Discrete-time Markovian stochastic Petri nets

NASA Technical Reports Server (NTRS)

Ciardo, Gianfranco

1995-01-01

We revisit and extend the original definition of discrete-time stochastic Petri nets, by allowing the firing times to have a 'defective discrete phase distribution'. We show that this formalism still corresponds to an underlying discrete-time Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for each transition, resulting in a large state space. We then modify the well-known power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation.

A Stochastic Diffusion Process for the Dirichlet Distribution

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2013-03-01

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability ofNcoupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded sample space, a coupled nonlinear diffusion process is required: the Wiener processes in the equivalent system of stochastic differential equations are multiplicative with coefficients dependent on all the stochastic variables. Individual samples of a discrete ensemble, obtained from the stochastic process, satisfy a unit-sum constraint at all times. The process may be used to represent realizations of a fluctuating ensemble ofNvariables subject to a conservation principle.more » Similar to the multivariate Wright-Fisher process, whose invariant is also Dirichlet, the univariate case yields a process whose invariant is the beta distribution. As a test of the results, Monte Carlo simulations are used to evolve numerical ensembles toward the invariant Dirichlet distribution.« less

Discrete stochastic analogs of Erlang epidemic models.

PubMed

Getz, Wayne M; Dougherty, Eric R

2018-12-01

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

An advanced environment for hybrid modeling of biological systems based on modelica.

PubMed

Pross, Sabrina; Bachmann, Bernhard

2011-01-20

Biological systems are often very complex so that an appropriate formalism is needed for modeling their behavior. Hybrid Petri Nets, consisting of time-discrete Petri Net elements as well as continuous ones, have proven to be ideal for this task. Therefore, a new Petri Net library was implemented based on the object-oriented modeling language Modelica which allows the modeling of discrete, stochastic and continuous Petri Net elements by differential, algebraic and discrete equations. An appropriate Modelica-tool performs the hybrid simulation with discrete events and the solution of continuous differential equations. A special sub-library contains so-called wrappers for specific reactions to simplify the modeling process. The Modelica-models can be connected to Simulink-models for parameter optimization, sensitivity analysis and stochastic simulation in Matlab. The present paper illustrates the implementation of the Petri Net component models, their usage within the modeling process and the coupling between the Modelica-tool Dymola and Matlab/Simulink. The application is demonstrated by modeling the metabolism of Chinese Hamster Ovary Cells.

Hybrid stochastic simplifications for multiscale gene networks.

PubMed

Crudu, Alina; Debussche, Arnaud; Radulescu, Ovidiu

2009-09-07

Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion [1-3] which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples. Hybrid simplifications can be used for onion-like (multi-layered) approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach.

Population density approach for discrete mRNA distributions in generalized switching models for stochastic gene expression.

PubMed

Stinchcombe, Adam R; Peskin, Charles S; Tranchina, Daniel

2012-06-01

We present a generalization of a population density approach for modeling and analysis of stochastic gene expression. In the model, the gene of interest fluctuates stochastically between an inactive state, in which transcription cannot occur, and an active state, in which discrete transcription events occur; and the individual mRNA molecules are degraded stochastically in an independent manner. This sort of model in simplest form with exponential dwell times has been used to explain experimental estimates of the discrete distribution of random mRNA copy number. In our generalization, the random dwell times in the inactive and active states, T_{0} and T_{1}, respectively, are independent random variables drawn from any specified distributions. Consequently, the probability per unit time of switching out of a state depends on the time since entering that state. Our method exploits a connection between the fully discrete random process and a related continuous process. We present numerical methods for computing steady-state mRNA distributions and an analytical derivation of the mRNA autocovariance function. We find that empirical estimates of the steady-state mRNA probability mass function from Monte Carlo simulations of laboratory data do not allow one to distinguish between underlying models with exponential and nonexponential dwell times in some relevant parameter regimes. However, in these parameter regimes and where the autocovariance function has negative lobes, the autocovariance function disambiguates the two types of models. Our results strongly suggest that temporal data beyond the autocovariance function is required in general to characterize gene switching.

