithm (Gillespie Tau Leap Method) developed in MATLAB was applied to predict the concentration of glucose, acids and methane formation at different time intervals. By this the performance of the digester system can be controlled. The processes given by ADM1 (Anaerobic Digestion Model 1) were taken for verification of the model. The proposed model was verified by comparing the results of Gillespie's algorithms with the deterministic solution for conversion of glucose into methane through degraders. At higher value of 'τ' (timestep), the computational time required for reaching the steady state is more since the number of chosen reactions is less. When the simulation time step is reduced, the results are similar to ODE solver. It was concluded that the stochastic algorithm is a suitable approach for the simulation of complex anaerobic digestion processes. The accuracy of the results depends on the optimum selection of tau value.
Monte carlo simulation for soot dynamics
Zhou, Kun
2012-01-01
A new Monte Carlo method termed Comb-like frame Monte Carlo is developed to simulate the soot dynamics. Detailed stochastic error analysis is provided. Comb-like frame Monte Carlo is coupled with the gas phase solver Chemkin II to simulate soot formation in a 1-D premixed burner stabilized flame. The simulated soot number density, volume fraction, and particle size distribution all agree well with the measurement available in literature. The origin of the bimodal distribution of particle size distribution is revealed with quantitative proof.
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.
Age distribution dynamics with stochastic jumps in mortality.
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.
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.
Hybrid Multilevel Monte Carlo Simulation of Stochastic Reaction Networks
Moraes, Alvaro
2015-01-01
even more, we want to achieve this objective with near optimal computational work. We first introduce a hybrid path-simulation scheme based on the well-known stochastic simulation algorithm (SSA)[3] and the tau-leap method [2]. Then, we introduce a Multilevel Monte Carlo strategy that allows us to achieve a computational complexity of order O(T OL−2), this is the same computational complexity as in an exact method but with a smaller constant. We provide numerical examples to show our results.
Stochastic series expansion simulation of the t -V model
Wang, Lei; Liu, Ye-Hua; Troyer, Matthias
2016-04-01
We present an algorithm for the efficient simulation of the half-filled spinless t -V model on bipartite lattices, which combines the stochastic series expansion method with determinantal quantum Monte Carlo techniques widely used in fermionic simulations. The algorithm scales linearly in the inverse temperature, cubically with the system size, and is free from the time-discretization error. We use it to map out the finite-temperature phase diagram of the spinless t -V model on the honeycomb lattice and observe a suppression of the critical temperature of the charge-density-wave phase in the vicinity of a fermionic quantum critical point.
Stochastic simulation of regional groundwater flow in Beishan area
International Nuclear Information System (INIS)
Dong Yanhui; Li Guomin
2010-01-01
Because of the hydrogeological complexity, traditional thinking of aquifer characteristics is not appropriate for groundwater system in Beishan area. Uncertainty analysis of groundwater models is needed to examine the hydrologic effects of spatial heterogeneity. In this study, fast Fourier transform spectral method (FFTS) was used to generate the random horizontal permeability parameters. Depth decay and vertical anisotropy of hydraulic conductivity were included to build random permeability models. Based on high-performance computers, hundreds of groundwater flow models were simulated. Through stochastic simulations, the effect of heterogeneity to groundwater flow pattern was analyzed. (authors)
Global sensitivity analysis in stochastic simulators of uncertain reaction networks.
Navarro Jimenez, M; Le Maître, O P; Knio, O M
2016-12-28
Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol's decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.
Global sensitivity analysis in stochastic simulators of uncertain reaction networks
Navarro, María
2016-12-26
Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.
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)
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)
Dynamic asset allocation for bank under stochastic interest rates.
Chakroun, Fatma; Abid, Fathi
2014-01-01
This paper considers the optimal asset allocation strategy for bank with stochastic interest rates when there are three types of asset: Bank account, loans and securities. The asset allocation problem is to maximize the expected utility from terminal wealth of a bank's shareholders over a finite time horizon. As a consequence, we apply a dynamic programming principle to solve the Hamilton-Jacobi-Bellman (HJB) equation explicitly in the case of the CRRA utility function. A case study is given ...
Nonperturbative stochastic dynamics driven by strongly correlated colored noise
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.
Stochastic dynamics of a delayed bistable system with multiplicative noise
Energy Technology Data Exchange (ETDEWEB)
Dung, Nguyen Tien, E-mail: dung-nguyentien10@yahoo.com, E-mail: dungnt@fpt.edu.vn [Department of Mathematics, FPT University, No 8 Ton That Thuyet, My Dinh, Tu Liem, Hanoi (Viet Nam)
2014-05-15
In this paper we investigate the properties of a delayed bistable system under the effect of multiplicative noise. We first prove the existence and uniqueness of the positive solution and show that its moments are uniformly bounded. Then, we study stochastic dynamics of the solution in long time, the lower and upper bounds for the paths and an estimate for the average value are provided.
Dynamic analysis of a stochastic delayed rumor propagation model
Jia, Fangju; Lv, Guangying; Wang, Shuangfeng; Zou, Guang-an
2018-02-01
The rapid development of the Internet, especially the emergence of the social networks, has led rumor propagation into a new media era. In this paper, we are concerned with a stochastic delayed rumor propagation model. Firstly, we obtain the existence of the global solution. Secondly, sufficient conditions for extinction of the rumor are established. Lastly, the boundedness of solution is proved and some simulations are given to verify our results.
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.
The stochastic network dynamics underlying perceptual discrimination
Directory of Open Access Journals (Sweden)
Genis Prat-Ortega
2015-04-01
Full Text Available The brain is able to interpret streams of high-dimensional ambiguous information and yield coherent percepts. The mechanisms governing sensory integration have been extensively characterized using time-varying visual stimuli (Britten et al. 1996; Roitman and Shadlen 2002, but some of the basic principles regarding the network dynamics underlying this process remain largely unknown. We captured the basic features of a neural integrator using three canonical one-dimensional models: (1 the Drift Diffusion Model (DDM, (2 the Perfect Integrator (PI which is a particular case of the DDM where the bounds are set to infinity and (3 the double-well potential (DW which captures the dynamics of the attractor networks (Wang 2002; Roxin and Ledberg 2008. Although these models has been widely studied (Bogacz et al. 2006; Roxin and Ledberg 2008; Gold and Shadlen 2002, it has been difficult to experimentally discriminate among them because most of the observables measured are only quantitatively different among these models (e.g. psychometric curves. Here we aim to find experimentally measurable quantities that can yield qualitatively different behaviors depending on the nature of the underlying network dynamics. We examined the categorization dynamics of these models in response to fluctuating stimuli of different duration (T. On each time step, stimuli are drawn from a Gaussian distribution N(μ, σ and the two stimulus categories are defined by μ > 0 and μ < 0. Psychometric curves can therefore be obtained by quantifying the probability of the integrator to yield one category versus μ . We find however that varying σ can reveal more clearly the differences among the different integrators. In the small σ regime, both the DW and the DDM perform transient integration and exhibit a decaying stimulus reverse correlation kernel revealing a primacy effect (Nienborg and Cumming 2009; Wimmer et al. 2015 . In the large σ regime, the integration in the DDM
Mavelli, Fabio; Ruiz-Mirazo, Kepa
2010-09-01
'ENVIRONMENT' is a computational platform that has been developed in the last few years with the aim to simulate stochastically the dynamics and stability of chemically reacting protocellular systems. Here we present and describe some of its main features, showing how the stochastic kinetics approach can be applied to study the time evolution of reaction networks in heterogeneous conditions, particularly when supramolecular lipid structures (micelles, vesicles, etc) coexist with aqueous domains. These conditions are of special relevance to understand the origins of cellular, self-reproducing compartments, in the context of prebiotic chemistry and evolution. We contrast our simulation results with real lab experiments, with the aim to bring together theoretical and experimental research on protocell and minimal artificial cell systems.
A stochastic phase-field model determined from molecular dynamics
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.
A stochastic phase-field model determined from molecular dynamics
von Schwerin, Erik
2010-03-17
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.
Stochastic 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)
Stochastic dynamics and logistic population growth
Méndez, Vicenç; Assaf, Michael; Campos, Daniel; Horsthemke, Werner
2015-06-01
The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations and are related to the reproductive fitness and the competition for limited resources, respectively. We investigate analytically and numerically the simplest possible microscopic scenarios that give rise to the logistic equation in the deterministic mean-field limit. We provide a definition of the two parameters of the Verhulst equation in terms of microscopic parameters. In addition, we derive the conditions for extinction or persistence of the population by employing either the momentum-space spectral theory or the real-space Wentzel-Kramers-Brillouin approximation to determine the probability distribution function and the mean time to extinction of the population. Our analytical results agree well with numerical simulations.
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.
Natural tracer test simulation by stochastic particle tracking method
International Nuclear Information System (INIS)
Ackerer, P.; Mose, R.; Semra, K.
1990-01-01
Stochastic particle tracking methods are well adapted to 3D transport simulations where discretization requirements of other methods usually cannot be satisfied. They do need a very accurate approximation of the velocity field. The described code is based on the mixed hybrid finite element method (MHFEM) to calculated the piezometric and velocity field. The random-walk method is used to simulate mass transport. The main advantages of the MHFEM over FD or FE are the simultaneous calculation of pressure and velocity, which are considered as unknowns; the possibility of interpolating velocities everywhere; and the continuity of the normal component of the velocity vector from one element to another. For these reasons, the MHFEM is well adapted for particle tracking methods. After a general description of the numerical methods, the model is used to simulate the observations made during the Twin Lake Tracer Test in 1983. A good match is found between observed and simulated heads and concentrations. (Author) (12 refs., 4 figs.)
A stochastic model for the simulation of wind turbine blades in static stall
DEFF Research Database (Denmark)
Bertagnolio, Franck; Rasmussen, Flemming; Sørensen, Niels N.
2010-01-01
The aim of this work is to improve aeroelastic simulation codes by accounting for the unsteady aerodynamic forces that a blade experiences in static stall. A model based on a spectral representation of the aerodynamic lift force is defined. The drag and pitching moment are derived using...... a conditional simulation technique for stochastic processes. The input data for the model can be collected either from measurements or from numerical results from a Computational Fluid Dynamics code for airfoil sections at constant angles of attack. An analysis of such data is provided, which helps to determine...
Coarse-graining stochastic biochemical networks: adiabaticity and fast simulations
Energy Technology Data Exchange (ETDEWEB)
Nemenman, Ilya [Los Alamos National Laboratory; Sinitsyn, Nikolai [Los Alamos National Laboratory; Hengartner, Nick [Los Alamos National Laboratory
2008-01-01
We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscoplc, non-Poissonian fluctuations of the slow ones. Our approach, which is similar to the Born-Oppenhelmer approximation in quantum mechanics, follows from the stochastic path Integral representation of the cumulant generating function of reaction events. In applications with a small number of chemIcal reactions, It produces analytical expressions for cumulants of chemical fluxes between the slow variables. This allows for a low-dimensional, Interpretable representation and can be used for coarse-grained numerical simulation schemes with a small computational complexity and yet high accuracy. As an example, we derive the coarse-grained description for a chain of biochemical reactions, and show that the coarse-grained and the microscopic simulations are in an agreement, but the coarse-gralned simulations are three orders of magnitude faster.
Iacus, Stefano M
2018-01-01
The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes or fractional Brownian motion, as well as CARMA processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these ...
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
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.
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.
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.
Interactive Dynamic-System Simulation
Korn, Granino A
2010-01-01
Showing you how to use personal computers for modeling and simulation, Interactive Dynamic-System Simulation, Second Edition provides a practical tutorial on interactive dynamic-system modeling and simulation. It discusses how to effectively simulate dynamical systems, such as aerospace vehicles, power plants, chemical processes, control systems, and physiological systems. Written by a pioneer in simulation, the book introduces dynamic-system models and explains how software for solving differential equations works. After demonstrating real simulation programs with simple examples, the author
Modeling and stochastic analysis of dynamic mechanisms of the perception
Pisarchik, A.; Bashkirtseva, I.; Ryashko, L.
2017-10-01
Modern studies in physiology and cognitive neuroscience consider a noise as an important constructive factor of the brain functionality. Under the adequate noise, the brain can rapidly access different ordered states, and provide decision-making by preventing deadlocks. Bistable dynamic models are often used for the study of the underlying mechanisms of the visual perception. In the present paper, we consider a bistable energy model subject to both additive and parametric noise. Using the catastrophe theory formalism and stochastic sensitivity functions technique, we analyze a response of the equilibria to noise, and study noise-induced transitions between equilibria. We demonstrate and analyse the effect of hysteresis squeezing when the intensity of noise is increased. Stochastic bifurcations connected with the suppression of oscillations by parametric noises are discussed.
A stochastic agent-based model of pathogen propagation in dynamic multi-relational social networks
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
Stochastic simulation of grain growth during continuous casting
Energy Technology Data Exchange (ETDEWEB)
Ramirez, A. [Department of Aerounatical Engineering, S.E.P.I., E.S.I.M.E., IPN, Instituto Politecnico Nacional (Unidad Profesional Ticoman), Av. Ticoman 600, Col. Ticoman, C.P.07340 (Mexico)]. E-mail: adalop123@mailbanamex.com; Carrillo, F. [Department of Processing Materials, CICATA-IPN Unidad Altamira Tamps (Mexico); Gonzalez, J.L. [Department of Metallurgy and Materials Engineering, E.S.I.Q.I.E.-IPN (Mexico); Lopez, S. [Department of Molecular Engineering of I.M.P., AP 14-805 (Mexico)
2006-04-15
The evolution of microstructure is a very important topic in material science engineering because the solidification conditions of steel billets during continuous casting process affect directly the properties of the final products. In this paper a mathematical model is described in order to simulate the dendritic growth using data of real casting operations; here a combination of deterministic and stochastic methods was used as a function of the solidification time of every node in order to create a reconstruction about the morphology of cast structures.
Stochastic simulation of grain growth during continuous casting
International Nuclear Information System (INIS)
Ramirez, A.; Carrillo, F.; Gonzalez, J.L.; Lopez, S.
2006-01-01
The evolution of microstructure is a very important topic in material science engineering because the solidification conditions of steel billets during continuous casting process affect directly the properties of the final products. In this paper a mathematical model is described in order to simulate the dendritic growth using data of real casting operations; here a combination of deterministic and stochastic methods was used as a function of the solidification time of every node in order to create a reconstruction about the morphology of cast structures
Parallel Monte Carlo simulation of aerosol dynamics
Zhou, K.
2014-01-01
A highly efficient Monte Carlo (MC) algorithm is developed for the numerical simulation of aerosol dynamics, that is, nucleation, surface growth, and coagulation. Nucleation and surface growth are handled with deterministic means, while coagulation is simulated with a stochastic method (Marcus-Lushnikov stochastic process). Operator splitting techniques are used to synthesize the deterministic and stochastic parts in the algorithm. The algorithm is parallelized using the Message Passing Interface (MPI). The parallel computing efficiency is investigated through numerical examples. Near 60% parallel efficiency is achieved for the maximum testing case with 3.7 million MC particles running on 93 parallel computing nodes. The algorithm is verified through simulating various testing cases and comparing the simulation results with available analytical and/or other numerical solutions. Generally, it is found that only small number (hundreds or thousands) of MC particles is necessary to accurately predict the aerosol particle number density, volume fraction, and so forth, that is, low order moments of the Particle Size Distribution (PSD) function. Accurately predicting the high order moments of the PSD needs to dramatically increase the number of MC particles. 2014 Kun Zhou et al.
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
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.
Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism
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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.
Stochastic population dynamics of a montane ground-dwelling squirrel.
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.
Noise-sustained fluctuations in stochastic dynamics with a delay.
D'Odorico, Paolo; Laio, Francesco; Ridolfi, Luca
2012-04-01
Delayed responses to external drivers are ubiquitous in environmental, social, and biological processes. Delays may induce oscillations, Hopf bifurcations, and instabilities in deterministic systems even in the absence of nonlinearities. Despite recent advances in the study of delayed stochastic differential equations, the interaction of random drivers with delays remains poorly understood. In particular, it is unclear whether noise-induced behaviors may emerge from these interactions. Here we show that noise may enhance and sustain transient periodic oscillations inherent to deterministic delayed systems. We investigate the conditions conducive to the emergence and disappearance of these dynamics in a linear system in the presence of both additive and multiplicative noise.
Stochastic population dynamics in spatially extended predator-prey systems
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
Automated planning through abstractions in dynamic and stochastic environments
Martínez Muñoz, Moisés
2016-01-01
Mención Internacional en el título de doctor Generating sequences of actions - plans - for an automatic system, like a robot, using Automated Planning is particularly diflicult in stochastic and/or dynamic environments. These plans are composed of actions whose execution, in certain scenarios, might fail, which in tum prevents the execution of the rest of the actions in the plan. Also, in some environments, plans must he generated fast, hoth at the start of the execution and after every ex...
Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics
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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
Stochastic dynamics for two biological species and ecological niches
Ruziska, Flávia M.; Arashiro, Everaldo; Tomé, Tânia
2018-01-01
We consider an ecological system in which two species interact with two niches. To this end we introduce a stochastic model with four states. Our analysis is founded in three approaches: Monte Carlo simulations of the model on a square lattice, mean-field approximation, and birth and death master equation. From this last approach we obtain a description in terms of Langevin equations which show in an explicit way the role of noise in population biology. We focus mainly on the description of time oscillations of the species population and the alternating dominance between them. The model treated here may provide insights on these properties.
A stochastic differential equation analysis of cerebrospinal fluid dynamics.
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.
A stochastic differential equation analysis of cerebrospinal fluid dynamics
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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.
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Giorgos Minas
2017-07-01
Full Text Available In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA overcomes the main limitations of the standard Linear Noise Approximation (LNA to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.
Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost
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Bokanowski, Olivier; Picarelli, Athena; Zidani, Hasnaa
2015-01-01
This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach
Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost
Energy Technology Data Exchange (ETDEWEB)
Bokanowski, Olivier, E-mail: boka@math.jussieu.fr [Laboratoire Jacques-Louis Lions, Université Paris-Diderot (Paris 7) UFR de Mathématiques - Bât. Sophie Germain (France); Picarelli, Athena, E-mail: athena.picarelli@inria.fr [Projet Commands, INRIA Saclay & ENSTA ParisTech (France); Zidani, Hasnaa, E-mail: hasnaa.zidani@ensta.fr [Unité de Mathématiques appliquées (UMA), ENSTA ParisTech (France)
2015-02-15
This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.
Outbreak and Extinction Dynamics in a Stochastic Ebola Model
Nieddu, Garrett; Bianco, Simone; Billings, Lora; Forgoston, Eric; Kaufman, James
A zoonotic disease is a disease that can be passed between animals and humans. In many cases zoonotic diseases can persist in the animal population even if there are no infections in the human population. In this case we call the infected animal population the reservoir for the disease. Ebola virus disease (EVD) and SARS are both notable examples of such diseases. There is little work devoted to understanding stochastic disease extinction and reintroduction in the presence of a reservoir. Here we build a stochastic model for EVD and explicitly consider the presence of an animal reservoir. Using a master equation approach and a WKB ansatz, we determine the associated Hamiltonian of the system. Hamilton's equations are then used to numerically compute the 12-dimensional optimal path to extinction, which is then used to estimate mean extinction times. We also numerically investigate the behavior of the model for dynamic population size. Our results provide an improved understanding of outbreak and extinction dynamics in diseases like EVD.
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
On the stochastic dynamics of disordered spin models
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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)
Interactive macroeconomics stochastic aggregate dynamics with heterogeneous and interacting agents
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...
Weiss, Charles J.
2017-01-01
An introduction to digital stochastic simulations for modeling a variety of physical and chemical processes is presented. Despite the importance of stochastic simulations in chemistry, the prevalence of turn-key software solutions can impose a layer of abstraction between the user and the underlying approach obscuring the methodology being…
Stochastic dynamics of melt ponds and sea ice-albedo climate feedback
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.
Experiences using DAKOTA stochastic expansion methods in computational simulations.
Energy Technology Data Exchange (ETDEWEB)
Templeton, Jeremy Alan; Ruthruff, Joseph R.
2012-01-01
Uncertainty quantification (UQ) methods bring rigorous statistical connections to the analysis of computational and experiment data, and provide a basis for probabilistically assessing margins associated with safety and reliability. The DAKOTA toolkit developed at Sandia National Laboratories implements a number of UQ methods, which are being increasingly adopted by modeling and simulation teams to facilitate these analyses. This report disseminates results as to the performance of DAKOTA's stochastic expansion methods for UQ on a representative application. Our results provide a number of insights that may be of interest to future users of these methods, including the behavior of the methods in estimating responses at varying probability levels, and the expansion levels for the methodologies that may be needed to achieve convergence.
Stochastic simulation and robust design optimization of integrated photonic filters
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Weng Tsui-Wei
2016-07-01
Full Text Available Manufacturing variations are becoming an unavoidable issue in modern fabrication processes; therefore, it is crucial to be able to include stochastic uncertainties in the design phase. In this paper, integrated photonic coupled ring resonator filters are considered as an example of significant interest. The sparsity structure in photonic circuits is exploited to construct a sparse combined generalized polynomial chaos model, which is then used to analyze related statistics and perform robust design optimization. Simulation results show that the optimized circuits are more robust to fabrication process variations and achieve a reduction of 11%–35% in the mean square errors of the 3 dB bandwidth compared to unoptimized nominal designs.
Hybrid Multilevel Monte Carlo Simulation of Stochastic Reaction Networks
Moraes, Alvaro
2015-01-07
Stochastic reaction networks (SRNs) is a class of continuous-time Markov chains intended to describe, from the kinetic point of view, the time-evolution of chemical systems in which molecules of different chemical species undergo a finite set of reaction channels. This talk is based on articles [4, 5, 6], where we are interested in the following problem: given a SRN, X, defined though its set of reaction channels, and its initial state, x0, estimate E (g(X(T))); that is, the expected value of a scalar observable, g, of the process, X, at a fixed time, T. This problem lead us to define a series of Monte Carlo estimators, M, such that, with high probability can produce values close to the quantity of interest, E (g(X(T))). More specifically, given a user-selected tolerance, TOL, and a small confidence level, η, find an estimator, M, based on approximate sampled paths of X, such that, P (|E (g(X(T))) − M| ≤ TOL) ≥ 1 − η; even more, we want to achieve this objective with near optimal computational work. We first introduce a hybrid path-simulation scheme based on the well-known stochastic simulation algorithm (SSA)[3] and the tau-leap method [2]. Then, we introduce a Multilevel Monte Carlo strategy that allows us to achieve a computational complexity of order O(T OL−2), this is the same computational complexity as in an exact method but with a smaller constant. We provide numerical examples to show our results.
International Nuclear Information System (INIS)
Yan-Mei, Kang; Yao-Lin, Jiang
2008-01-01
To explore the influence of anomalous diffusion on stochastic resonance (SR) more deeply and effectively, the method of moments is extended to subdiffusive overdamped bistable fractional Fokker-Planck systems for calculating the long-time linear dynamic response. It is found that the method of moments attains high accuracy with the truncation order N = 10, and in normal diffusion such obtained spectral amplification factor (SAF) of the first-order harmonic is also confirmed by stochastic simulation. Observing the SAF of the odd-order harmonics we find some interesting results, i.e. for smaller driving frequency the decrease of sub diffusion exponent inhibits the stochastic resonance (SR), while for larger driving frequency the decrease of sub diffusion exponent enhances the second SR peak, but the first one vanishes and a double SR is induced in the third-order harmonic at the same time. These observations suggest that the anomalous diffusion has important influence on the bistable dynamics
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)
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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
The stochastic system approach for estimating dynamic treatments effect.
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.
Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical Networks
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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.
Setting development goals using stochastic dynamical system models.
Ranganathan, Shyam; Nicolis, Stamatios C; Bali Swain, Ranjula; Sumpter, David J T
2017-01-01
The Millennium Development Goals (MDG) programme was an ambitious attempt to encourage a globalised solution to important but often-overlooked development problems. The programme led to wide-ranging development but it has also been criticised for unrealistic and arbitrary targets. In this paper, we show how country-specific development targets can be set using stochastic, dynamical system models built from historical data. In particular, we show that the MDG target of two-thirds reduction of child mortality from 1990 levels was infeasible for most countries, especially in sub-Saharan Africa. At the same time, the MDG targets were not ambitious enough for fast-developing countries such as Brazil and China. We suggest that model-based setting of country-specific targets is essential for the success of global development programmes such as the Sustainable Development Goals (SDG). This approach should provide clear, quantifiable targets for policymakers.
The sequence relay selection strategy based on stochastic dynamic programming
Zhu, Rui; Chen, Xihao; Huang, Yangchao
2017-07-01
Relay-assisted (RA) network with relay node selection is a kind of effective method to improve the channel capacity and convergence performance. However, most of the existing researches about the relay selection did not consider the statically channel state information and the selection cost. This shortage limited the performance and application of RA network in practical scenarios. In order to overcome this drawback, a sequence relay selection strategy (SRSS) was proposed. And the performance upper bound of SRSS was also analyzed in this paper. Furthermore, in order to make SRSS more practical, a novel threshold determination algorithm based on the stochastic dynamic program (SDP) was given to work with SRSS. Numerical results are also presented to exhibit the performance of SRSS with SDP.
Sindhikara, Daniel J; Kim, Seonah; Voter, Arthur F; Roitberg, Adrian E
2009-06-09
Molecular dynamics simulations starting from different initial conditions are commonly used to mimic the behavior of an experimental ensemble. We show in this article that when a Langevin thermostat is used to maintain constant temperature during such simulations, extreme care must be taken when choosing the random number seeds to prevent statistical correlation among the MD trajectories. While recent studies have shown that stochastically thermostatted trajectories evolving within a single potential basin with identical random number seeds tend to synchronize, we show that there is a synchronization effect even for complex, biologically relevant systems. We demonstrate this effect in simulations of alanine trimer and pentamer and in a simulation of a temperature-jump experiment for peptide folding of a 14-residue peptide. Even in replica-exchange simulations, in which the trajectories are at different temperatures, we find partial synchronization occurring when the same random number seed is employed. We explain this by extending the recent derivation of the synchronization effect for two trajectories in a harmonic well to the case in which the trajectories are at two different temperatures. Our results suggest several ways in which mishandling selection of a pseudorandom number generator initial seed can lead to corruption of simulation data. Simulators can fall into this trap in simple situations such as neglecting to specifically indicate different random seeds in either parallel or sequential restart simulations, utilizing a simulation package with a weak pseudorandom number generator, or using an advanced simulation algorithm that has not been programmed to distribute initial seeds.
STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB
Klingbeil, G.
2011-02-25
Motivation: The importance of stochasticity in biological systems is becoming increasingly recognized and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new software tool STOCHSIMGPU that exploits graphics processing units (GPUs) for parallel stochastic simulations of biological/chemical reaction systems and show that significant gains in efficiency can be made. It is integrated into MATLAB and works with the Systems Biology Toolbox 2 (SBTOOLBOX2) for MATLAB. Results: The GPU-based parallel implementation of the Gillespie stochastic simulation algorithm (SSA), the logarithmic direct method (LDM) and the next reaction method (NRM) is approximately 85 times faster than the sequential implementation of the NRM on a central processing unit (CPU). Using our software does not require any changes to the user\\'s models, since it acts as a direct replacement of the stochastic simulation software of the SBTOOLBOX2. © The Author 2011. Published by Oxford University Press. All rights reserved.
Abdullaev, Sadrilla
2014-01-01
This is the first book to systematically consider the modern aspects of chaotic dynamics of magnetic field lines and charged particles in magnetically confined fusion plasmas. The analytical models describing the generic features of equilibrium magnetic fields and magnetic perturbations in modern fusion devices are presented. It describes mathematical and physical aspects of onset of chaos, generic properties of the structure of stochastic magnetic fields, transport of charged particles in tokamaks induced by magnetic perturbations, new aspects of particle turbulent transport, etc. The presentation is based on the classical and new unique mathematical tools of Hamiltonian dynamics, like the action--angle formalism, classical perturbation theory, canonical transformations of variables, symplectic mappings, the Poincaré-Melnikov integrals. They are extensively used for analytical studies as well as for numerical simulations of magnetic field lines, particle dynamics, their spatial structures and statisti...
On the precision of quasi steady state assumptions in stochastic dynamics
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.
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.
The stochastic dynamics of intermittent porescale particle motion
Dentz, Marco; Morales, Veronica; Puyguiraud, Alexandre; Gouze, Philippe; Willmann, Matthias; Holzner, Markus
2017-04-01
Numerical and experimental data for porescale particle dynamics show intermittent patterns in Lagrangian velocities and accelerations, which manifest in long time intervals of low and short durations of high velocities [1, 2]. This phenomenon is due to the spatial persistence of particle velocities on characteristic heterogeneity length scales. In order to systematically quantify these behaviors and extract the stochastic dynamics of particle motion, we focus on the analysis of Lagrangian velocities sampled equidistantly along trajectories [3]. This method removes the intermittency observed under isochrone sampling. The space-Lagrangian velocity series can be quantified by a Markov process that is continuous in distance along streamline. It is fully parameterized in terms of the flux-weighted Eulerian velocity PDF and the characteristic pore-length. The resulting stochastic particle motion describes a continuous time random walk (CTRW). This approach allows for the process based interpretation of experimental and numerical porescale velocity, acceleration and displacement data. It provides a framework for the characterization and upscaling of particle transport and dispersion from the pore to the Darcy-scale based on the medium geometry and Eulerian flow attributes. [1] P. De Anna, T. Le Borgne, M. Dentz, A.M. Tartakovsky, D. Bolster, and P. Davy, "Flow intermittency, dispersion, and correlated continuous time random walks in porous media," Phys. Rev. Lett. 110, 184502 (2013). [2] M. Holzner, V. L. Morales, M. Willmann, and M. Dentz, "Intermittent Lagrangian velocities and accelerations in three- dimensional porous medium flow," Phys. Rev. E 92, 013015 (2015). [3] M. Dentz, P. K. Kang, A. Comolli, T. Le Borgne, and D. R. Lester, "Continuous time random walks for the evolution of Lagrangian velocities," Phys. Rev. Fluids (2016).
Quasi-continuous stochastic simulation framework for flood modelling
Moustakis, Yiannis; Kossieris, Panagiotis; Tsoukalas, Ioannis; Efstratiadis, Andreas
2017-04-01
Typically, flood modelling in the context of everyday engineering practices is addressed through event-based deterministic tools, e.g., the well-known SCS-CN method. A major shortcoming of such approaches is the ignorance of uncertainty, which is associated with the variability of soil moisture conditions and the variability of rainfall during the storm event.In event-based modeling, the sole expression of uncertainty is the return period of the design storm, which is assumed to represent the acceptable risk of all output quantities (flood volume, peak discharge, etc.). On the other hand, the varying antecedent soil moisture conditions across the basin are represented by means of scenarios (e.g., the three AMC types by SCS),while the temporal distribution of rainfall is represented through standard deterministic patterns (e.g., the alternative blocks method). In order to address these major inconsistencies,simultaneously preserving the simplicity and parsimony of the SCS-CN method, we have developed a quasi-continuous stochastic simulation approach, comprising the following steps: (1) generation of synthetic daily rainfall time series; (2) update of potential maximum soil moisture retention, on the basis of accumulated five-day rainfall; (3) estimation of daily runoff through the SCS-CN formula, using as inputs the daily rainfall and the updated value of soil moisture retention;(4) selection of extreme events and application of the standard SCS-CN procedure for each specific event, on the basis of synthetic rainfall.This scheme requires the use of two stochastic modelling components, namely the CastaliaR model, for the generation of synthetic daily data, and the HyetosMinute model, for the disaggregation of daily rainfall to finer temporal scales. Outcomes of this approach are a large number of synthetic flood events, allowing for expressing the design variables in statistical terms and thus properly evaluating the flood risk.
Effect of Stochastic Charge Fluctuations on Dust Dynamics
Matthews, Lorin; Shotorban, Babak; Hyde, Truell
2017-10-01
The charging of particles in a plasma environment occurs through the collection of electrons and ions on the particle surface. Depending on the particle size and the plasma density, the standard deviation of the number of collected elementary charges, which fluctuates due to the randomness in times of collisions with electrons or ions, may be a significant fraction of the equilibrium charge. We use a discrete stochastic charging model to simulate the variations in charge across the dust surface as well as in time. The resultant asymmetric particle potentials, even for spherical grains, has a significant impact on the particle coagulation rate as well as the structure of the resulting aggregates. We compare the effects on particle collisions and growth in typical laboratory and astrophysical plasma environments. This work was supported by the National Science Foundation under Grant PHY-1414523.
Moraes, Alvaro
2015-01-01
Epidemics have shaped, sometimes more than wars and natural disasters, demo- graphic aspects of human populations around the world, their health habits and their economies. Ebola and the Middle East Respiratory Syndrome (MERS) are clear and current examples of potential hazards at planetary scale. During the spread of an epidemic disease, there are phenomena, like the sudden extinction of the epidemic, that can not be captured by deterministic models. As a consequence, stochastic models have been proposed during the last decades. A typical forward problem in the stochastic setting could be the approximation of the expected number of infected individuals found in one month from now. On the other hand, a typical inverse problem could be, given a discretely observed set of epidemiological data, infer the transmission rate of the epidemic or its basic reproduction number. Markovian epidemic models are stochastic models belonging to a wide class of pure jump processes known as Stochastic Reaction Networks (SRNs), that are intended to describe the time evolution of interacting particle systems where one particle interacts with the others through a finite set of reaction channels. SRNs have been mainly developed to model biochemical reactions but they also have applications in neural networks, virus kinetics, and dynamics of social networks, among others. 4 This PhD thesis is focused on novel fast simulation algorithms and statistical inference methods for SRNs. Our novel Multi-level Monte Carlo (MLMC) hybrid simulation algorithms provide accurate estimates of expected values of a given observable of SRNs at a prescribed final time. They are designed to control the global approximation error up to a user-selected accuracy and up to a certain confidence level, and with near optimal computational work. We also present novel dual-weighted residual expansions for fast estimation of weak and strong errors arising from the MLMC methodology. Regarding the statistical inference
Stochastic simulation of destruction processes in self-irradiated materials
Directory of Open Access Journals (Sweden)
T. Patsahan
2017-09-01
Full Text Available Self-irradiation damages resulting from fission processes are common phenomena observed in nuclear fuel containing (NFC materials. Numerous α-decays lead to local structure transformations in NFC materials. The damages appearing due to the impacts of heavy nuclear recoils in the subsurface layer can cause detachments of material particles. Such a behaviour is similar to sputtering processes observed during a bombardment of the material surface by a flux of energetic particles. However, in the NFC material, the impacts are initiated from the bulk. In this work we propose a two-dimensional mesoscopic model to perform a stochastic simulation of the destruction processes occurring in a subsurface region of NFC material. We describe the erosion of the material surface, the evolution of its roughness and predict the detachment of the material particles. Size distributions of the emitted particles are obtained in this study. The simulation results of the model are in a qualitative agreement with the size histogram of particles produced from the material containing lava-like fuel formed during the Chernobyl nuclear power plant disaster.
Stochastic simulations of normal aging and Werner's syndrome.
Qi, Qi
2014-04-26
Human cells typically consist of 23 pairs of chromosomes. Telomeres are repetitive sequences of DNA located at the ends of chromosomes. During cell replication, a number of basepairs are lost from the end of the chromosome and this shortening restricts the number of divisions that a cell can complete before it becomes senescent, or non-replicative. In this paper, we use Monte Carlo simulations to form a stochastic model of telomere shortening to investigate how telomere shortening affects normal aging. Using this model, we study various hypotheses for the way in which shortening occurs by comparing their impact on aging at the chromosome and cell levels. We consider different types of length-dependent loss and replication probabilities to describe these processes. After analyzing a simple model for a population of independent chromosomes, we simulate a population of cells in which each cell has 46 chromosomes and the shortest telomere governs the replicative potential of the cell. We generalize these simulations to Werner\\'s syndrome, a condition in which large sections of DNA are removed during cell division and, amongst other conditions, results in rapid aging. Since the mechanisms governing the loss of additional basepairs are not known, we use our model to simulate a variety of possible forms for the rate at which additional telomeres are lost per replication and several expressions for how the probability of cell division depends on telomere length. As well as the evolution of the mean telomere length, we consider the standard deviation and the shape of the distribution. We compare our results with a variety of data from the literature, covering both experimental data and previous models. We find good agreement for the evolution of telomere length when plotted against population doubling.
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.
Molecular dynamics simulations
International Nuclear Information System (INIS)
Alder, B.J.
1985-07-01
The molecular dynamics computer simulation discovery of the slow decay of the velocity autocorrelation function in fluids is briefly reviewed in order to contrast that long time tail with those observed for the stress autocorrelation function in fluids and the velocity autocorrelation function in the Lorentz gas. For a non-localized particle in the Lorentz gas it is made plausible that even if it behaved quantum mechanically its long time tail would be the same as the classical one. The generalization of Fick's law for diffusion for the Lorentz gas, necessary to avoid divergences due to the slow decay of correlations, is presented. For fluids, that generalization has not yet been established, but the region of validity of generalized hydrodynamics is discussed. 20 refs., 5 figs
Energy Technology Data Exchange (ETDEWEB)
Chorošajev, Vladimir [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius (Lithuania); Gelzinis, Andrius; Valkunas, Leonas [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius (Lithuania); Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Sauletekio 3, 10222 Vilnius (Lithuania); Abramavicius, Darius, E-mail: darius.abramavicius@ff.vu.lt [Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius (Lithuania)
2016-12-20
Highlights: • The Davydov ansatze can be used for finite temperature simulations with an extension. • The accuracy is high if the system is strongly coupled to the environmental phonons. • The approach can simulate time-resolved fluorescence spectra. - Abstract: Time dependent variational approach is a convenient method to characterize the excitation dynamics in molecular aggregates for different strengths of system-bath interaction a, which does not require any additional perturbative schemes. Until recently, however, this method was only applicable in zero temperature case. It has become possible to extend this method for finite temperatures with the introduction of stochastic time dependent variational approach. Here we present a comparison between this approach and the exact hierarchical equations of motion approach for describing excitation dynamics in a broad range of temperatures. We calculate electronic population evolution, absorption and auxiliary time resolved fluorescence spectra in different regimes and find that the stochastic approach shows excellent agreement with the exact approach when the system-bath coupling is sufficiently large and temperatures are high. The differences between the two methods are larger, when temperatures are lower or the system-bath coupling is small.