Stochastic Evolution Equations Driven by Fractional Noises

DTIC Science & Technology

2016-11-28

rate of convergence to zero or the error and the limit in distribution of the error fluctuations. We have studied time discrete numerical schemes...error fluctuations. We have studied time discrete numerical schemes based on Taylor expansions for rough differential equations and for stochastic...variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian

Path integrals and large deviations in stochastic hybrid systems.

PubMed

Bressloff, Paul C; Newby, Jay M

2014-04-01

We construct a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics. The differential equations for the continuous variables are coupled to a set of discrete variables that satisfy a continuous-time Markov process, which means that the differential equations are only valid between jumps in the discrete variables. Examples of stochastic hybrid systems arise in biophysical models of stochastic ion channels, motor-driven intracellular transport, gene networks, and stochastic neural networks. We use the path-integral representation to derive a large deviation action principle for a stochastic hybrid system. Minimizing the associated action functional with respect to the set of all trajectories emanating from a metastable state (assuming that such a minimization scheme exists) then determines the most probable paths of escape. Moreover, evaluating the action functional along a most probable path generates the so-called quasipotential used in the calculation of mean first passage times. We illustrate the theory by considering the optimal paths of escape from a metastable state in a bistable neural network.

Fluctuations and Noise in Stochastic Spread of Respiratory Infection Epidemics in Social Networks

NASA Astrophysics Data System (ADS)

Yulmetyev, Renat; Emelyanova, Natalya; Demin, Sergey; Gafarov, Fail; Hänggi, Peter; Yulmetyeva, Dinara

2003-05-01

For the analysis of epidemic and disease dynamics complexity, it is necessary to understand the basic principles and notions of its spreading in long-time memory media. Here we considering the problem from a theoretical and practical viewpoint, presenting the quantitative evidence confirming the existence of stochastic long-range memory and robust chaos in a real time series of respiratory infections of human upper respiratory track. In this work we present a new statistical method of analyzing the spread of grippe and acute respiratory track infections epidemic process of human upper respiratory track by means of the theory of discrete non-Markov stochastic processes. We use the results of our recent theory (Phys. Rev. E 65, 046107 (2002)) for the study of statistical effects of memory in real data series, describing the epidemic dynamics of human acute respiratory track infections and grippe. The obtained results testify to an opportunity of the strict quantitative description of the regular and stochastic components in epidemic dynamics of social networks with a view to time discreteness and effects of statistical memory.

Stochastic switching in biology: from genotype to phenotype

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.

2017-03-01

There has been a resurgence of interest in non-equilibrium stochastic processes in recent years, driven in part by the observation that the number of molecules (genes, mRNA, proteins) involved in gene expression are often of order 1-1000. This means that deterministic mass-action kinetics tends to break down, and one needs to take into account the discrete, stochastic nature of biochemical reactions. One of the major consequences of molecular noise is the occurrence of stochastic biological switching at both the genotypic and phenotypic levels. For example, individual gene regulatory networks can switch between graded and binary responses, exhibit translational/transcriptional bursting, and support metastability (noise-induced switching between states that are stable in the deterministic limit). If random switching persists at the phenotypic level then this can confer certain advantages to cell populations growing in a changing environment, as exemplified by bacterial persistence in response to antibiotics. Gene expression at the single-cell level can also be regulated by changes in cell density at the population level, a process known as quorum sensing. In contrast to noise-driven phenotypic switching, the switching mechanism in quorum sensing is stimulus-driven and thus noise tends to have a detrimental effect. A common approach to modeling stochastic gene expression is to assume a large but finite system and to approximate the discrete processes by continuous processes using a system-size expansion. However, there is a growing need to have some familiarity with the theory of stochastic processes that goes beyond the standard topics of chemical master equations, the system-size expansion, Langevin equations and the Fokker-Planck equation. Examples include stochastic hybrid systems (piecewise deterministic Markov processes), large deviations and the Wentzel-Kramers-Brillouin (WKB) method, adiabatic reductions, and queuing/renewal theory. The major aim of this review is to provide a self-contained survey of these mathematical methods, mainly within the context of biological switching processes at both the genotypic and phenotypic levels. However, applications to other examples of biological switching are also discussed, including stochastic ion channels, diffusion in randomly switching environments, bacterial chemotaxis, and stochastic neural networks.

Stochastic Adaptive Estimation and Control.