A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds
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.
GillesPy: A Python Package for Stochastic Model Building and Simulation
Abel, John H.; Drawert, Brian; Hellander, Andreas; Petzold, Linda R.
2016-01-01
GillesPy is an open-source Python package for model construction and simulation of stochastic biochemical systems. GillesPy consists of a Python framework for model building and an interface to the StochKit2 suite of efficient simulation algorithms based on the Gillespie stochastic simulation algorithms (SSA). To enable intuitive model construction and seamless integration into the scientific Python stack, we present an easy to understand, action-oriented programming interface. Here, we descr...
FERN - a Java framework for stochastic simulation and evaluation of reaction networks.
Erhard, Florian; Friedel, Caroline C; Zimmer, Ralf
2008-08-29
Stochastic simulation can be used to illustrate the development of biological systems over time and the stochastic nature of these processes. Currently available programs for stochastic simulation, however, are limited in that they either a) do not provide the most efficient simulation algorithms and are difficult to extend, b) cannot be easily integrated into other applications or c) do not allow to monitor and intervene during the simulation process in an easy and intuitive way. Thus, in order to use stochastic simulation in innovative high-level modeling and analysis approaches more flexible tools are necessary. In this article, we present FERN (Framework for Evaluation of Reaction Networks), a Java framework for the efficient simulation of chemical reaction networks. FERN is subdivided into three layers for network representation, simulation and visualization of the simulation results each of which can be easily extended. It provides efficient and accurate state-of-the-art stochastic simulation algorithms for well-mixed chemical systems and a powerful observer system, which makes it possible to track and control the simulation progress on every level. To illustrate how FERN can be easily integrated into other systems biology applications, plugins to Cytoscape and CellDesigner are included. These plugins make it possible to run simulations and to observe the simulation progress in a reaction network in real-time from within the Cytoscape or CellDesigner environment. FERN addresses shortcomings of currently available stochastic simulation programs in several ways. First, it provides a broad range of efficient and accurate algorithms both for exact and approximate stochastic simulation and a simple interface for extending to new algorithms. FERN's implementations are considerably faster than the C implementations of gillespie2 or the Java implementations of ISBJava. Second, it can be used in a straightforward way both as a stand-alone program and within new
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.
A low-bias simulation scheme for the SABR stochastic volatility model
B. Chen (Bin); C.W. Oosterlee (Cornelis); J.A.M. van der Weide
2012-01-01
htmlabstractThe Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop an lowbias simulation scheme for the SABR-SV model, which deals efficiently with (undesired)
Simulation of nuclear plant operation into a stochastic energy production model
International Nuclear Information System (INIS)
Pacheco, R.L.
1983-04-01
A simulation model of nuclear plant operation is developed to fit into a stochastic energy production model. In order to improve the stochastic model used, and also reduce its computational time burdened by the aggregation of the model of nuclear plant operation, a study of tail truncation of the unsupplied demand distribution function has been performed. (E.G.) [pt
Stochastic Simulation of Soot Formation Evolution in Counterflow Diffusion Flames
Directory of Open Access Journals (Sweden)
Xiao Jiang
2018-01-01
Full Text Available Soot generally refers to carbonaceous particles formed during incomplete combustion of hydrocarbon fuels. A typical simulation of soot formation and evolution contains two parts: gas chemical kinetics, which models the chemical reaction from hydrocarbon fuels to soot precursors, that is, polycyclic aromatic hydrocarbons or PAHs, and soot dynamics, which models the soot formation from PAHs and evolution due to gas-soot and soot-soot interactions. In this study, two detailed gas kinetic mechanisms (ABF and KM2 have been compared during the simulation (using the solver Chemkin II of ethylene combustion in counterflow diffusion flames. Subsequently, the operator splitting Monte Carlo method is used to simulate the soot dynamics. Both the simulated data from the two mechanisms for gas and soot particles are compared with experimental data available in the literature. It is found that both mechanisms predict similar profiles for the gas temperature and velocity, agreeing well with measurements. However, KM2 mechanism provides much closer prediction compared to measurements for soot gas precursors. Furthermore, KM2 also shows much better predictions for soot number density and volume fraction than ABF. The effect of nozzle exit velocity on soot dynamics has also been investigated. Higher nozzle exit velocity renders shorter residence time for soot particles, which reduces the soot number density and volume fraction accordingly.
A Stochastic Fractional Dynamics Model of Rainfall Statistics
Kundu, Prasun; Travis, James
2013-04-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.
International Nuclear Information System (INIS)
Fivaz, M.; Fasoli, A.; Appert, K.; Trans, T.M.; Tran, M.Q.; Skiff, F.
1993-08-01
Dynamical chaos is produced by the interaction between plasma particles and two electrostatic waves. Experiments performed in a linear magnetized plasma and a 1D particle-in-cell simulation agree qualitatively: above a threshold wave amplitude, ion stochastic diffusion and heating occur on a fast time scale. Self-consistency appears to limit the extent of the heating process. (author) 5 figs., 18 refs
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
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
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.
DEFF Research Database (Denmark)
Sørensen, J.T.; Enevoldsen, Carsten; Houe, H.
1995-01-01
A dynamic, stochastic model simulating the technical and economic consequences of bovine virus diarrhoea virus (BVDV) infections for a dairy cattle herd for use on a personal computer was developed. The production and state changes of the herd were simulated by state changes of the individual cows...... and heifers. All discrete events at the cow level were triggered stochastically. Each cow and heifer was characterized by state variables such as stage of lactation, parity, oestrous status, decision for culling, milk production potential, and immune status for BVDV. The model was controlled by 170 decision...... variables describing biologic and management variables including 21 decision variables describing the effect of BVDV infection on the production of the individual animal. Two markedly different scenarios were simulated to demonstrate the behaviour of the developed model and the potentials of the applied...
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....
Optically levitated nanoparticle as a model system for stochastic bistable dynamics.
Ricci, F; Rica, R A; Spasenović, M; Gieseler, J; Rondin, L; Novotny, L; Quidant, R
2017-05-09
Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.
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.
Ekofisk chalk: core measurements, stochastic reconstruction, network modeling and simulation
Energy Technology Data Exchange (ETDEWEB)
Talukdar, Saifullah
2002-07-01
This dissertation deals with (1) experimental measurements on petrophysical, reservoir engineering and morphological properties of Ekofisk chalk, (2) numerical simulation of core flood experiments to analyze and improve relative permeability data, (3) stochastic reconstruction of chalk samples from limited morphological information, (4) extraction of pore space parameters from the reconstructed samples, development of network model using pore space information, and computation of petrophysical and reservoir engineering properties from network model, and (5) development of 2D and 3D idealized fractured reservoir models and verification of the applicability of several widely used conventional up scaling techniques in fractured reservoir simulation. Experiments have been conducted on eight Ekofisk chalk samples and porosity, absolute permeability, formation factor, and oil-water relative permeability, capillary pressure and resistivity index are measured at laboratory conditions. Mercury porosimetry data and backscatter scanning electron microscope images have also been acquired for the samples. A numerical simulation technique involving history matching of the production profiles is employed to improve the relative permeability curves and to analyze hysteresis of the Ekofisk chalk samples. The technique was found to be a powerful tool to supplement the uncertainties in experimental measurements. Porosity and correlation statistics obtained from backscatter scanning electron microscope images are used to reconstruct microstructures of chalk and particulate media. The reconstruction technique involves a simulated annealing algorithm, which can be constrained by an arbitrary number of morphological parameters. This flexibility of the algorithm is exploited to successfully reconstruct particulate media and chalk samples using more than one correlation functions. A technique based on conditional simulated annealing has been introduced for exact reproduction of vuggy
Sedwards, Sean; Mazza, Tommaso
2007-10-15
Compartments and membranes are the basis of cell topology and more than 30% of the human genome codes for membrane proteins. While it is possible to represent compartments and membrane proteins in a nominal way with many mathematical formalisms used in systems biology, few, if any, explicitly model the topology of the membranes themselves. Discrete stochastic simulation potentially offers the most accurate representation of cell dynamics. Since the details of every molecular interaction in a pathway are often not known, the relationship between chemical species in not necessarily best described at the lowest level, i.e. by mass action. Simulation is a form of computer-aided analysis, relying on human interpretation to derive meaning. To improve efficiency and gain meaning in an automatic way, it is necessary to have a formalism based on a model which has decidable properties. We present Cyto-Sim, a stochastic simulator of membrane-enclosed hierarchies of biochemical processes, where the membranes comprise an inner, outer and integral layer. The underlying model is based on formal language theory and has been shown to have decidable properties (Cavaliere and Sedwards, 2006), allowing formal analysis in addition to simulation. The simulator provides variable levels of abstraction via arbitrary chemical kinetics which link to ordinary differential equations. In addition to its compact native syntax, Cyto-Sim currently supports models described as Petri nets, can import all versions of SBML and can export SBML and MATLAB m-files. Cyto-Sim is available free, either as an applet or a stand-alone Java program via the web page (http://www.cosbi.eu/Rpty_Soft_CytoSim.php). Other versions can be made available upon request.
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.
MarkoLAB: A simulator to study ionic channel's stochastic behavior.
da Silva, Robson Rodrigues; Goroso, Daniel Gustavo; Bers, Donald M; Puglisi, José Luis
2017-08-01
Mathematical models of the cardiac cell have started to include markovian representations of the ionic channels instead of the traditional Hodgkin & Huxley formulations. There are many reasons for this: Markov models are not restricted to the idea of independent gates defining the channel, they allow more complex description with specific transitions between open, closed or inactivated states, and more importantly those states can be closely related to the underlying channel structure and conformational changes. We used the LabVIEW ® and MATLAB ® programs to implement the simulator MarkoLAB that allow a dynamical 3D representation of the markovian model of the channel. The Monte Carlo simulation was used to implement the stochastic transitions among states. The user can specify the voltage protocol by setting the holding potential, the step-to voltage and the duration of the stimuli. The most studied feature of a channel is the current flowing through it. This happens when the channel stays in the open state, but most of the time, as revealed by the low open probability values, the channel remains on the inactive or closed states. By focusing only when the channel enters or leaves the open state we are missing most of its activity. MarkoLAB proved to be quite useful to visualize the whole behavior of the channel and not only when the channel produces a current. Such dynamic representation provides more complete information about channel kinetics and will be a powerful tool to demonstrate the effect of gene mutations or drugs on the channel function. MarkoLAB provides an original way of visualizing the stochastic behavior of a channel. It clarifies concepts, such as recovery from inactivation, calcium- versus voltage-dependent inactivation, and tail currents. It is not restricted to ionic channels only but it can be extended to other transporters, such as exchangers and pumps. This program is intended as a didactical tool to illustrate the dynamical behavior of a
Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture
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.
The two-regime method for optimizing stochastic reaction-diffusion simulations
Flegg, M. B.; Chapman, S. J.; Erban, R.
2011-01-01
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches
Database of Nucleon-Nucleon Scattering Cross Sections by Stochastic Simulation, Phase I
National Aeronautics and Space Administration — A database of nucleon-nucleon elastic differential and total cross sections will be generated by stochastic simulation of the quantum Liouville equation in the...
A constrained approach to multiscale stochastic simulation of chemically reacting systems
Cotter, Simon L.; Zygalakis, Konstantinos C.; Kevrekidis, Ioannis G.; Erban, Radek
2011-01-01
Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address
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.
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.
Project Evaluation and Cash Flow Forecasting by Stochastic Simulation
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Odd A. Asbjørnsen
1983-10-01
Full Text Available The net present value of a discounted cash flow is used to evaluate projects. It is shown that the LaPlace transform of the cash flow time function is particularly useful when the cash flow profiles may be approximately described by ordinary linear differential equations in time. However, real cash flows are stochastic variables due to the stochastic nature of the disturbances during production.
Mean, covariance, and effective dimension of stochastic distributed delay dynamics
René, Alexandre; Longtin, André
2017-11-01
Dynamical models are often required to incorporate both delays and noise. However, the inherently infinite-dimensional nature of delay equations makes formal solutions to stochastic delay differential equations (SDDEs) challenging. Here, we present an approach, similar in spirit to the analysis of functional differential equations, but based on finite-dimensional matrix operators. This results in a method for obtaining both transient and stationary solutions that is directly amenable to computation, and applicable to first order differential systems with either discrete or distributed delays. With fewer assumptions on the system's parameters than other current solution methods and no need to be near a bifurcation, we decompose the solution to a linear SDDE with arbitrary distributed delays into natural modes, in effect the eigenfunctions of the differential operator, and show that relatively few modes can suffice to approximate the probability density of solutions. Thus, we are led to conclude that noise makes these SDDEs effectively low dimensional, which opens the possibility of practical definitions of probability densities over their solution space.
Stochastic Dynamics of Clay Translocation and Formation of Argillic Horizons
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.
Systemic risk in dynamical networks with stochastic failure criterion
Podobnik, B.; Horvatic, D.; Bertella, M. A.; Feng, L.; Huang, X.; Li, B.
2014-06-01
Complex non-linear interactions between banks and assets we model by two time-dependent Erdős-Renyi network models where each node, representing a bank, can invest either to a single asset (model I) or multiple assets (model II). We use a dynamical network approach to evaluate the collective financial failure —systemic risk— quantified by the fraction of active nodes. The systemic risk can be calculated over any future time period, divided into sub-periods, where within each sub-period banks may contiguously fail due to links to either i) assets or ii) other banks, controlled by two parameters, probability of internal failure p and threshold Th (“solvency” parameter). The systemic risk decreases with the average network degree faster when all assets are equally distributed across banks than if assets are randomly distributed. The more inactive banks each bank can sustain (smaller Th), the smaller the systemic risk —for some Th values in I we report a discontinuity in systemic risk. When contiguous spreading becomes stochastic ii) controlled by probability p2 —a condition for the bank to be solvent (active) is stochastic— the systemic risk decreases with decreasing p2. We analyse the asset allocation for the U.S. banks.
International Nuclear Information System (INIS)
Fu, Jin; Wu, Sheng; Li, Hong; Petzold, Linda R.
2014-01-01
The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy
Stochastic dynamics: Crossover from 1/f3 to flicker noise
International Nuclear Information System (INIS)
Canessa, E.; Nguyen, V.L.
1993-01-01
Finite time processes within the limits of the Newton equation and zero inertia motion (i.e., road to chaos) are studied by numerically solving the ordinary, stochastic Langevin equation in 1D for a free particle with inertial moving in a medium with viscosity γ. In this simulations, the scaling behaviour of particle trajectories χ(t) and velocities v(t) with time are derived and the inclusion of non-zero particle masses is shown to define the asymptotic time limit τ c at which - independently of γ - the system evolves into the well-known statistically stationary state characterized by 2 (t) > is proportional to t and flicker noise. The time τ c is further analysed from the correlation length given by the 2-point autocorrelation function of the particle velocity at each value of γ. It is found that the noise power spectrum of v(t) is characterized by flicker noise for frequencies f ≤ f c ∼ 1/τ c , whereas for f > f c , the noise power spectra behave as 1/f υ , where υ varies between the limits of Newton's equation (i.e., υ = 3) and road to chaos (i.e., υ = 1). Furthermore, at times τ c and 0 f (γ) while the single particle trajectories are shown to display a rather different subset of exponents on increasing γ. Generic features of this transition are nicely given by Poincare maps in the velocity space. (author). 23 refs, 8 figs
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
Stochastic dynamics of penetrable rods in one dimension: occupied volume and spatial order.
Craven, Galen T; Popov, Alexander V; Hernandez, Rigoberto
2013-06-28
The occupied volume of a penetrable hard rod (HR) system in one dimension is probed through the use of molecular dynamics simulations. In these dynamical simulations, collisions between penetrable rods are governed by a stochastic penetration algorithm (SPA), which allows for rods to either interpenetrate with a probability δ, or collide elastically otherwise. The limiting values of this parameter, δ = 0 and δ = 1, correspond to the HR and the ideal limits, respectively. At intermediate values, 0 exclusive and independent events is observed, making prediction of the occupied volume nontrivial. At high hard core volume fractions φ0, the occupied volume expression derived by Rikvold and Stell [J. Chem. Phys. 82, 1014 (1985)] for permeable systems does not accurately predict the occupied volume measured from the SPA simulations. Multi-body effects contribute significantly to the pair correlation function g2(r) and the simplification by Rikvold and Stell that g2(r) = δ in the penetrative region is observed to be inaccurate for the SPA model. We find that an integral over the penetrative region of g2(r) is the principal quantity that describes the particle overlap ratios corresponding to the observed penetration probabilities. Analytic formulas are developed to predict the occupied volume of mixed systems and agreement is observed between these theoretical predictions and the results measured from simulation.
Dynamic UAV-based traffic monitoring under uncertainty as a stochastic arc-inventory routing policy
Directory of Open Access Journals (Sweden)
Joseph Y.J. Chow
2016-10-01
Full Text Available Given the rapid advances in unmanned aerial vehicles, or drones, and increasing need to monitor at a city level, one of the current research gaps is how to systematically deploy drones over multiple periods. We propose a real-time data-driven approach: we formulate the first deterministic arc-inventory routing problem and derive its stochastic dynamic policy. The policy is expected to be of greatest value in scenarios where uncertainty is highest and costliest, such as city monitoring during major events. The Bellman equation for an approximation of the proposed inventory routing policy is formulated as a selective vehicle routing problem. We propose an approximate dynamic programming algorithm based on Least Squares Monte Carlo simulation to find that policy. The algorithm has been modified so that the least squares dependent variable is defined to be the “expected stock out cost upon the next replenishment”. The new algorithm is tested on 30 simulated instances of real time trajectories over 5 time periods of the selective vehicle routing problem to evaluate the proposed policy and algorithm. Computational results on the selected instances show that the algorithm on average outperforms the myopic policy by 23–28%, depending on the parametric design. Further tests are conducted on classic benchmark arc routing problem instances. The 11-link instance gdb19 (Golden et al., 1983 is expanded into a sequential 15-period stochastic dynamic example and used to demonstrate why a naïve static multi-period deployment plan would not be effective in real networks.
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
On the stochastic approach to marine population dynamics
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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
International Nuclear Information System (INIS)
Voter, A. F.; Sindhikara, Daniel J.; Kim, Seonah; Roitberg, Adrian E.
2009-01-01
Molecular dynamics simulations starting from different initial conditions are commonly used to mimic the behavior of an experimental ensemble. We show in this article that when a Langevin thermostat is used to maintain constant temperature during such simulations, extreme care must be taken when choosing the random number seeds used in order to prevent statistical correlation among the MD trajectories. While recent studies have shown that stochastically thermostatted trajectories evolving within a single potential basin with identical random number seeds tend to synchronize, we show that there is a synchronization effect even for complex, biologically relevant systems. We demonstrate this effect in simulations of Alanine trimer and pentamer and in a simulation of a temperature-jump experiment for peptide folding of a 14-residue peptide. Even in replica-exchange simulations, in which the trajectories are at different temperatures, we find partial synchronization occurring when the same random number seed is employed. We explain this by extending the recent derivation of the synchronization effect for two trajectories in a harmonic well to the case in which the trajectories are at two different temperatures. Our results suggest several ways in which mishandling selection of a pseudo random number generator initial seed can lead to corruption of simulation data. Simulators can fall into this trap in simple situations such as neglecting to specifically indicate different random seeds in either parallel or sequential restart simulations, utilizing a simulation package with a weak pseudorandom number generator, or using an advanced simulation algorithm that hasn't been programmed to distribute initial seeds
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.
On the theory of stochastic dynamics of magnetically confined plasma
Energy Technology Data Exchange (ETDEWEB)
El-Sharif, R.N.; El-Atoy, N.S. [Plasma and Nuclear Fusion Dept., N.R.C, Atomic Energy Authority, Cairo (Egypt)]|[Physics Dept., Girls Colleges, KSA (Saudi Arabia)
2004-07-01
This work is devoted to a study of the motion of plasma electrons in a system of two fields, a magnetic field along z-axis and wave-packet field, which propagates in the x-z plane. The strongest interaction between plasma electrons and both fields is due to their resonance with these fields. The motion of plasma electrons become stochastic when a set of resonance overlapping. Conditions for stochasticity are obtained. (orig.)
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.
On the theory of stochastic dynamics of magnetically confined plasma
International Nuclear Information System (INIS)
El-Sharif, R.N.; El-Atoy, N.S.
2004-01-01
This work is devoted to a study of the motion of plasma electrons in a system of two fields, a magnetic field along z-axis and wave-packet field, which propagates in the x-z plane. The strongest interaction between plasma electrons and both fields is due to their resonance with these fields. The motion of plasma electrons become stochastic when a set of resonance overlapping. Conditions for stochasticity are obtained. (orig.)
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.
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.
Stochastic dynamical model of a growing citation network based on a self-exciting point process.
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.
Advanced models of neural networks nonlinear dynamics and stochasticity in biological neurons
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.
Stochastic optimal control in infinite dimension dynamic programming and HJB equations
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 ...
A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis
Directory of Open Access Journals (Sweden)
Linda J.S. Allen
2017-05-01
Full Text Available Some mathematical methods for formulation and numerical simulation of stochastic epidemic models are presented. Specifically, models are formulated for continuous-time Markov chains and stochastic differential equations. Some well-known examples are used for illustration such as an SIR epidemic model and a host-vector malaria model. Analytical methods for approximating the probability of a disease outbreak are also discussed. Keywords: Branching process, Continuous-time Markov chain, Minor outbreak, Stochastic differential equation, 2000 MSC: 60H10, 60J28, 92D30
Ahmet, Kara
2015-01-01
This paper presents a simple model of the provision of higher educational services that considers and exemplifies nonlinear, stochastic, and potentially chaotic processes. I use the methods of system dynamics to simulate these processes in the context of a particular sociologically interesting case, namely that of the Turkish higher education…
Directory of Open Access Journals (Sweden)
Mark D McDonnell
2013-05-01
Full Text Available The release of neurotransmitter vesicles after arrival of a pre-synaptic action potential at cortical synapses is known to be a stochastic process, as is the availability of vesicles for release. These processes are known to also depend on the recent history of action-potential arrivals, and this can be described in terms of time-varying probabilities of vesicle release. Mathematical models of such synaptic dynamics frequently are based only on the mean number of vesicles released by each pre-synaptic action potential, since if it is assumed there are sufficiently many vesicle sites, then variance is small. However, it has been shown recently that variance across sites can be significant for neuron and network dynamics, and this suggests the potential importance of studying short-term plasticity using simulations that do generate trial-to-trial variability. Therefore, in this paper we study several well-known conceptual models for stochastic availability and release. We state explicitly the random variables that these models describe and propose efficient algorithms for accurately implementing stochastic simulations of these random variables in software or hardware. Our results are complemented by mathematical analysis and statement of pseudo-code algorithms.
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.
Dynamic simulation of a reboiler
International Nuclear Information System (INIS)
Moeck, E.O.; McMorran, P.D.
1977-07-01
A hybrid-computer simulation of reboiler dynamics was prepared, comprising models of steam condensation in tubes, heat conduction, steam generation, a surge tank, steam transmission line and flow-control valve. Time and frequency responses were obtained to illustrate the dynamics of this multivariable process. (author)
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)
GillesPy: A Python Package for Stochastic Model Building and Simulation.
Abel, John H; Drawert, Brian; Hellander, Andreas; Petzold, Linda R
2016-09-01
GillesPy is an open-source Python package for model construction and simulation of stochastic biochemical systems. GillesPy consists of a Python framework for model building and an interface to the StochKit2 suite of efficient simulation algorithms based on the Gillespie stochastic simulation algorithms (SSA). To enable intuitive model construction and seamless integration into the scientific Python stack, we present an easy to understand, action-oriented programming interface. Here, we describe the components of this package and provide a detailed example relevant to the computational biology community.
Stochastic model simulation using Kronecker product analysis and Zassenhaus formula approximation.
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.
Stochastic Simulation and Forecast of Hydrologic Time Series Based on Probabilistic Chaos Expansion
Li, Z.; Ghaith, M.
2017-12-01
Hydrological processes are characterized by many complex features, such as nonlinearity, dynamics and uncertainty. How to quantify and address such complexities and uncertainties has been a challenging task for water engineers and managers for decades. To support robust uncertainty analysis, an innovative approach for the stochastic simulation and forecast of hydrologic time series is developed is this study. Probabilistic Chaos Expansions (PCEs) are established through probabilistic collocation to tackle uncertainties associated with the parameters of traditional hydrological models. The uncertainties are quantified in model outputs as Hermite polynomials with regard to standard normal random variables. Sequentially, multivariate analysis techniques are used to analyze the complex nonlinear relationships between meteorological inputs (e.g., temperature, precipitation, evapotranspiration, etc.) and the coefficients of the Hermite polynomials. With the established relationships between model inputs and PCE coefficients, forecasts of hydrologic time series can be generated and the uncertainties in the future time series can be further tackled. The proposed approach is demonstrated using a case study in China and is compared to a traditional stochastic simulation technique, the Markov-Chain Monte-Carlo (MCMC) method. Results show that the proposed approach can serve as a reliable proxy to complicated hydrological models. It can provide probabilistic forecasting in a more computationally efficient manner, compared to the traditional MCMC method. This work provides technical support for addressing uncertainties associated with hydrological modeling and for enhancing the reliability of hydrological modeling results. Applications of the developed approach can be extended to many other complicated geophysical and environmental modeling systems to support the associated uncertainty quantification and risk analysis.
Spatially explicit and stochastic simulation of forest landscape fire disturbance and succession
Hong S. He; David J. Mladenoff
1999-01-01
Understanding disturbance and recovery of forest landscapes is a challenge because of complex interactions over a range of temporal and spatial scales. Landscape simulation models offer an approach to studying such systems at broad scales. Fire can be simulated spatially using mechanistic or stochastic approaches. We describe the fire module in a spatially explicit,...
Theory of time-averaged neutral dynamics with environmental stochasticity
Danino, Matan; Shnerb, Nadav M.
2018-04-01
Competition is the main driver of population dynamics, which shapes the genetic composition of populations and the assembly of ecological communities. Neutral models assume that all the individuals are equivalent and that the dynamics is governed by demographic (shot) noise, with a steady state species abundance distribution (SAD) that reflects a mutation-extinction equilibrium. Recently, many empirical and theoretical studies emphasized the importance of environmental variations that affect coherently the relative fitness of entire populations. Here we consider two generic time-averaged neutral models; in both the relative fitness of each species fluctuates independently in time but its mean is zero. The first (model A) describes a system with local competition and linear fitness dependence of the birth-death rates, while in the second (model B) the competition is global and the fitness dependence is nonlinear. Due to this nonlinearity, model B admits a noise-induced stabilization mechanism that facilitates the invasion of new mutants. A self-consistent mean-field approach is used to reduce the multispecies problem to two-species dynamics, and the large-N asymptotics of the emerging set of Fokker-Planck equations is presented and solved. Our analytic expressions are shown to fit the SADs obtained from extensive Monte Carlo simulations and from numerical solutions of the corresponding master equations.
Dynamic-stochastic modeling of snow cover formation on the European territory of Russia
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 ...
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.
International Nuclear Information System (INIS)
Trucco, A.; Corallo, C.; Pini Prato, A.; Porro, S.
1999-01-01
Among the innovative cycle recently proposed in literature, the Humid Air Turbine Cycle - Hat better seems to fulfil the main energy market requirements of today: High efficiency in a large power ranger, low pollution, low specific capital cost. The previous results of an analysis at partial load and transient conditions are here presented, where the Hat plant has been simulated using the original model implemented in LEGO environment [it
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)
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)
Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics
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
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...
STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB.
Klingbeil, Guido; Erban, Radek; Giles, Mike; Maini, Philip K
2011-04-15
The importance of stochasticity in biological systems is becoming increasingly recognized and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new software tool STOCHSIMGPU that exploits graphics processing units (GPUs) for parallel stochastic simulations of biological/chemical reaction systems and show that significant gains in efficiency can be made. It is integrated into MATLAB and works with the Systems Biology Toolbox 2 (SBTOOLBOX2) for MATLAB. The GPU-based parallel implementation of the Gillespie stochastic simulation algorithm (SSA), the logarithmic direct method (LDM) and the next reaction method (NRM) is approximately 85 times faster than the sequential implementation of the NRM on a central processing unit (CPU). Using our software does not require any changes to the user's models, since it acts as a direct replacement of the stochastic simulation software of the SBTOOLBOX2. The software is open source under the GPL v3 and available at http://www.maths.ox.ac.uk/cmb/STOCHSIMGPU. The web site also contains supplementary information. klingbeil@maths.ox.ac.uk Supplementary data are available at Bioinformatics online.
A higher-order numerical framework for stochastic simulation of chemical reaction systems.
Székely, Tamás
2012-07-15
BACKGROUND: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulation, biochemical cascades and cell-cell interaction. However most discrete stochastic simulation techniques are slow. We apply Richardson extrapolation to the moments of three fixed-step methods, the Euler, midpoint and θ-trapezoidal τ-leap methods, to demonstrate the power of stochastic extrapolation. The extrapolation framework can increase the order of convergence of any fixed-step discrete stochastic solver and is very easy to implement; the only condition for its use is knowledge of the appropriate terms of the global error expansion of the solver in terms of its stepsize. In practical terms, a higher-order method with a larger stepsize can achieve the same level of accuracy as a lower-order method with a smaller one, potentially reducing the computational time of the system. RESULTS: By obtaining a global error expansion for a general weak first-order method, we prove that extrapolation can increase the weak order of convergence for the moments of the Euler and the midpoint τ-leap methods, from one to two. This is supported by numerical simulations of several chemical systems of biological importance using the Euler, midpoint and θ-trapezoidal τ-leap methods. In almost all cases, extrapolation results in an improvement of accuracy. As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations. CONCLUSIONS: Extrapolation is a general framework for increasing the order of accuracy of any fixed-step stochastic solver. This enables the simulation of complicated systems in less time, allowing for more realistic biochemical problems to be solved.
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.
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.
Klingbeil, Guido; Erban, Radek; Giles, Mike; Maini, Philip K.
2012-01-01
We explore two different threading approaches on a graphics processing unit (GPU) exploiting two different characteristics of the current GPU architecture. The fat thread approach tries to minimize data access time by relying on shared memory and registers potentially sacrificing parallelism. The thin thread approach maximizes parallelism and tries to hide access latencies. We apply these two approaches to the parallel stochastic simulation of chemical reaction systems using the stochastic simulation algorithm (SSA) by Gillespie [14]. In these cases, the proposed thin thread approach shows comparable performance while eliminating the limitation of the reaction system's size. © 2006 IEEE.
Stochastic simulation of PWR vessel integrity for pressurized thermal shock conditions
International Nuclear Information System (INIS)
Jackson, P.S.; Moelling, D.S.
1984-01-01
A stochastic simulation methodology is presented for performing probabilistic analyses of Pressurized Water Reactor vessel integrity. Application of the methodology to vessel-specific integrity analyses is described in the context of Pressurized Thermal Shock (PTS) conditions. A Bayesian method is described for developing vessel-specific models of the density of undetected volumetric flaws from ultrasonic inservice inspection results. Uncertainty limits on the probabilistic results due to sampling errors are determined from the results of the stochastic simulation. An example is provided to illustrate the methodology
Klingbeil, Guido
2012-02-01
We explore two different threading approaches on a graphics processing unit (GPU) exploiting two different characteristics of the current GPU architecture. The fat thread approach tries to minimize data access time by relying on shared memory and registers potentially sacrificing parallelism. The thin thread approach maximizes parallelism and tries to hide access latencies. We apply these two approaches to the parallel stochastic simulation of chemical reaction systems using the stochastic simulation algorithm (SSA) by Gillespie [14]. In these cases, the proposed thin thread approach shows comparable performance while eliminating the limitation of the reaction system\\'s size. © 2006 IEEE.
International Nuclear Information System (INIS)
Hu, Yan; Wen, Jing-ya; Li, Xiao-li; Wang, Da-zhou; Li, Yu
2013-01-01
Highlights: • Using interval mathematics to describe spatial and temporal variability and parameter uncertainty. • Using fuzzy theory to quantify variability of environmental guideline values. • Using probabilistic approach to integrate interval concentrations and fuzzy environmental guideline. • Establishment of dynamic multimedia environmental integrated risk assessment framework. -- Abstract: A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach was developed for contaminated sites management. The contaminant concentrations were simulated by a validated interval dynamic multimedia fugacity model, and different guideline values for the same contaminant were represented as a fuzzy environmental guideline. Then, the probability of violating environmental guideline (Pv) can be determined by comparison between the modeled concentrations and the fuzzy environmental guideline, and the constructed relationship between the Pvs and environmental risk levels was used to assess the environmental risk level. The developed approach was applied to assess the integrated environmental risk at a case study site in China, simulated from 1985 to 2020. Four scenarios were analyzed, including “residential land” and “industrial land” environmental guidelines under “strict” and “loose” strictness. It was found that PAH concentrations will increase steadily over time, with soil found to be the dominant sink. Source emission in soil was the leading input and atmospheric sedimentation was the dominant transfer process. The integrated environmental risks primarily resulted from petroleum spills and coke ovens, while the soil environmental risks came from coal combustion. The developed approach offers an effective tool for quantifying variability and uncertainty in the dynamic multimedia integrated environmental risk assessment and the contaminated site management
Energy Technology Data Exchange (ETDEWEB)
Hu, Yan; Wen, Jing-ya; Li, Xiao-li; Wang, Da-zhou; Li, Yu, E-mail: liyuxx8@hotmail.com
2013-10-15
Highlights: • Using interval mathematics to describe spatial and temporal variability and parameter uncertainty. • Using fuzzy theory to quantify variability of environmental guideline values. • Using probabilistic approach to integrate interval concentrations and fuzzy environmental guideline. • Establishment of dynamic multimedia environmental integrated risk assessment framework. -- Abstract: A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach was developed for contaminated sites management. The contaminant concentrations were simulated by a validated interval dynamic multimedia fugacity model, and different guideline values for the same contaminant were represented as a fuzzy environmental guideline. Then, the probability of violating environmental guideline (Pv) can be determined by comparison between the modeled concentrations and the fuzzy environmental guideline, and the constructed relationship between the Pvs and environmental risk levels was used to assess the environmental risk level. The developed approach was applied to assess the integrated environmental risk at a case study site in China, simulated from 1985 to 2020. Four scenarios were analyzed, including “residential land” and “industrial land” environmental guidelines under “strict” and “loose” strictness. It was found that PAH concentrations will increase steadily over time, with soil found to be the dominant sink. Source emission in soil was the leading input and atmospheric sedimentation was the dominant transfer process. The integrated environmental risks primarily resulted from petroleum spills and coke ovens, while the soil environmental risks came from coal combustion. The developed approach offers an effective tool for quantifying variability and uncertainty in the dynamic multimedia integrated environmental risk assessment and the contaminated site management.
International Nuclear Information System (INIS)
Do, Duy Minh; Gao, Wei; Song, Chongmin; Tangaramvong, Sawekchai
2014-01-01
This paper presents the non-deterministic dynamic analysis and reliability assessment of structures with uncertain-but-bounded parameters under stochastic process excitations. Random ground acceleration from earthquake motion is adopted to illustrate the stochastic process force. The exact change ranges of natural frequencies, random vibration displacement and stress responses of structures are investigated under the interval analysis framework. Formulations for structural reliability are developed considering the safe boundary and structural random vibration responses as interval parameters. An improved particle swarm optimization algorithm, namely randomised lower sequence initialized high-order nonlinear particle swarm optimization algorithm, is employed to capture the better bounds of structural dynamic characteristics, random vibration responses and reliability. Three numerical examples are used to demonstrate the presented method for interval random vibration analysis and reliability assessment of structures. The accuracy of the results obtained by the presented method is verified by the randomised Quasi-Monte Carlo simulation method (QMCSM) and direct Monte Carlo simulation method (MCSM). - Highlights: • Interval uncertainty is introduced into structural random vibration responses. • Interval dynamic reliability assessments of structures are implemented. • Boundaries of structural dynamic response and reliability are achieved
Green function simulation of Hamiltonian lattice models with stochastic reconfiguration
International Nuclear Information System (INIS)
Beccaria, M.
2000-01-01
We apply a recently proposed Green function Monte Carlo procedure to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By means of a procedure called stochastic reconfiguration the long standing problem of keeping fixed the walker population without a priori knowledge of the ground state is completely solved. In the U(1) 2 model, which we choose as our theoretical laboratory, we evaluate the mean plaquette and the vacuum energy per plaquette. We find good agreement with previous works using model-dependent guiding functions for the random walkers. (orig.)
Simulation of conditional diffusions via forward-reverse stochastic representations
Bayer, Christian
2015-01-01
We derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval,conditioned on the terminal state. The conditioning can be with respect to a fixed measurement point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced by Milstein, Schoenmakers and Spokoiny in the context of density estimation. The corresponding Monte Carlo estimators have essentially root-N accuracy, and hence they do not suffer from the curse of dimensionality. We also present an application in statistics, in the context of the EM algorithm.
Simulation of conditional diffusions via forward-reverse stochastic representations
Bayer, Christian
2015-01-07
We derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval,conditioned on the terminal state. The conditioning can be with respect to a fixed measurement point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced by Milstein, Schoenmakers and Spokoiny in the context of density estimation. The corresponding Monte Carlo estimators have essentially root-N accuracy, and hence they do not suffer from the curse of dimensionality. We also present an application in statistics, in the context of the EM algorithm.
FluTE, a publicly available stochastic influenza epidemic simulation model.