DTIC Science & Technology

1994-10-26

Marcus, "Language Stability and Stabilizability of Discrete Event Dynamical Systems ," SIAM Journal on Control and Optimization, 31, September 1993...in the hierarchical control of flexible manufacturing systems ; in this problem, the model involves a hybrid process in continuous time whose state is...of the average cost control problem for discrete- time Markov processes. Our exposition covers from finite to Borel state and action spaces and

Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

PubMed

Allen, Edward J

2014-06-01

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

Discrete, continuous, and stochastic models of protein sorting in the Golgi apparatus

PubMed Central

Gong, Haijun; Guo, Yusong; Linstedt, Adam

2017-01-01

The Golgi apparatus plays a central role in processing and sorting proteins and lipids in eukaryotic cells. Golgi compartments constantly exchange material with each other and with other cellular components, allowing them to maintain and reform distinct identities despite dramatic changes in structure and size during cell division, development, and osmotic stress. We have developed three minimal models of membrane and protein exchange in the Golgi—a discrete, stochastic model, a continuous ordinary differential equation model, and a continuous stochastic differential equation model—each based on two fundamental mechanisms: vesicle-coat-mediated selective concentration of cargoes and soluble N-ethylmaleimide-sensitive factor attachment protein receptor SNARE proteins during vesicle formation and SNARE-mediated selective fusion of vesicles. By exploring where the models differ, we hope to discover whether the discrete, stochastic nature of vesicle-mediated transport is likely to have appreciable functional consequences for the Golgi. All three models show similar ability to restore and maintain distinct identities over broad parameter ranges. They diverge, however, in conditions corresponding to collapse and reassembly of the Golgi. The results suggest that a continuum model provides a good description of Golgi maintenance but that considering the discrete nature of vesicle-based traffic is important to understanding assembly and disassembly of the Golgi. Experimental analysis validates a prediction of the models that altering guanine nucleotide exchange factor expression levels will modulate Golgi size. PMID:20365406

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

NASA Astrophysics Data System (ADS)

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.

Hybrid stochastic simplifications for multiscale gene networks

PubMed Central

Crudu, Alina; Debussche, Arnaud; Radulescu, Ovidiu

2009-01-01

Background Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. Results We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion [1-3] which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples. Conclusion Hybrid simplifications can be used for onion-like (multi-layered) approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach. PMID:19735554

About the discrete-continuous nature of a hematopoiesis model for Chronic Myeloid Leukemia.

PubMed

Gaudiano, Marcos E; Lenaerts, Tom; Pacheco, Jorge M

2016-12-01

Blood of mammals is composed of a variety of cells suspended in a fluid medium known as plasma. Hematopoiesis is the biological process of birth, replication and differentiation of blood cells. Despite of being essentially a stochastic phenomenon followed by a huge number of discrete entities, blood formation has naturally an associated continuous dynamics, because the cellular populations can - on average - easily be described by (e.g.) differential equations. This deterministic dynamics by no means contemplates some important stochastic aspects related to abnormal hematopoiesis, that are especially significant for studying certain blood cancer deceases. For instance, by mere stochastic competition against the normal cells, leukemic cells sometimes do not reach the population thereshold needed to kill the organism. Of course, a pure discrete model able to follow the stochastic paths of billons of cells is computationally impossible. In order to avoid this difficulty, we seek a trade-off between the computationally feasible and the biologically realistic, deriving an equation able to size conveniently both the discrete and continuous parts of a model for hematopoiesis in terrestrial mammals, in the context of Chronic Myeloid Leukemia. Assuming the cancer is originated from a single stem cell inside of the bone marrow, we also deduce a theoretical formula for the probability of non-diagnosis as a function of the mammal average adult mass. In addition, this work cellular dynamics analysis may shed light on understanding Peto's paradox, which is shown here as an emergent property of the discrete-continuous nature of the system. Copyright © 2016 Elsevier Inc. All rights reserved.