Directory of Open Access Journals (Sweden)
Dennis L Chao
2010-01-01
Full Text Available Mathematical and computer models of epidemics have contributed to our understanding of the spread of infectious disease and the measures needed to contain or mitigate them. To help prepare for future influenza seasonal epidemics or pandemics, we developed a new stochastic model of the spread of influenza across a large population. Individuals in this model have realistic social contact networks, and transmission and infections are based on the current state of knowledge of the natural history of influenza. The model has been calibrated so that outcomes are consistent with the 1957/1958 Asian A(H2N2 and 2009 pandemic A(H1N1 influenza viruses. We present examples of how this model can be used to study the dynamics of influenza epidemics in the United States and simulate how to mitigate or delay them using pharmaceutical interventions and social distancing measures. Computer simulation models play an essential role in informing public policy and evaluating pandemic preparedness plans. We have made the source code of this model publicly available to encourage its use and further development.
FluTE, a publicly available stochastic influenza epidemic simulation model.
Chao, Dennis L; Halloran, M Elizabeth; Obenchain, Valerie J; Longini, Ira M
2010-01-29
Mathematical and computer models of epidemics have contributed to our understanding of the spread of infectious disease and the measures needed to contain or mitigate them. To help prepare for future influenza seasonal epidemics or pandemics, we developed a new stochastic model of the spread of influenza across a large population. Individuals in this model have realistic social contact networks, and transmission and infections are based on the current state of knowledge of the natural history of influenza. The model has been calibrated so that outcomes are consistent with the 1957/1958 Asian A(H2N2) and 2009 pandemic A(H1N1) influenza viruses. We present examples of how this model can be used to study the dynamics of influenza epidemics in the United States and simulate how to mitigate or delay them using pharmaceutical interventions and social distancing measures. Computer simulation models play an essential role in informing public policy and evaluating pandemic preparedness plans. We have made the source code of this model publicly available to encourage its use and further development.
Quantum dynamical time evolutions as stochastic flows on phase space
International Nuclear Information System (INIS)
Combe, P.; Rodriguez, R.; Guerra, F.; Sirigue, M.; Sirigue-Collin, M.
1984-01-01
We are mainly interested in describing the time development of the Wigner functions by means of stochastic processes. In the second section we recall the main properties of the Wigner functions as well as those of their Fourier transform. In the next one we derive the evolution equation of these functions for a class of Hamiltonians and we give a probabilistic expression for the solution of these equations by means of a stochastic flow in phase space which reminds of the classical flows. In the last section we remark that the previously defined flow can be extended to the bounded continuous functions on phase space and that this flow conserves the cone generated by the Wigner functions. (orig./HSI)
A stochastic approach to multi-gene expression dynamics
International Nuclear Information System (INIS)
Ochiai, T.; Nacher, J.C.; Akutsu, T.
2005-01-01
In the last years, tens of thousands gene expression profiles for cells of several organisms have been monitored. Gene expression is a complex transcriptional process where mRNA molecules are translated into proteins, which control most of the cell functions. In this process, the correlation among genes is crucial to determine the specific functions of genes. Here, we propose a novel multi-dimensional stochastic approach to deal with the gene correlation phenomena. Interestingly, our stochastic framework suggests that the study of the gene correlation requires only one theoretical assumption-Markov property-and the experimental transition probability, which characterizes the gene correlation system. Finally, a gene expression experiment is proposed for future applications of the model
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 ...
Liang, Faming
2014-04-03
Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to use this much CPU time. This article proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation, it is shown that the new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, for example, a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors. Supplementary materials for this article are available online.
Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist.
Directory of Open Access Journals (Sweden)
Brian Drawert
2016-12-01
Full Text Available We present StochSS: Stochastic Simulation as a Service, an integrated development environment for modeling and simulation of both deterministic and discrete stochastic biochemical systems in up to three dimensions. An easy to use graphical user interface enables researchers to quickly develop and simulate a biological model on a desktop or laptop, which can then be expanded to incorporate increasing levels of complexity. StochSS features state-of-the-art simulation engines. As the demand for computational power increases, StochSS can seamlessly scale computing resources in the cloud. In addition, StochSS can be deployed as a multi-user software environment where collaborators share computational resources and exchange models via a public model repository. We demonstrate the capabilities and ease of use of StochSS with an example of model development and simulation at increasing levels of complexity.
Diffusion approximation-based simulation of stochastic ion channels: which method to use?
Directory of Open Access Journals (Sweden)
Danilo ePezo
2014-11-01
Full Text Available To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie’s method for Markov Chains (MC simulation is highly accurate, yet it becomes computationally intensive in the regime of high channel numbers. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA. Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties – such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Dangerfield et al., 2012; Linaro et al., 2011; Huang et al., 2013a; Orio and Soudry, 2012; Schmandt and Galán, 2012; Goldwyn et al., 2011; Güler, 2013, comparing all of them in a set of numerical simulations that asses numerical accuracy and computational efficiency on three different models: the original Hodgkin and Huxley model, a model with faster sodium channels, and a multi-compartmental model inspired in granular cells. We conclude that for low channel numbers (usually below 1000 per simulated compartment one should use MC – which is both the most accurate and fastest method. For higher channel numbers, we recommend using the method by Orio and Soudry (2012, possibly combined with the method by Schmandt and Galán (2012 for increased speed and slightly reduced accuracy. Consequently, MC modelling may be the best method for detailed multicompartment neuron models – in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels.
Diffusion approximation-based simulation of stochastic ion channels: which method to use?
Pezo, Danilo; Soudry, Daniel; Orio, Patricio
2014-01-01
To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie's method for Markov Chains (MC) simulation is highly accurate, yet it becomes computationally intensive in the regime of a high number of channels. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA). Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties—such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Goldwyn et al., 2011; Linaro et al., 2011; Dangerfield et al., 2012; Orio and Soudry, 2012; Schmandt and Galán, 2012; Güler, 2013; Huang et al., 2013a), comparing all of them in a set of numerical simulations that assess numerical accuracy and computational efficiency on three different models: (1) the original Hodgkin and Huxley model, (2) a model with faster sodium channels, and (3) a multi-compartmental model inspired in granular cells. We conclude that for a low number of channels (usually below 1000 per simulated compartment) one should use MC—which is the fastest and most accurate method. For a high number of channels, we recommend using the method by Orio and Soudry (2012), possibly combined with the method by Schmandt and Galán (2012) for increased speed and slightly reduced accuracy. Consequently, MC modeling may be the best method for detailed multicompartment neuron models—in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels. PMID:25404914
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.
Multivariate stochastic simulation with subjective multivariate normal distributions
P. J. Ince; J. Buongiorno
1991-01-01
In many applications of Monte Carlo simulation in forestry or forest products, it may be known that some variables are correlated. However, for simplicity, in most simulations it has been assumed that random variables are independently distributed. This report describes an alternative Monte Carlo simulation technique for subjectively assesed multivariate normal...
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.
Cambridge Rocketry Simulator – A Stochastic Six-Degrees-of-Freedom Rocket Flight Simulator
Eerland, Willem J.; Box, Simon; Sóbester, András
2017-01-01
The Cambridge Rocketry Simulator can be used to simulate the flight of unguided rockets for both design and operational applications. The software consists of three parts: The first part is a GUI that enables the user to design a rocket. The second part is a verified and peer-reviewed physics model that simulates the rocket flight. This includes a Monte Carlo wrapper to model the uncertainty in the rocket’s dynamics and the atmospheric conditions. The third part generates visualizations of th...
Modeling Group Perceptions Using Stochastic Simulation: Scaling Issues in the Multiplicative AHP
DEFF Research Database (Denmark)
Barfod, Michael Bruhn; van den Honert, Robin; Salling, Kim Bang
2016-01-01
This paper proposes a new decision support approach for applying stochastic simulation to the multiplicative analytic hierarchy process (AHP) in order to deal with issues concerning the scale parameter. The paper suggests a new approach that captures the influence from the scale parameter by maki...
DEFF Research Database (Denmark)
Debrabant, Kristian; Samaey, Giovanni; Zieliński, Przemysław
2017-01-01
We present and analyse a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time-scale of individual trajectories and the (slow) time-scale of the macroscopic function of interest. The algorithm combines short...
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.
Dynamic analysis of a stochastic rumor propagation model
Jia, Fangju; Lv, Guangying
2018-01-01
The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. In this paper, we are concerned with a stochastic rumor propagation model. Sufficient conditions for extinction and persistence in the mean of the rumor are established. The threshold between persistence in the mean and extinction of the rumor is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.
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.
Extracting Markov Models of Peptide Conformational Dynamics from Simulation Data.
Schultheis, Verena; Hirschberger, Thomas; Carstens, Heiko; Tavan, Paul
2005-07-01
A high-dimensional time series obtained by simulating a complex and stochastic dynamical system (like a peptide in solution) may code an underlying multiple-state Markov process. We present a computational approach to most plausibly identify and reconstruct this process from the simulated trajectory. Using a mixture of normal distributions we first construct a maximum likelihood estimate of the point density associated with this time series and thus obtain a density-oriented partition of the data space. This discretization allows us to estimate the transfer operator as a matrix of moderate dimension at sufficient statistics. A nonlinear dynamics involving that matrix and, alternatively, a deterministic coarse-graining procedure are employed to construct respective hierarchies of Markov models, from which the model most plausibly mapping the generating stochastic process is selected by consideration of certain observables. Within both procedures the data are classified in terms of prototypical points, the conformations, marking the various Markov states. As a typical example, the approach is applied to analyze the conformational dynamics of a tripeptide in solution. The corresponding high-dimensional time series has been obtained from an extended molecular dynamics simulation.
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.
Parallel discrete-event simulation of FCFS stochastic queueing networks
Nicol, David M.
1988-01-01
Physical systems are inherently parallel. Intuition suggests that simulations of these systems may be amenable to parallel execution. The parallel execution of a discrete-event simulation requires careful synchronization of processes in order to ensure the execution's correctness; this synchronization can degrade performance. Largely negative results were recently reported in a study which used a well-known synchronization method on queueing network simulations. Discussed here is a synchronization method (appointments), which has proven itself to be effective on simulations of FCFS queueing networks. The key concept behind appointments is the provision of lookahead. Lookahead is a prediction on a processor's future behavior, based on an analysis of the processor's simulation state. It is shown how lookahead can be computed for FCFS queueing network simulations, give performance data that demonstrates the method's effectiveness under moderate to heavy loads, and discuss performance tradeoffs between the quality of lookahead, and the cost of computing lookahead.
Explicit calibration and simulation of stochastic fields by low-order ARMA processes
DEFF Research Database (Denmark)
Krenk, Steen
2011-01-01
A simple framework for autoregressive simulation of stochastic fields is presented. The autoregressive format leads to a simple exponential correlation structure in the time-dimension. In the case of scalar processes a more detailed correlation structure can be obtained by adding memory...... to the process via an extension to autoregressive moving average (ARMA) processes. The ARMA format incorporates a more detailed correlation structure by including previous values of the simulated process. Alternatively, a more detailed correlation structure can be obtained by including additional 'state......-space' variables in the simulation. For a scalar process this would imply an increase of the dimension of the process to be simulated. In the case of a stochastic field the correlation in the time-dimension is represented, although indirectly, in the simultaneous spatial correlation. The model with the shortest...
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.
STOCHASTIC SIMULATION FOR BUFFELGRASS (Cenchrus ciliaris L.) PASTURES IN MARIN, N. L., MEXICO
JosÃ© Romualdo MartÃnez-LÃ³pez; Erasmo Gutierrez-Ornelas; Miguel Angel Barrera-Silva; Rafael Retes-LÃ³pez
2014-01-01
A stochastic simulation model was constructed to determine the response of net primary production of buffelgrass (Cenchrus ciliaris L.) and its dry matter intake by cattle, in MarÃn, NL, MÃ©xico. Buffelgrass is very important for extensive livestock industry in arid and semiarid areas of northeastern Mexico. To evaluate the behavior of the model by comparing the model results with those reported in the literature was the objective in this experiment. Model simulates the monthly production of...
Threshold Dynamics of a Stochastic SIR Model with Vertical Transmission and Vaccination
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.
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.
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
Inter-species competition-facilitation in stochastic riparian vegetation dynamics.
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.
Directory of Open Access Journals (Sweden)
Jingtao Shi
2013-01-01
Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
A Volterra series approach to the approximation of stochastic nonlinear dynamics
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
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...
Sharp asymptotics for stochastic dynamics with parallel updating rule with self-interaction
Bovier, A.; Nardi, F.R.; Spitoni, C.
2011-01-01
In this paper we study metastability for a stochastic dynamics with a parallel updating rule in particular for a probabilistic cellular automata. The problem is addressed in the Freidlin Wentzel regime, i.e., finite volume, small magnetic field, and in the limit when temperature tends to zero. We
Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays
Directory of Open Access Journals (Sweden)
Li Wan
2012-01-01
Full Text Available This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.
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...
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...
Who Is Afraid of Liquidity Risk? : Dynamic Portfolio Choice with Stochastic Illiquidity
J.J.A.G. Driessen (Joost); R. Xing (Rang)
2016-01-01
textabstractRecent empirical work documents large liquidity risk premiums in stock markets. We calculate the liquidity risk premiums demanded by large investors by solving a dynamic portfolio choice problem with stochastic price impact of trading, CRRA utility and a time-varying investment
Is There Really a Global Business Cycle? : A Dynamic Factor Model with Stochastic Factor Selection
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
P.A.N. Bosman (Peter); J.A. La Poutré (Han); D. Thierens (Dirk)
2007-01-01
htmlabstractThe focus of this paper is on how to design evolutionary algorithms (EAs) for solving stochastic dynamic optimization problems online, i.e. as time goes by. For a proper design, the EA must not only be capable of tracking shifting optima, it must also take into account the future
Who Is Afraid of Liquidity Risk? : Dynamic Portfolio Choice with Stochastic Illiquidity
Driessen, Joost; Xing, R.
Recent empirical work documents large liquidity risk premiums in stock markets. We calculate the liquidity risk premiums demanded by large investors by solving a dynamic portfolio choice problem with stochastic price impact of trading, CRRA utility and a time-varying investment opportunity set. We
Energy Technology Data Exchange (ETDEWEB)
Van Kessel, L.B.M.
2003-06-11
with the on-line calorific value sensor from chapter 2 and a validated dynamic model of the process is available, the theory from stochastic processes can be applied to MSWC. This new application field of stochastics is discussed in chapter 4. The results obtained in chapter 2 will be used in this analysis. Also new linear transfer functions for thermal processes will be given and applied to MSWC. Finally, applications of the new developed tools will be discussed. As already mentioned, the validation experiments lead to the conclusion that the dynamics of the combustion process can change when the primary air temperature changes. This was a new result, which has never been reported in literature before. For that reason during the research it was decided to start an extensive study into the influence of the primary air temperature on the combustion process. This has been performed by using laboratory experiments. In chapter 5 the results from this search will be presented. The existing theory for combustion of solid fuels is extended with a qualitative as well as a quantitative description of the influence of primary preheating. The new theory is used to explain observations from real plants and the results from system identification. Furthermore, the value of laboratory experiments to simulate the real combustion process on a grate is discussed.
Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
Cotter, Simon L.; Vejchodský , Tomá š; Erban, Radek
2013-01-01
Stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods. © 2013 Society for Industrial and Applied Mathematics.
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)
Vehicle dynamics modeling and simulation
Schramm, Dieter; Bardini, Roberto
2014-01-01
The authors examine in detail the fundamentals and mathematical descriptions of the dynamics of automobiles. In this context different levels of complexity will be presented, starting with basic single-track models up to complex three-dimensional multi-body models. A particular focus is on the process of establishing mathematical models on the basis of real cars and the validation of simulation results. The methods presented are explained in detail by means of selected application scenarios.
Stochastic soil water dynamics of phreatophyte vegetation with dimorphic root systems
Vervoort, R.W.; Zee, van der S.E.A.T.M.
2009-01-01
As the direct uptake of deep groundwater by vegetation may be essential in semiarid regions, we incorporated this process in stochastic root zone water balance models. The direct water uptake by vegetation via deep tap roots is simulated using one additional empirical parameter. This is considered
Stochastic Processes and Queueing Theory used in Cloud Computer Performance Simulations
Directory of Open Access Journals (Sweden)
Florin-Catalin ENACHE
2015-10-01
Full Text Available The growing character of the cloud business has manifested exponentially in the last 5 years. The capacity managers need to concentrate on a practical way to simulate the random demands a cloud infrastructure could face, even if there are not too many mathematical tools to simulate such demands.This paper presents an introduction into the most important stochastic processes and queueing theory concepts used for modeling computer performance. Moreover, it shows the cases where such concepts are applicable and when not, using clear programming examples on how to simulate a queue, and how to use and validate a simulation, when there are no mathematical concepts to back it up.
Cambridge Rocketry Simulator – A Stochastic Six-Degrees-of-Freedom Rocket Flight Simulator
Directory of Open Access Journals (Sweden)
Willem J. Eerland
2017-02-01
Full Text Available The Cambridge Rocketry Simulator can be used to simulate the flight of unguided rockets for both design and operational applications. The software consists of three parts: The first part is a GUI that enables the user to design a rocket. The second part is a verified and peer-reviewed physics model that simulates the rocket flight. This includes a Monte Carlo wrapper to model the uncertainty in the rocket’s dynamics and the atmospheric conditions. The third part generates visualizations of the resulting trajectories, including nominal performance and uncertainty analysis, e.g. a splash-down region with confidence bounds. The project is available on SourceForge, and is written in Java (GUI, C++ (simulation core, and Python (visualization. While all parts can be executed from the GUI, the three components share information via XML, accommodating modifications, and re-use of individual components.
Stochastic dynamics of spatial effects in fragmentation of clusters
International Nuclear Information System (INIS)
Salinas-Rodriguez, E.; Rodriguez, R.F.; Zamora, J.M.
1991-01-01
We use a stochastic approach to study the effects of spatial in homogeneities in the kinetics of a fragmentation model which occurs in cluster breakup and polymer degradation. The analytical form of the cluster size distribution function is obtained for both the discrete and continuous limits. From it we calculate numerically the average size and volume of the clusters, their total concentration and the total scattering of the dispersion in both limits. The influence of spatial effects is explicitly shown in the last two quantities. From our description the equations for the equal-time and the two times density correlation functions are also derived in the continuous limit. Finally, the perspectives and limitations of our approach are discussed (Author)
Nonlinear dynamics of mushy layers induced by external stochastic fluctuations.
Alexandrov, Dmitri V; Bashkirtseva, Irina A; Ryashko, Lev B
2018-02-28
The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the 'solid phase-mushy layer' and 'mushy layer-liquid phase' phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found. If the atmospheric temperature and friction velocity are constant, the analytical solution takes a parametric form. In the more common case when they represent arbitrary functions of time, the analytical solution is given by means of the standard Cauchy problem. The deterministic and stochastic behaviour of the phase transition process is analysed on the basis of the obtained analytical solutions. In the case of stochastic fluctuations in the atmospheric temperature and friction velocity, the phase transition interfaces (mushy layer boundaries) move faster than in the deterministic case. A cumulative effect of these noise contributions is revealed as well. In other words, when the atmospheric temperature and friction velocity fluctuate simultaneously due to the influence of different external processes and phenomena, the phase transition boundaries move even faster. This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'. © 2018 The Author(s).
An adaptive algorithm for simulation of stochastic reaction-diffusion processes
International Nuclear Information System (INIS)
Ferm, Lars; Hellander, Andreas; Loetstedt, Per
2010-01-01
We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.
D-leaping: Accelerating stochastic simulation algorithms for reactions with delays
International Nuclear Information System (INIS)
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2009-01-01
We propose a novel, accelerated algorithm for the approximate stochastic simulation of biochemical systems with delays. The present work extends existing accelerated algorithms by distributing, in a time adaptive fashion, the delayed reactions so as to minimize the computational effort while preserving their accuracy. The accuracy of the present algorithm is assessed by comparing its results to those of the corresponding delay differential equations for a representative biochemical system. In addition, the fluctuations produced from the present algorithm are comparable to those from an exact stochastic simulation with delays. The algorithm is used to simulate biochemical systems that model oscillatory gene expression. The results indicate that the present algorithm is competitive with existing works for several benchmark problems while it is orders of magnitude faster for certain systems of biochemical reactions.
MOSES: A Matlab-based open-source stochastic epidemic simulator.
Varol, Huseyin Atakan
2016-08-01
This paper presents an open-source stochastic epidemic simulator. Discrete Time Markov Chain based simulator is implemented in Matlab. The simulator capable of simulating SEQIJR (susceptible, exposed, quarantined, infected, isolated and recovered) model can be reduced to simpler models by setting some of the parameters (transition probabilities) to zero. Similarly, it can be extended to more complicated models by editing the source code. It is designed to be used for testing different control algorithms to contain epidemics. The simulator is also designed to be compatible with a network based epidemic simulator and can be used in the network based scheme for the simulation of a node. Simulations show the capability of reproducing different epidemic model behaviors successfully in a computationally efficient manner.
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.
Stochastic annealing simulations of defect interactions among subcascades
Energy Technology Data Exchange (ETDEWEB)
Heinisch, H.L. [Pacific Northwest National Lab., Richland, WA (United States); Singh, B.N.
1997-04-01
The effects of the subcascade structure of high energy cascades on the temperature dependencies of annihilation, clustering and free defect production are investigated. The subcascade structure is simulated by closely spaced groups of lower energy MD cascades. The simulation results illustrate the strong influence of the defect configuration existing in the primary damage state on subsequent intracascade evolution. Other significant factors affecting the evolution of the defect distribution are the large differences in mobility and stability of vacancy and interstitial defects and the rapid one-dimensional diffusion of small, glissile interstitial loops produced directly in cascades. Annealing simulations are also performed on high-energy, subcascade-producing cascades generated with the binary collision approximation and calibrated to MD results.
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.
The global dynamics for a stochastic SIS epidemic model with isolation
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.
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.
International Nuclear Information System (INIS)
Woo, Mingko; Lonergan, S.
1990-01-01
Winter roads constitute an important part of the transportation network in the MacKenzie Delta, the Yellowknife area, and between the MacKenzie Highway and the Canol Road. Climatic changes in the MacKenzie Valley will alter the probabilities of ice cover thickness and duration, impacting on the periods when ice road river crossings are viable. Stochastic models were developed to generate air temperature and precipitation data to analyze climate impacts on when ice road crossing of the MacKenzie River at Norman Wells is feasible. The data were employed to simulate river ice growth and decay. Several general circulation models were employed to determine the impacts of climatic change on the ice regime. For precipitation simulation, the occurrence of wet or dry days was determined from Markov chain transition probabilities. In general, the Goddard Institute of Space Studies (GISS) model predicted the largest increase in monthly precipitation and the Oregon State University (OSU) model predicted the least changes. The various scenarios indicated that the duration for vehicular traffic over ice will be significantly reduced, compared to present day Norman Wells ice crossing operation. For 20 tonne vehicles, the current duration for safe crossing averages 169±14.6 days per year, while for the OSU scenario it will be reduced to 148±14.7 days, is further reduced to 127±24.9 days for the GISS scenario, and drops to 122±21.7 days for the GFDL (General Fluid Dynamics Laboratory) scenario. 5 refs., 1 fig
Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports.
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.
A fire management simulation model using stochastic arrival times
Eric L. Smith
1987-01-01
Fire management simulation models are used to predict the impact of changes in the fire management program on fire outcomes. As with all models, the goal is to abstract reality without seriously distorting relationships between variables of interest. One important variable of fire organization performance is the length of time it takes to get suppression units to the...
Stochastic feeding dynamics arise from the need for information and energy.
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.
Computing the optimal path in stochastic dynamical systems
International Nuclear Information System (INIS)
Bauver, Martha; Forgoston, Eric; Billings, Lora
2016-01-01
In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.
Kernel methods and flexible inference for complex stochastic dynamics
Capobianco, Enrico
2008-07-01
Approximation theory suggests that series expansions and projections represent standard tools for random process applications from both numerical and statistical standpoints. Such instruments emphasize the role of both sparsity and smoothness for compression purposes, the decorrelation power achieved in the expansion coefficients space compared to the signal space, and the reproducing kernel property when some special conditions are met. We consider these three aspects central to the discussion in this paper, and attempt to analyze the characteristics of some known approximation instruments employed in a complex application domain such as financial market time series. Volatility models are often built ad hoc, parametrically and through very sophisticated methodologies. But they can hardly deal with stochastic processes with regard to non-Gaussianity, covariance non-stationarity or complex dependence without paying a big price in terms of either model mis-specification or computational efficiency. It is thus a good idea to look at other more flexible inference tools; hence the strategy of combining greedy approximation and space dimensionality reduction techniques, which are less dependent on distributional assumptions and more targeted to achieve computationally efficient performances. Advantages and limitations of their use will be evaluated by looking at algorithmic and model building strategies, and by reporting statistical diagnostics.
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.
International Nuclear Information System (INIS)
Jang, Hong; Lee, Jay H.; Braatz, Richard D.
2016-01-01
This paper proposes a maximum likelihood estimation (MLE) method for estimating time varying local concentration of the target molecule proximate to the sensor from the time profile of monomolecular adsorption and desorption on the surface of the sensor at nanoscale. Recently, several carbon nanotube sensors have been developed that can selectively detect target molecules at a trace concentration level. These sensors use light intensity changes mediated by adsorption or desorption phenomena on their surfaces. The molecular events occurring at trace concentration levels are inherently stochastic, posing a challenge for optimal estimation. The stochastic behavior is modeled by the chemical master equation (CME), composed of a set of ordinary differential equations describing the time evolution of probabilities for the possible adsorption states. Given the significant stochastic nature of the underlying phenomena, rigorous stochastic estimation based on the CME should lead to an improved accuracy over than deterministic estimation formulated based on the continuum model. Motivated by this expectation, we formulate the MLE based on an analytical solution of the relevant CME, both for the constant and the time-varying local concentrations, with the objective of estimating the analyte concentration field in real time from the adsorption readings of the sensor array. The performances of the MLE and the deterministic least squares are compared using data generated by kinetic Monte Carlo (KMC) simulations of the stochastic process. Some future challenges are described for estimating and controlling the concentration field in a distributed domain using the sensor technology.
An efficient parallel stochastic simulation method for analysis of nonviral gene delivery systems
Kuwahara, Hiroyuki
2011-01-01
Gene therapy has a great potential to become an effective treatment for a wide variety of diseases. One of the main challenges to make gene therapy practical in clinical settings is the development of efficient and safe mechanisms to deliver foreign DNA molecules into the nucleus of target cells. Several computational and experimental studies have shown that the design process of synthetic gene transfer vectors can be greatly enhanced by computational modeling and simulation. This paper proposes a novel, effective parallelization of the stochastic simulation algorithm (SSA) for pharmacokinetic models that characterize the rate-limiting, multi-step processes of intracellular gene delivery. While efficient parallelizations of the SSA are still an open problem in a general setting, the proposed parallel simulation method is able to substantially accelerate the next reaction selection scheme and the reaction update scheme in the SSA by exploiting and decomposing the structures of stochastic gene delivery models. This, thus, makes computationally intensive analysis such as parameter optimizations and gene dosage control for specific cell types, gene vectors, and transgene expression stability substantially more practical than that could otherwise be with the standard SSA. Here, we translated the nonviral gene delivery model based on mass-action kinetics by Varga et al. [Molecular Therapy, 4(5), 2001] into a more realistic model that captures intracellular fluctuations based on stochastic chemical kinetics, and as a case study we applied our parallel simulation to this stochastic model. Our results show that our simulation method is able to increase the efficiency of statistical analysis by at least 50% in various settings. © 2011 ACM.
Katsoulakis, Markos A.; Vlachos, Dionisios G.
2003-11-01
We derive a hierarchy of successively coarse-grained stochastic processes and associated coarse-grained Monte Carlo (CGMC) algorithms directly from the microscopic processes as approximations in larger length scales for the case of diffusion of interacting particles on a lattice. This hierarchy of models spans length scales between microscopic and mesoscopic, satisfies a detailed balance, and gives self-consistent fluctuation mechanisms whose noise is asymptotically identical to the microscopic MC. Rigorous, detailed asymptotics justify and clarify these connections. Gradient continuous time microscopic MC and CGMC simulations are compared under far from equilibrium conditions to illustrate the validity of our theory and delineate the errors obtained by rigorous asymptotics. Information theory estimates are employed for the first time to provide rigorous error estimates between the solutions of microscopic MC and CGMC, describing the loss of information during the coarse-graining process. Simulations under periodic boundary conditions are used to verify the information theory error estimates. It is shown that coarse-graining in space leads also to coarse-graining in time by q2, where q is the level of coarse-graining, and overcomes in part the hydrodynamic slowdown. Operation counting and CGMC simulations demonstrate significant CPU savings in continuous time MC simulations that vary from q3 for short potentials to q4 for long potentials. Finally, connections of the new coarse-grained stochastic processes to stochastic mesoscopic and Cahn-Hilliard-Cook models are made.
Dimension reduction of Karhunen-Loeve expansion for simulation of stochastic processes
Liu, Zhangjun; Liu, Zixin; Peng, Yongbo
2017-11-01
Conventional Karhunen-Loeve expansions for simulation of stochastic processes often encounter the challenge of dealing with hundreds of random variables. For breaking through the barrier, a random function embedded Karhunen-Loeve expansion method is proposed in this paper. The updated scheme has a similar form to the conventional Karhunen-Loeve expansion, both involving a summation of a series of deterministic orthonormal basis and uncorrelated random variables. While the difference from the updated scheme lies in the dimension reduction of Karhunen-Loeve expansion through introducing random functions as a conditional constraint upon uncorrelated random variables. The random function is expressed as a single-elementary-random-variable orthogonal function in polynomial format (non-Gaussian variables) or trigonometric format (non-Gaussian and Gaussian variables). For illustrative purposes, the simulation of seismic ground motion is carried out using the updated scheme. Numerical investigations reveal that the Karhunen-Loeve expansion with random functions could gain desirable simulation results in case of a moderate sample number, except the Hermite polynomials and the Laguerre polynomials. It has the sound applicability and efficiency in simulation of stochastic processes. Besides, the updated scheme has the benefit of integrating with probability density evolution method, readily for the stochastic analysis of nonlinear structures.
Neural network stochastic simulation applied for quantifying uncertainties
Directory of Open Access Journals (Sweden)
N Foudil-Bey
2016-09-01
Full Text Available Generally the geostatistical simulation methods are used to generate several realizations of physical properties in the sub-surface, these methods are based on the variogram analysis and limited to measures correlation between variables at two locations only. In this paper, we propose a simulation of properties based on supervised Neural network training at the existing drilling data set. The major advantage is that this method does not require a preliminary geostatistical study and takes into account several points. As a result, the geological information and the diverse geophysical data can be combined easily. To do this, we used a neural network with multi-layer perceptron architecture like feed-forward, then we used the back-propagation algorithm with conjugate gradient technique to minimize the error of the network output. The learning process can create links between different variables, this relationship can be used for interpolation of the properties on the one hand, or to generate several possible distribution of physical properties on the other hand, changing at each time and a random value of the input neurons, which was kept constant until the period of learning. This method was tested on real data to simulate multiple realizations of the density and the magnetic susceptibility in three-dimensions at the mining camp of Val d'Or, Québec (Canada.
arXiv Stochastic locality and master-field simulations of very large lattices
Lüscher, Martin
2018-01-01
In lattice QCD and other field theories with a mass gap, the field variables in distant regions of a physically large lattice are only weakly correlated. Accurate stochastic estimates of the expectation values of local observables may therefore be obtained from a single representative field. Such master-field simulations potentially allow very large lattices to be simulated, but require various conceptual and technical issues to be addressed. In this talk, an introduction to the subject is provided and some encouraging results of master-field simulations of the SU(3) gauge theory are reported.
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
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.
Numerical simulation of nonlinear dynamical systems driven by commutative noise
International Nuclear Information System (INIS)
Carbonell, F.; Biscay, R.J.; Jimenez, J.C.; Cruz, H. de la
2007-01-01
The local linearization (LL) approach has become an effective technique for the numerical integration of ordinary, random and stochastic differential equations. One of the reasons for this success is that the LL method achieves a convenient trade-off between numerical stability and computational cost. Besides, the LL method reproduces well the dynamics of nonlinear equations for which other classical methods fail. However, in the stochastic case, most of the reported works has been focused in Stochastic Differential Equations (SDE) driven by additive noise. This limits the applicability of the LL method since there is a number of interesting dynamics observed in equations with multiplicative noise. On the other hand, recent results show that commutative noise SDEs can be transformed into a random differential equation (RDE) by means of a random diffeomorfism (conjugacy). This paper takes advantages of such conjugacy property and the LL approach for defining a LL scheme for SDEs driven by commutative noise. The performance of the proposed method is illustrated by means of numerical simulations
A stochastic dynamic programming model for stream water quality ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
constraints of the water quality management problem; (ii) a water quality simulation model ... of acceptance and limited implementation of optimisation techniques. .... The response of river system to these sources of pollution can be integrated ...
Dynamic simulation of LMFBR systems
International Nuclear Information System (INIS)
Agrawal, A.K.; Khatib-Rahbar, M.
1980-01-01
This review article focuses on the dynamic analysis of liquid-metal-cooled fast breeder reactor systems in the context of protected transients. Following a brief discussion on various design and simulation approaches, a critical review of various models for in-reactor components, intermediate heat exchangers, heat transport systems and the steam generating system is presented. A brief discussion on choice of fuels as well as core and blanket system designs is also included. Numerical considerations for obtaining system-wide steady-state and transient solutions are discussed, and examples of various system transients are presented. Another area of major interest is verification of phenomenological models. Various steps involved in the code and model verification are briefly outlined. The review concludes by posing some further areas of interest in fast reactor dynamics and safety. (author)
International Nuclear Information System (INIS)
De Santis, Emilio; Marinelli, Carlo
2007-01-01
We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove 'fixation', i.e. players will adopt a constant strategy after a finite time. The resulting dynamics is related to zero-temperature Glauber dynamics on random graphs of possibly infinite volume
Human motion simulation predictive dynamics
Abdel-Malek, Karim
2013-01-01
Simulate realistic human motion in a virtual world with an optimization-based approach to motion prediction. With this approach, motion is governed by human performance measures, such as speed and energy, which act as objective functions to be optimized. Constraints on joint torques and angles are imposed quite easily. Predicting motion in this way allows one to use avatars to study how and why humans move the way they do, given specific scenarios. It also enables avatars to react to infinitely many scenarios with substantial autonomy. With this approach it is possible to predict dynamic motion without having to integrate equations of motion -- rather than solving equations of motion, this approach solves for a continuous time-dependent curve characterizing joint variables (also called joint profiles) for every degree of freedom. Introduces rigorous mathematical methods for digital human modelling and simulation Focuses on understanding and representing spatial relationships (3D) of biomechanics Develops an i...
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.
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.
Duan, Xiaofeng F; Burggraf, Larry W; Huang, Lingyu
2013-07-22
To find low energy Si(n)C(n) structures out of hundreds to thousands of isomers we have developed a general method to search for stable isomeric structures that combines Stochastic Potential Surface Search and Pseudopotential Plane-Wave Density Functional Theory Car-Parinello Molecular Dynamics simulated annealing (PSPW-CPMD-SA). We enhanced the Sunders stochastic search method to generate random cluster structures used as seed structures for PSPW-CPMD-SA simulations. This method ensures that each SA simulation samples a different potential surface region to find the regional minimum structure. By iterations of this automated, parallel process on a high performance computer we located hundreds to more than a thousand stable isomers for each Si(n)C(n) cluster. Among these, five to 10 of the lowest energy isomers were further optimized using B3LYP/cc-pVTZ method. We applied this method to Si(n)C(n) (n = 4-12) clusters and found the lowest energy structures, most not previously reported. By analyzing the bonding patterns of low energy structures of each Si(n)C(n) cluster, we observed that carbon segregations tend to form condensed conjugated rings while Si connects to unsaturated bonds at the periphery of the carbon segregation as single atoms or clusters when n is small and when n is large a silicon network spans over the carbon segregation region.
Directory of Open Access Journals (Sweden)
Larry W. Burggraf
2013-07-01
Full Text Available To find low energy SinCn structures out of hundreds to thousands of isomers we have developed a general method to search for stable isomeric structures that combines Stochastic Potential Surface Search and Pseudopotential Plane-Wave Density Functional Theory Car-Parinello Molecular Dynamics simulated annealing (PSPW-CPMD-SA. We enhanced the Sunders stochastic search method to generate random cluster structures used as seed structures for PSPW-CPMD-SA simulations. This method ensures that each SA simulation samples a different potential surface region to find the regional minimum structure. By iterations of this automated, parallel process on a high performance computer we located hundreds to more than a thousand stable isomers for each SinCn cluster. Among these, five to 10 of the lowest energy isomers were further optimized using B3LYP/cc-pVTZ method. We applied this method to SinCn (n = 4–12 clusters and found the lowest energy structures, most not previously reported. By analyzing the bonding patterns of low energy structures of each SinCn cluster, we observed that carbon segregations tend to form condensed conjugated rings while Si connects to unsaturated bonds at the periphery of the carbon segregation as single atoms or clusters when n is small and when n is large a silicon network spans over the carbon segregation region.
StochKit2: software for discrete stochastic simulation of biochemical systems with events.
Sanft, Kevin R; Wu, Sheng; Roh, Min; Fu, Jin; Lim, Rone Kwei; Petzold, Linda R
2011-09-01
StochKit2 is the first major upgrade of the popular StochKit stochastic simulation software package. StochKit2 provides highly efficient implementations of several variants of Gillespie's stochastic simulation algorithm (SSA), and tau-leaping with automatic step size selection. StochKit2 features include automatic selection of the optimal SSA method based on model properties, event handling, and automatic parallelism on multicore architectures. The underlying structure of the code has been completely updated to provide a flexible framework for extending its functionality. StochKit2 runs on Linux/Unix, Mac OS X and Windows. It is freely available under GPL version 3 and can be downloaded from http://sourceforge.net/projects/stochkit/. petzold@engineering.ucsb.edu.
DEFF Research Database (Denmark)
Foddai, Alessandro; Enøe, Claes; Krogh, Kaspar
2014-01-01
A stochastic simulation model was developed to estimate the time from introduction ofBovine Viral Diarrhea Virus (BVDV) in a herd to detection of antibodies in bulk tank milk(BTM) samples using three ELISAs. We assumed that antibodies could be detected, after afixed threshold prevalence of seroco......A stochastic simulation model was developed to estimate the time from introduction ofBovine Viral Diarrhea Virus (BVDV) in a herd to detection of antibodies in bulk tank milk(BTM) samples using three ELISAs. We assumed that antibodies could be detected, after afixed threshold prevalence......, which was the most efficient ELISA, could detect antibodiesin the BTM of a large herd 280 days (95% prediction interval: 218; 568) after a transientlyinfected (TI) milking cow has been introduced into the herd. The estimated time to detectionafter introduction of one PI calf was 111 days (44; 605...
Directory of Open Access Journals (Sweden)
Ryota Mori
2015-01-01
Full Text Available Airport congestion, in particular congestion of departure aircraft, has already been discussed by other researches. Most solutions, though, fail to account for uncertainties. Since it is difficult to remove uncertainties of the operations in the real world, a strategy should be developed assuming such uncertainties exist. Therefore, this research develops a fast-time stochastic simulation model used to validate various methods in order to decrease airport congestion level under existing uncertainties. The surface movement data is analyzed first, and the uncertainty level is obtained. Next, based on the result of data analysis, the stochastic simulation model is developed. The model is validated statistically and the characteristics of airport operation under existing uncertainties are investigated.
Energy Technology Data Exchange (ETDEWEB)
Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan); Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610 (Belgium); Chen, W. [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan)
2016-08-07
Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.
Dynamic benchmarking of simulation codes
International Nuclear Information System (INIS)
Henry, R.E.; Paik, C.Y.; Hauser, G.M.
1996-01-01
Computer simulation of nuclear power plant response can be a full-scope control room simulator, an engineering simulator to represent the general behavior of the plant under normal and abnormal conditions, or the modeling of the plant response to conditions that would eventually lead to core damage. In any of these, the underlying foundation for their use in analysing situations, training of vendor/utility personnel, etc. is how well they represent what has been known from industrial experience, large integral experiments and separate effects tests. Typically, simulation codes are benchmarked with some of these; the level of agreement necessary being dependent upon the ultimate use of the simulation tool. However, these analytical models are computer codes, and as a result, the capabilities are continually enhanced, errors are corrected, new situations are imposed on the code that are outside of the original design basis, etc. Consequently, there is a continual need to assure that the benchmarks with important transients are preserved as the computer code evolves. Retention of this benchmarking capability is essential to develop trust in the computer code. Given the evolving world of computer codes, how is this retention of benchmarking capabilities accomplished? For the MAAP4 codes this capability is accomplished through a 'dynamic benchmarking' feature embedded in the source code. In particular, a set of dynamic benchmarks are included in the source code and these are exercised every time the archive codes are upgraded and distributed to the MAAP users. Three different types of dynamic benchmarks are used: plant transients; large integral experiments; and separate effects tests. Each of these is performed in a different manner. The first is accomplished by developing a parameter file for the plant modeled and an input deck to describe the sequence; i.e. the entire MAAP4 code is exercised. The pertinent plant data is included in the source code and the computer
Vijaykumar, Adithya; Ouldridge, Thomas E.; ten Wolde, Pieter Rein; Bolhuis, Peter G.
2017-03-01
The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic Brownian, Langevin, or deterministic molecular dynamics to treat reactants at the microscopic scale [A. Vijaykumar, P. G. Bolhuis, and P. R. ten Wolde, J. Chem. Phys. 143, 214102 (2015)]. Here we extend this multiscale MD-GFRD approach to include the orientational dynamics that is crucial to describe the anisotropic interactions often prevalent in biomolecular systems. We present the novel algorithm focusing on Brownian dynamics only, although the methodology is generic. We illustrate the novel algorithm using a simple patchy particle model. After validation of the algorithm, we discuss its performance. The rotational Brownian dynamics MD-GFRD multiscale method will open up the possibility for large scale simulations of protein signalling networks.
Structure Learning in Stochastic Non-linear Dynamical Systems
Morris, R. D.; Smelyanskiy, V. N.; Luchinsky, D. G.
2005-12-01
A great many systems can be modeled in the non-linear dynamical systems framework, as x˙ = f(x) + ξ(t), where f(x) is the potential function for the system, and ξ(t) is the driving noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications, for example in predator-prey systems, where the very structure of the coupling between predator-prey pairs can have great ecological significance.
Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks.
Billiard, Sylvain; Ferrière, Régis; Méléard, Sylvie; Tran, Viet Chi
2015-11-01
How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and maintenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of a favorable mutation, a genetical bottleneck occurs and the marker associated with this favorable mutant is hitchhiked. By rigorously analysing the hitchhiking effect and how the neutral diversity is restored afterwards, we obtain the condition for a time-scale separation; under this condition, we show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions. We discuss the implications of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint importance of mutations, ecological parameters, and trait values in the restoration of neutral diversity after a selective sweep.
DEFF Research Database (Denmark)
Davidsen, Claus; Liu, Suxia; Mo, Xinguo
2014-01-01
. A stochastic dynamic programming (SDP) approach is used to minimize the basin-wide total costs arising from water allocations and water curtailments. Dynamic allocation problems with inclusion of groundwater resources proved to be more complex to solve with SDP than pure surface water allocation problems due...... to head-dependent pumping costs. These dynamic pumping costs strongly affect the total costs and can lead to non-convexity of the future cost function. The water user groups (agriculture, industry, domestic) are characterized by inelastic demands and fixed water allocation and water supply curtailment...
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.
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.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes
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.
Stochastic entangled chain dynamics of dense polymer solutions.
Kivotides, Demosthenes; Wilkin, S Louise; Theofanous, Theo G
2010-10-14
We propose an adjustable-parameter-free, entangled chain dynamics model of dense polymer solutions. The model includes the self-consistent dynamics of molecular chains and solvent by describing the former via coarse-grained polymer dynamics that incorporate hydrodynamic interaction effects, and the latter via the forced Stokes equation. Real chain elasticity is modeled via the inclusion of a Pincus regime in the polymer's force-extension curve. Excluded volume effects are taken into account via the combined action of coarse-grained intermolecular potentials and explicit geometric tracking of chain entanglements. We demonstrate that entanglements are responsible for a new (compared to phantom chain dynamics), slow relaxation mode whose characteristic time scale agrees very well with experiment. Similarly good agreement between theory and experiment is also obtained for the equilibrium chain size. We develop methods for the solution of the model in periodic flow domains and apply them to the computation of entangled polymer solutions in equilibrium. We show that the number of entanglements Π agrees well with the number of entanglements expected on the basis of tube theory, satisfactorily reproducing the latter's scaling of Π with the polymer volume fraction φ. Our model predicts diminishing chain size with concentration, thus vindicating Flory's suggestion of excluded volume effects screening in dense solutions. The predicted scaling of chain size with φ is consistent with the heuristic, Flory theory based value.
Combining molecular dynamics with mesoscopic Green’s function reaction dynamics simulations
Energy Technology Data Exchange (ETDEWEB)
Vijaykumar, Adithya, E-mail: vijaykumar@amolf.nl [FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam (Netherlands); van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam (Netherlands); Bolhuis, Peter G. [van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam (Netherlands); Rein ten Wolde, Pieter, E-mail: p.t.wolde@amolf.nl [FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam (Netherlands)
2015-12-07
In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. We propose a novel approach that combines GFRD for simulating the system at the mesoscopic scale where particles are far apart, with a microscopic technique such as Langevin dynamics or Molecular Dynamics (MD), for simulating the system at the microscopic scale where reactants are in close proximity. This scheme defines the regions where the particles are close together and simulated with high microscopic resolution and those where they are far apart and simulated with lower mesoscopic resolution, adaptively on the fly. The new multi-scale scheme, called MD-GFRD, is generic and can be used to efficiently simulate reaction-diffusion systems at the particle level.
Combining molecular dynamics with mesoscopic Green’s function reaction dynamics simulations
International Nuclear Information System (INIS)
Vijaykumar, Adithya; Bolhuis, Peter G.; Rein ten Wolde, Pieter
2015-01-01
In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. We propose a novel approach that combines GFRD for simulating the system at the mesoscopic scale where particles are far apart, with a microscopic technique such as Langevin dynamics or Molecular Dynamics (MD), for simulating the system at the microscopic scale where reactants are in close proximity. This scheme defines the regions where the particles are close together and simulated with high microscopic resolution and those where they are far apart and simulated with lower mesoscopic resolution, adaptively on the fly. The new multi-scale scheme, called MD-GFRD, is generic and can be used to efficiently simulate reaction-diffusion systems at the particle level
Dodov, B.
2017-12-01
Stochastic simulation of realistic and statistically robust patterns of Tropical Cyclone (TC) induced precipitation is a challenging task. It is even more challenging in a catastrophe modeling context, where tens of thousands of typhoon seasons need to be simulated in order to provide a complete view of flood risk. Ultimately, one could run a coupled global climate model and regional Numerical Weather Prediction (NWP) model, but this approach is not feasible in the catastrophe modeling context and, most importantly, may not provide TC track patterns consistent with observations. Rather, we propose to leverage NWP output for the observed TC precipitation patterns (in terms of downscaled reanalysis 1979-2015) collected on a Lagrangian frame along the historical TC tracks and reduced to the leading spatial principal components of the data. The reduced data from all TCs is then grouped according to timing, storm evolution stage (developing, mature, dissipating, ETC transitioning) and central pressure and used to build a dictionary of stationary (within a group) and non-stationary (for transitions between groups) covariance models. Provided that the stochastic storm tracks with all the parameters describing the TC evolution are already simulated, a sequence of conditional samples from the covariance models chosen according to the TC characteristics at a given moment in time are concatenated, producing a continuous non-stationary precipitation pattern in a Lagrangian framework. The simulated precipitation for each event is finally distributed along the stochastic TC track and blended with a non-TC background precipitation using a data assimilation technique. The proposed framework provides means of efficient simulation (10000 seasons simulated in a couple of days) and robust typhoon precipitation patterns consistent with observed regional climate and visually undistinguishable from high resolution NWP output. The framework is used to simulate a catalog of 10000 typhoon
Research on neutron noise analysis stochastic simulation method for α calculation
International Nuclear Information System (INIS)
Zhong Bin; Shen Huayun; She Ruogu; Zhu Shengdong; Xiao Gang
2014-01-01
The prompt decay constant α has significant application on the physical design and safety analysis in nuclear facilities. To overcome the difficulty of a value calculation with Monte-Carlo method, and improve the precision, a new method based on the neutron noise analysis technology was presented. This method employs the stochastic simulation and the theory of neutron noise analysis technology. Firstly, the evolution of stochastic neutron was simulated by discrete-events Monte-Carlo method based on the theory of generalized Semi-Markov process, then the neutron noise in detectors was solved from neutron signal. Secondly, the neutron noise analysis methods such as Rossia method, Feynman-α method, zero-probability method, and cross-correlation method were used to calculate a value. All of the parameters used in neutron noise analysis method were calculated based on auto-adaptive arithmetic. The a value from these methods accords with each other, the largest relative deviation is 7.9%, which proves the feasibility of a calculation method based on neutron noise analysis stochastic simulation. (authors)
Stochastic four-way coupling of gas-solid flows for Large Eddy Simulations
Curran, Thomas; Denner, Fabian; van Wachem, Berend
2017-11-01
The interaction of solid particles with turbulence has for long been a topic of interest for predicting the behavior of industrially relevant flows. For the turbulent fluid phase, Large Eddy Simulation (LES) methods are widely used for their low computational cost, leaving only the sub-grid scales (SGS) of turbulence to be modelled. Although LES has seen great success in predicting the behavior of turbulent single-phase flows, the development of LES for turbulent gas-solid flows is still in its infancy. This contribution aims at constructing a model to describe the four-way coupling of particles in an LES framework, by considering the role particles play in the transport of turbulent kinetic energy across the scales. Firstly, a stochastic model reconstructing the sub-grid velocities for the particle tracking is presented. Secondly, to solve particle-particle interaction, most models involve a deterministic treatment of the collisions. We finally introduce a stochastic model for estimating the collision probability. All results are validated against fully resolved DNS-DPS simulations. The final goal of this contribution is to propose a global stochastic method adapted to two-phase LES simulation where the number of particles considered can be significantly increased. Financial support from PetroBras is gratefully acknowledged.
Hydrodynamics in adaptive resolution particle simulations: Multiparticle collision dynamics
Energy Technology Data Exchange (ETDEWEB)
Alekseeva, Uliana, E-mail: Alekseeva@itc.rwth-aachen.de [Jülich Supercomputing Centre (JSC), Institute for Advanced Simulation (IAS), Forschungszentrum Jülich, D-52425 Jülich (Germany); German Research School for Simulation Sciences (GRS), Forschungszentrum Jülich, D-52425 Jülich (Germany); Winkler, Roland G., E-mail: r.winkler@fz-juelich.de [Theoretical Soft Matter and Biophysics, Institute for Advanced Simulation (IAS), Forschungszentrum Jülich, D-52425 Jülich (Germany); Sutmann, Godehard, E-mail: g.sutmann@fz-juelich.de [Jülich Supercomputing Centre (JSC), Institute for Advanced Simulation (IAS), Forschungszentrum Jülich, D-52425 Jülich (Germany); ICAMS, Ruhr-University Bochum, D-44801 Bochum (Germany)
2016-06-01
A new adaptive resolution technique for particle-based multi-level simulations of fluids is presented. In the approach, the representation of fluid and solvent particles is changed on the fly between an atomistic and a coarse-grained description. The present approach is based on a hybrid coupling of the multiparticle collision dynamics (MPC) method and molecular dynamics (MD), thereby coupling stochastic and deterministic particle-based methods. Hydrodynamics is examined by calculating velocity and current correlation functions for various mixed and coupled systems. We demonstrate that hydrodynamic properties of the mixed fluid are conserved by a suitable coupling of the two particle methods, and that the simulation results agree well with theoretical expectations.
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
International Nuclear Information System (INIS)
Ueckermann, M.P.; Lermusiaux, P.F.J.; Sapsis, T.P.
2013-01-01
The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier–Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.
Tong, Shaocheng; Wang, Tong; Li, Yongming; Zhang, Huaguang
2014-06-01
This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.
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)
A Multilevel Adaptive Reaction-splitting Simulation Method for Stochastic Reaction Networks
Moraes, Alvaro; Tempone, Raul; Vilanova, Pedro
2016-01-01
In this work, we present a novel multilevel Monte Carlo method for kinetic simulation of stochastic reaction networks characterized by having simultaneously fast and slow reaction channels. To produce efficient simulations, our method adaptively classifies the reactions channels into fast and slow channels. To this end, we first introduce a state-dependent quantity named level of activity of a reaction channel. Then, we propose a low-cost heuristic that allows us to adaptively split the set of reaction channels into two subsets characterized by either a high or a low level of activity. Based on a time-splitting technique, the increments associated with high-activity channels are simulated using the tau-leap method, while those associated with low-activity channels are simulated using an exact method. This path simulation technique is amenable for coupled path generation and a corresponding multilevel Monte Carlo algorithm. To estimate expected values of observables of the system at a prescribed final time, our method bounds the global computational error to be below a prescribed tolerance, TOL, within a given confidence level. This goal is achieved with a computational complexity of order O(TOL-2), the same as with a pathwise-exact method, but with a smaller constant. We also present a novel low-cost control variate technique based on the stochastic time change representation by Kurtz, showing its performance on a numerical example. We present two numerical examples extracted from the literature that show how the reaction-splitting method obtains substantial gains with respect to the standard stochastic simulation algorithm and the multilevel Monte Carlo approach by Anderson and Higham. © 2016 Society for Industrial and Applied Mathematics.
A Multilevel Adaptive Reaction-splitting Simulation Method for Stochastic Reaction Networks
Moraes, Alvaro
2016-07-07
In this work, we present a novel multilevel Monte Carlo method for kinetic simulation of stochastic reaction networks characterized by having simultaneously fast and slow reaction channels. To produce efficient simulations, our method adaptively classifies the reactions channels into fast and slow channels. To this end, we first introduce a state-dependent quantity named level of activity of a reaction channel. Then, we propose a low-cost heuristic that allows us to adaptively split the set of reaction channels into two subsets characterized by either a high or a low level of activity. Based on a time-splitting technique, the increments associated with high-activity channels are simulated using the tau-leap method, while those associated with low-activity channels are simulated using an exact method. This path simulation technique is amenable for coupled path generation and a corresponding multilevel Monte Carlo algorithm. To estimate expected values of observables of the system at a prescribed final time, our method bounds the global computational error to be below a prescribed tolerance, TOL, within a given confidence level. This goal is achieved with a computational complexity of order O(TOL-2), the same as with a pathwise-exact method, but with a smaller constant. We also present a novel low-cost control variate technique based on the stochastic time change representation by Kurtz, showing its performance on a numerical example. We present two numerical examples extracted from the literature that show how the reaction-splitting method obtains substantial gains with respect to the standard stochastic simulation algorithm and the multilevel Monte Carlo approach by Anderson and Higham. © 2016 Society for Industrial and Applied Mathematics.
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.
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...
Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons
Guillermo Gallego; Garrett van Ryzin
1994-01-01
In many industries, managers face the problem of selling a given stock of items by a deadline. We investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm's objective is to maximize expected revenues. Examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry, which markets space such as seats on airline flights, cabins on vacation cruises, and rooms in hotels that ...
Zhang, Huifeng; Lei, Xiaohui; Wang, Chao; Yue, Dong; Xie, Xiangpeng
2017-01-01
Since wind power is integrated into the thermal power operation system, dynamic economic emission dispatch (DEED) has become a new challenge due to its uncertain characteristics. This paper proposes an adaptive grid based multi-objective Cauchy differential evolution (AGB-MOCDE) for solving stochastic DEED with wind power uncertainty. To properly deal with wind power uncertainty, some scenarios are generated to simulate those possible situations by dividing the uncertainty domain into different intervals, the probability of each interval can be calculated using the cumulative distribution function, and a stochastic DEED model can be formulated under different scenarios. For enhancing the optimization efficiency, Cauchy mutation operation is utilized to improve differential evolution by adjusting the population diversity during the population evolution process, and an adaptive grid is constructed for retaining diversity distribution of Pareto front. With consideration of large number of generated scenarios, the reduction mechanism is carried out to decrease the scenarios number with covariance relationships, which can greatly decrease the computational complexity. Moreover, the constraint-handling technique is also utilized to deal with the system load balance while considering transmission loss among thermal units and wind farms, all the constraint limits can be satisfied under the permitted accuracy. After the proposed method is simulated on three test systems, the obtained results reveal that in comparison with other alternatives, the proposed AGB-MOCDE can optimize the DEED problem while handling all constraint limits, and the optimal scheme of stochastic DEED can decrease the conservation of interval optimization, which can provide a more valuable optimal scheme for real-world applications.
Simulating local measurements on a quantum many-body system with stochastic matrix product states
DEFF Research Database (Denmark)
Gammelmark, Søren; Mølmer, Klaus
2010-01-01
We demonstrate how to simulate both discrete and continuous stochastic evolutions of a quantum many-body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a simple representation in terms of matrix product operators...... is found. The technique is exemplified by numerical simulations of the antiferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular, we focus on local measurements with small support and nonlocal measurements, which induce long-range correlations....
International Nuclear Information System (INIS)
Tahvili, Sahar; Österberg, Jonas; Silvestrov, Sergei; Biteus, Jonas
2014-01-01
One of the most important factors in the operations of many cooperations today is to maximize profit and one important tool to that effect is the optimization of maintenance activities. Maintenance activities is at the largest level divided into two major areas, corrective maintenance (CM) and preventive maintenance (PM). When optimizing maintenance activities, by a maintenance plan or policy, we seek to find the best activities to perform at each point in time, be it PM or CM. We explore the use of stochastic simulation, genetic algorithms and other tools for solving complex maintenance planning optimization problems in terms of a suggested framework model based on discrete event simulation
Efficient rejection-based simulation of biochemical reactions with stochastic noise and delays
Energy Technology Data Exchange (ETDEWEB)
Thanh, Vo Hong, E-mail: vo@cosbi.eu [The Microsoft Research - University of Trento Centre for Computational and Systems Biology, Piazza Manifattura 1, Rovereto 38068 (Italy); Priami, Corrado, E-mail: priami@cosbi.eu [The Microsoft Research - University of Trento Centre for Computational and Systems Biology, Piazza Manifattura 1, Rovereto 38068 (Italy); Department of Mathematics, University of Trento (Italy); Zunino, Roberto, E-mail: roberto.zunino@unitn.it [Department of Mathematics, University of Trento (Italy)
2014-10-07
We propose a new exact stochastic rejection-based simulation algorithm for biochemical reactions and extend it to systems with delays. Our algorithm accelerates the simulation by pre-computing reaction propensity bounds to select the next reaction to perform. Exploiting such bounds, we are able to avoid recomputing propensities every time a (delayed) reaction is initiated or finished, as is typically necessary in standard approaches. Propensity updates in our approach are still performed, but only infrequently and limited for a small number of reactions, saving computation time and without sacrificing exactness. We evaluate the performance improvement of our algorithm by experimenting with concrete biological models.
Energy Technology Data Exchange (ETDEWEB)
Tahvili, Sahar [Mälardalen University (Sweden); Österberg, Jonas; Silvestrov, Sergei [Division of Applied Mathematics, Mälardalen University (Sweden); Biteus, Jonas [Scania CV (Sweden)
2014-12-10
One of the most important factors in the operations of many cooperations today is to maximize profit and one important tool to that effect is the optimization of maintenance activities. Maintenance activities is at the largest level divided into two major areas, corrective maintenance (CM) and preventive maintenance (PM). When optimizing maintenance activities, by a maintenance plan or policy, we seek to find the best activities to perform at each point in time, be it PM or CM. We explore the use of stochastic simulation, genetic algorithms and other tools for solving complex maintenance planning optimization problems in terms of a suggested framework model based on discrete event simulation.
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...
Stochastic Calculus: Application to Dynamic Bifurcations and Threshold Crossings
Jansons, Kalvis M.; Lythe, G. D.
1998-01-01
For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function of the noise level ∈ and the rate of change of the parameter μ. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density, and last crossing time of zero are compared with results from numerical generation of paths.
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)
A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
International Nuclear Information System (INIS)
Atzberger, Paul J.; Kramer, Peter R.; Peskin, Charles S.
2007-01-01
In modeling many biological systems, it is important to take into account flexible structures which interact with a fluid. At the length scale of cells and cell organelles, thermal fluctuations of the aqueous environment become significant. In this work, it is shown how the immersed boundary method of [C.S. Peskin, The immersed boundary method, Acta Num. 11 (2002) 1-39.] for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps. An important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved, partially resolved, or fully resolved while retaining a good level of accuracy. Error estimates in each of these regimes are given for the method. A number of theoretical and numerical checks are furthermore performed to assess its physical fidelity. For a conservative force, the method is found to simulate particles with the correct Boltzmann equilibrium statistics. It is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters. The method is also shown to reproduce a well-known hydrodynamic effect of a Brownian particle in which the velocity autocorrelation function exhibits an algebraic (τ -3/2 ) decay for long times [B.J. Alder, T.E. Wainwright, Decay of the Velocity Autocorrelation Function, Phys. Rev. A 1(1) (1970) 18-21]. A few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method. Specifically, we present simulations of osmotic effects of molecular dimers, worm-like chain polymer knots, and a basic model of a molecular motor immersed in fluid subject to a
Directory of Open Access Journals (Sweden)
S. Sofana Reka
2016-09-01
Full Text Available This paper proposes a cloud computing framework in smart grid environment by creating small integrated energy hub supporting real time computing for handling huge storage of data. A stochastic programming approach model is developed with cloud computing scheme for effective demand side management (DSM in smart grid. Simulation results are obtained using GUI interface and Gurobi optimizer in Matlab in order to reduce the electricity demand by creating energy networks in a smart hub approach.
Stochastic evolutionary dynamics in minimum-effort coordination games
Li, Kun; Cong, Rui; Wang, Long
2016-08-01
The minimum-effort coordination game draws recently more attention for the fact that human behavior in this social dilemma is often inconsistent with the predictions of classical game theory. Here, we combine evolutionary game theory and coalescence theory to investigate this game in finite populations. Both analytic results and individual-based simulations show that effort costs play a key role in the evolution of contribution levels, which is in good agreement with those observed experimentally. Besides well-mixed populations, set structured populations have also been taken into consideration. Therein we find that large number of sets and moderate migration rate greatly promote effort levels, especially for high effort costs.
Monte Carlo simulation of induction time and metastable zone width; stochastic or deterministic?
Kubota, Noriaki
2018-03-01
The induction time and metastable zone width (MSZW) measured for small samples (say 1 mL or less) both scatter widely. Thus, these two are observed as stochastic quantities. Whereas, for large samples (say 1000 mL or more), the induction time and MSZW are observed as deterministic quantities. The reason for such experimental differences is investigated with Monte Carlo simulation. In the simulation, the time (under isothermal condition) and supercooling (under polythermal condition) at which a first single crystal is detected are defined as the induction time t and the MSZW ΔT for small samples, respectively. The number of crystals just at the moment of t and ΔT is unity. A first crystal emerges at random due to the intrinsic nature of nucleation, accordingly t and ΔT become stochastic. For large samples, the time and supercooling at which the number density of crystals N/V reaches a detector sensitivity (N/V)det are defined as t and ΔT for isothermal and polythermal conditions, respectively. The points of t and ΔT are those of which a large number of crystals have accumulated. Consequently, t and ΔT become deterministic according to the law of large numbers. Whether t and ΔT may stochastic or deterministic in actual experiments should not be attributed to change in nucleation mechanisms in molecular level. It could be just a problem caused by differences in the experimental definition of t and ΔT.
Energy Technology Data Exchange (ETDEWEB)
Sun, Kaiyu; Yan, Da; Hong, Tianzhen; Guo, Siyue
2014-02-28
Overtime is a common phenomenon around the world. Overtime drives both internal heat gains from occupants, lighting and plug-loads, and HVAC operation during overtime periods. Overtime leads to longer occupancy hours and extended operation of building services systems beyond normal working hours, thus overtime impacts total building energy use. Current literature lacks methods to model overtime occupancy because overtime is stochastic in nature and varies by individual occupants and by time. To address this gap in the literature, this study aims to develop a new stochastic model based on the statistical analysis of measured overtime occupancy data from an office building. A binomial distribution is used to represent the total number of occupants working overtime, while an exponential distribution is used to represent the duration of overtime periods. The overtime model is used to generate overtime occupancy schedules as an input to the energy model of a second office building. The measured and simulated cooling energy use during the overtime period is compared in order to validate the overtime model. A hybrid approach to energy model calibration is proposed and tested, which combines ASHRAE Guideline 14 for the calibration of the energy model during normal working hours, and a proposed KS test for the calibration of the energy model during overtime. The developed stochastic overtime model and the hybrid calibration approach can be used in building energy simulations to improve the accuracy of results, and better understand the characteristics of overtime in office buildings.
Lin, Yen Ting; Chylek, Lily A; Lemons, Nathan W; Hlavacek, William S
2018-06-21
The chemical kinetics of many complex systems can be concisely represented by reaction rules, which can be used to generate reaction events via a kinetic Monte Carlo method that has been termed network-free simulation. Here, we demonstrate accelerated network-free simulation through a novel approach to equation-free computation. In this process, variables are introduced that approximately capture system state. Derivatives of these variables are estimated using short bursts of exact stochastic simulation and finite differencing. The variables are then projected forward in time via a numerical integration scheme, after which a new exact stochastic simulation is initialized and the whole process repeats. The projection step increases efficiency by bypassing the firing of numerous individual reaction events. As we show, the projected variables may be defined as populations of building blocks of chemical species. The maximal number of connected molecules included in these building blocks determines the degree of approximation. Equation-free acceleration of network-free simulation is found to be both accurate and efficient.
Hussain, Faraz; Jha, Sumit K; Jha, Susmit; Langmead, Christopher J
2014-01-01
Stochastic models are increasingly used to study the behaviour of biochemical systems. While the structure of such models is often readily available from first principles, unknown quantitative features of the model are incorporated into the model as parameters. Algorithmic discovery of parameter values from experimentally observed facts remains a challenge for the computational systems biology community. We present a new parameter discovery algorithm that uses simulated annealing, sequential hypothesis testing, and statistical model checking to learn the parameters in a stochastic model. We apply our technique to a model of glucose and insulin metabolism used for in-silico validation of artificial pancreata and demonstrate its effectiveness by developing parallel CUDA-based implementation for parameter synthesis in this model.
Kucza, Witold
2013-07-25
Stochastic and deterministic simulations of dispersion in cylindrical channels on the Poiseuille flow have been presented. The random walk (stochastic) and the uniform dispersion (deterministic) models have been used for computations of flow injection analysis responses. These methods coupled with the genetic algorithm and the Levenberg-Marquardt optimization methods, respectively, have been applied for determination of diffusion coefficients. The diffusion coefficients of fluorescein sodium, potassium hexacyanoferrate and potassium dichromate have been determined by means of the presented methods and FIA responses that are available in literature. The best-fit results agree with each other and with experimental data thus validating both presented approaches. Copyright © 2013 The Author. Published by Elsevier B.V. All rights reserved.
Analysis of dynamic characteristics of stochastic influences in cognitive systems
Directory of Open Access Journals (Sweden)
Alexander A. Solodov
2017-01-01
Full Text Available The aim of the study is to provide an analytical description of the dynamics of the processes to form images in the cognitive system and their subsequent processing by the consciousness, as well as the study of the simplest characteristics of the quality of the cognitive system functioning in the form of the signal/noise ratio.In accordance with the ideas of the cognitive theory, it is believed that images (schemes, categories, Gestalt, systems, archetypes, etc. are firstly generated in the human brain and then processed by the consciousness.These images are formed at random in time and are characterized by a random force of effects and subsequently processed by the consciousness.The images are characterized by random numbers, the common interpretation of which is the amount of information corresponding to the appearance of a certain image. The times of appearance are points on the time axis; their number and position are random as well.The work consists of a logically completed model including the following components:• Justification of a statistical model of the appearance of effects during the operation of the cognitive system in the form of the Poisson point process, characterized by the intensity of occurrence of effects and the random values of those effects.• Development of a mathematical model in the consciousness processing of the random effects in the form of reducing response function, which depends on the current time, the time of occurrence of effects and the magnitudes of these effects. To obtain applied results, exponential response function was applied and the analytical results for the mathematical expectations of the processed and not processed information by the consciousness were received.• Introduction for consideration of the signal/noise ratio, characterizing the performance of cognitive systems in the presence of interference and study of its behavior in the situations with the presence of random background noise
A eural etwork Model for Dynamics Simulation
African Journals Online (AJOL)
Nafiisah
Results 5 - 18 ... situations, such as a dynamic environment (e.g., a molecular dynamics (MD) simulation whereby an atom constantly changes its local environment and number ..... of systems including both small clusters and bulk structures. 7.
A stochastic approach for the description of the water balance dynamics in a river basin
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S. Manfreda
2008-09-01
Full Text Available The present paper introduces an analytical approach for the description of the soil water balance dynamics over a schematic river basin. The model is based on a stochastic differential equation where the rainfall forcing is interpreted as an additive noise in the soil water balance. This equation can be solved assuming known the spatial distribution of the soil moisture over the basin transforming the two-dimensional problem in space in a one dimensional one. This assumption is particularly true in the case of humid and semihumid environments, where spatial redistribution becomes dominant producing a well defined soil moisture pattern. The model allowed to derive the probability density function of the saturated portion of a basin and of its relative saturation. This theory is based on the assumption that the soil water storage capacity varies across the basin following a parabolic distribution and the basin has homogeneous soil texture and vegetation cover. The methodology outlined the role played by the soil water storage capacity distribution of the basin on soil water balance. In particular, the resulting probability density functions of the relative basin saturation were found to be strongly controlled by the maximum water storage capacity of the basin, while the probability density functions of the relative saturated portion of the basin are strongly influenced by the spatial heterogeneity of the soil water storage capacity. Moreover, the saturated areas reach their maximum variability when the mean rainfall rate is almost equal to the soil water loss coefficient given by the sum of the maximum rate of evapotranspiration and leakage loss in the soil water balance. The model was tested using the results of a continuous numerical simulation performed with a semi-distributed model in order to validate the proposed theoretical distributions.
Synthetic chloride-selective carbon nanotubes examined by using molecular and stochastic dynamics.
Hilder, Tamsyn A; Gordon, Dan; Chung, Shin-Ho
2010-09-22
Synthetic channels, such as nanotubes, offer the possibility of ion-selective nanoscale pores which can broadly mimic the functions of various biological ion channels, and may one day be used as antimicrobial agents, or for treatment of cystic fibrosis. We have designed a carbon nanotube that is selectively permeable to anions. The virtual nanotubes are constructed from a hexagonal array of carbon atoms (graphene) rolled up to form a tubular structure, with an effective radius of 4.53 Å and length of 34 Å. The pore ends are terminated with polar carbonyl groups. The nanotube thus formed is embedded in a lipid bilayer and a reservoir containing ionic solutions is added at each end of the pore. The conductance properties of these synthetic channels are then examined with molecular and stochastic dynamics simulations. Profiles of the potential of mean force at 0 mM reveal that a cation moving across the pore encounters an insurmountable free energy barrier of ∼25 kT in height. In contrast, for anions, there are two energy wells of ∼12 kT near each end of the tube, separated by a central free energy barrier of 4 kT. The conductance of the pore, with symmetrical 500 mM solutions in the reservoirs, is 72 pS at 100 mV. The current saturates with an increasing ionic concentration, obeying a Michaelis-Menten relationship. The pore is normally occupied by two ions, and the rate-limiting step in conduction is the time taken for the resident ion near the exit gate to move out of the energy well. Copyright © 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Seasonal Synchronization of a Simple Stochastic Dynamical Model Capturing El Niño Diversity
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.
Drawert, Brian; Engblom, Stefan; Hellander, Andreas
2012-06-22
Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at
A stochastic model of epigenetic dynamics in somatic cell reprogramming
Directory of Open Access Journals (Sweden)
Max eFloettmann
2012-06-01
Full Text Available Somatic cell reprogramming has dramatically changed stem cell research inrecent years. The high pace of new findings in the field and an ever increasingamount of data from new high throughput techniques make it challengingto isolate core principles of the process. In order to analyze suchmechanisms, we developed an abstract mechanistic model of a subset of theknown regulatory processes during cell differentiation and production of inducedpluripotent stem cells. This probabilistic Boolean network describesthe interplay between gene expression, chromatin modifications and DNAmethylation. The model incorporates recent findings in epigenetics and reproducesexperimentally observed reprogramming efficiencies and changes inmethylation and chromatin remodeling. It enables us to investigate in detail,how the temporal progression of the process is regulated. It also explicitlyincludes the transduction of factors using viral vectors and their silencing inreprogrammed cells, since this is still a standard procedure in somatic cellreprogramming. Based on the model we calculate an epigenetic landscape.Simulation results show good reproduction of experimental observations duringreprogramming, despite the simple stucture of the model. An extensiveanalysis and introduced variations hint towards possible optimizations of theprocess, that could push the technique closer to clinical applications. Fasterchanges in DNA methylation increase the speed of reprogramming at theexpense of efficiency, while accelerated chromatin modifications moderatelyimprove efficiency.
The two-regime method for optimizing stochastic reaction-diffusion simulations
Flegg, M. B.
2011-10-19
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less detailed compartment-based simulations. Compartment-based approaches yield quick and accurate mesoscopic results, but lack the level of detail that is characteristic of the computationally intensive molecular-based models. Often microscopic detail is only required in a small region (e.g. close to the cell membrane). Currently, the best way to achieve microscopic detail is to use a resource-intensive simulation over the whole domain. We develop the two-regime method (TRM) in which a molecular-based algorithm is used where desired and a compartment-based approach is used elsewhere. We present easy-to-implement coupling conditions which ensure that the TRM results have the same accuracy as a detailed molecular-based model in the whole simulation domain. Therefore, the TRM combines strengths of previously developed stochastic reaction-diffusion software to efficiently explore the behaviour of biological models. Illustrative examples and the mathematical justification of the TRM are also presented.
International Nuclear Information System (INIS)
Ren Xiaoan; Wu Wenquan; Xanthis, Leonidas S.
2011-01-01
Highlights: → New approach for stochastic computations based on polynomial chaos. → Development of dynamically adaptive wavelet multiscale solver using space refinement. → Accurate capture of steep gradients and multiscale features in stochastic problems. → All scales of each random mode are captured on independent grids. → Numerical examples demonstrate the need for different space resolutions per mode. - Abstract: In stochastic computations, or uncertainty quantification methods, the spectral approach based on the polynomial chaos expansion in random space leads to a coupled system of deterministic equations for the coefficients of the expansion. The size of this system increases drastically when the number of independent random variables and/or order of polynomial chaos expansions increases. This is invariably the case for large scale simulations and/or problems involving steep gradients and other multiscale features; such features are variously reflected on each solution component or random/uncertainty mode requiring the development of adaptive methods for their accurate resolution. In this paper we propose a new approach for treating such problems based on a dynamically adaptive wavelet methodology involving space-refinement on physical space that allows all scales of each solution component to be refined independently of the rest. We exemplify this using the convection-diffusion model with random input data and present three numerical examples demonstrating the salient features of the proposed method. Thus we establish a new, elegant and flexible approach for stochastic problems with steep gradients and multiscale features based on polynomial chaos expansions.
Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?
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.