Practical Unitary Simulator for Non-Markovian Complex Processes

NASA Astrophysics Data System (ADS)

Binder, Felix C.; Thompson, Jayne; Gu, Mile

2018-06-01

Stochastic processes are as ubiquitous throughout the quantitative sciences as they are notorious for being difficult to simulate and predict. In this Letter, we propose a unitary quantum simulator for discrete-time stochastic processes which requires less internal memory than any classical analogue throughout the simulation. The simulator's internal memory requirements equal those of the best previous quantum models. However, in contrast to previous models, it only requires a (small) finite-dimensional Hilbert space. Moreover, since the simulator operates unitarily throughout, it avoids any unnecessary information loss. We provide a stepwise construction for simulators for a large class of stochastic processes hence directly opening the possibility for experimental implementations with current platforms for quantum computation. The results are illustrated for an example process.

Optimal generalized multistep integration formulae for real-time digital simulation

NASA Technical Reports Server (NTRS)

Moerder, D. D.; Halyo, N.

1985-01-01

The problem of discretizing a dynamical system for real-time digital simulation is considered. Treating the system and its simulation as stochastic processes leads to a statistical characterization of simulator fidelity. A plant discretization procedure based on an efficient matrix generalization of explicit linear multistep discrete integration formulae is introduced, which minimizes a weighted sum of the mean squared steady-state and transient error between the system and simulator outputs.

ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology.

PubMed

Bittig, Arne T; Uhrmacher, Adelinde M

2017-01-01

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

Stochastic dynamics of extended objects in driven systems II: Current quantization in the low-temperature limit

NASA Astrophysics Data System (ADS)

Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R.

2016-12-01

Driven Langevin processes have appeared in a variety of fields due to the relevance of natural phenomena having both deterministic and stochastic effects. The stochastic currents and fluxes in these systems provide a convenient set of observables to describe their non-equilibrium steady states. Here we consider stochastic motion of a (k - 1) -dimensional object, which sweeps out a k-dimensional trajectory, and gives rise to a higher k-dimensional current. By employing the low-temperature (low-noise) limit, we reduce the problem to a discrete Markov chain model on a CW complex, a topological construction which generalizes the notion of a graph. This reduction allows the mean fluxes and currents of the process to be expressed in terms of solutions to the discrete Supersymmetric Fokker-Planck (SFP) equation. Taking the adiabatic limit, we show that generic driving leads to rational quantization of the generated higher dimensional current. The latter is achieved by implementing the recently developed tools, coined the higher-dimensional Kirchhoff tree and co-tree theorems. This extends the study of motion of extended objects in the continuous setting performed in the prequel (Catanzaro et al.) to this manuscript.

Method of conditional moments (MCM) for the Chemical Master Equation: a unified framework for the method of moments and hybrid stochastic-deterministic models.

PubMed

Hasenauer, J; Wolf, V; Kazeroonian, A; Theis, F J

2014-09-01

The time-evolution of continuous-time discrete-state biochemical processes is governed by the Chemical Master Equation (CME), which describes the probability of the molecular counts of each chemical species. As the corresponding number of discrete states is, for most processes, large, a direct numerical simulation of the CME is in general infeasible. In this paper we introduce the method of conditional moments (MCM), a novel approximation method for the solution of the CME. The MCM employs a discrete stochastic description for low-copy number species and a moment-based description for medium/high-copy number species. The moments of the medium/high-copy number species are conditioned on the state of the low abundance species, which allows us to capture complex correlation structures arising, e.g., for multi-attractor and oscillatory systems. We prove that the MCM provides a generalization of previous approximations of the CME based on hybrid modeling and moment-based methods. Furthermore, it improves upon these existing methods, as we illustrate using a model for the dynamics of stochastic single-gene expression. This application example shows that due to the more general structure, the MCM allows for the approximation of multi-modal distributions.

A computational framework for prime implicants identification in noncoherent dynamic systems.

PubMed

Di Maio, Francesco; Baronchelli, Samuele; Zio, Enrico

2015-01-01

Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., event trees [ETs] and fault trees [FTs]) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time-dependent model that includes the dependencies with the stochastic transition events. In this article, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the prime implicants (PIs) of the dynamic system. The framework entails adopting a multiple-valued logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a differential evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic noncoherent system composed of five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases. © 2014 Society for Risk Analysis.

Simulated maximum likelihood method for estimating kinetic rates in gene expression.

PubMed

Tian, Tianhai; Xu, Songlin; Gao, Junbin; Burrage, Kevin

2007-01-01

Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment. In this paper, we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of non-parametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimization algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy.

Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches.

PubMed

Li, Michael; Dushoff, Jonathan; Bolker, Benjamin M

2018-07-01

Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known, to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Chuchu, E-mail: chenchuchu@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Zhang, Liying, E-mail: lyzhang@lsec.cc.ac.cn

Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the correspondingmore » discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.« less

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

PubMed

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries

NASA Astrophysics Data System (ADS)

Shafiey, Hassan; Gan, Xinjun; Waxman, David

2017-11-01

To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

Towards Stability Analysis of Jump Linear Systems with State-Dependent and Stochastic Switching

NASA Technical Reports Server (NTRS)

Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven

2004-01-01

This paper analyzes the stability of hierarchical jump linear systems where the supervisor is driven by a Markovian stochastic process and by the values of the supervised jump linear system s states. The stability framework for this class of systems is developed over infinite and finite time horizons. The framework is then used to derive sufficient stability conditions for a specific class of hybrid jump linear systems with performance supervision. New sufficient stochastic stability conditions for discrete-time jump linear systems are also presented.

Analytical pricing formulas for hybrid variance swaps with regime-switching

NASA Astrophysics Data System (ADS)

Roslan, Teh Raihana Nazirah; Cao, Jiling; Zhang, Wenjun

2017-11-01

The problem of pricing discretely-sampled variance swaps under stochastic volatility, stochastic interest rate and regime-switching is being considered in this paper. An extension of the Heston stochastic volatility model structure is done by adding the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. In addition, the parameters of the model are permitted to have transitions following a Markov chain process which is continuous and discoverable. This hybrid model can be used to illustrate certain macroeconomic conditions, for example the changing phases of business stages. The outcome of our regime-switching hybrid model is presented in terms of analytical pricing formulas for variance swaps.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres).

PubMed

Di Costanzo, Ezio; Giacomello, Alessandro; Messina, Elisa; Natalini, Roberto; Pontrelli, Giuseppe; Rossi, Fabrizio; Smits, Robert; Twarogowska, Monika

2018-03-14

We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.

Dynamic Noise and its Role in Understanding Epidemiological Processes

NASA Astrophysics Data System (ADS)

Stollenwerk, Nico; Aguiar, Maíra

2010-09-01

We investigate the role of dynamic noise in understanding epidemiological systems, such as influenza or dengue fever by deriving stochastic ordinary differential equations from markov processes for discrete populations. This approach allows for an easy analysis of dynamical noise transitions between co-existing attractors.

A stochastic diffusion process for Lochner's generalized Dirichlet distribution

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2013-10-01

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner’s generalized Dirichlet distribution as its asymptotic solution. Individual samples of a discrete ensemble, obtained from the system of stochastic differential equations, equivalent to the Fokker-Planck equation developed here, satisfy a unit-sum constraint at all times and ensure a bounded sample space, similarly to the process developed in for the Dirichlet distribution. Consequently, the generalized Dirichlet diffusion process may be used to represent realizations of a fluctuating ensemble of N variables subject to a conservation principle.more » Compared to the Dirichlet distribution and process, the additional parameters of the generalized Dirichlet distribution allow a more general class of physical processes to be modeled with a more general covariance matrix.« less

Stochastic model for fatigue crack size and cost effective design decisions. [for aerospace structures

NASA Technical Reports Server (NTRS)

Hanagud, S.; Uppaluri, B.

1975-01-01

This paper describes a methodology for making cost effective fatigue design decisions. The methodology is based on a probabilistic model for the stochastic process of fatigue crack growth with time. The development of a particular model for the stochastic process is also discussed in the paper. The model is based on the assumption of continuous time and discrete space of crack lengths. Statistical decision theory and the developed probabilistic model are used to develop the procedure for making fatigue design decisions on the basis of minimum expected cost or risk function and reliability bounds. Selections of initial flaw size distribution, NDT, repair threshold crack lengths, and inspection intervals are discussed.

Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009).

PubMed

Nishiura, Hiroshi

2011-02-16

Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.

Elegant anti-disturbance control for discrete-time stochastic systems with nonlinearity and multiple disturbances

NASA Astrophysics Data System (ADS)

Wei, Xinjiang; Sun, Shixiang

2018-03-01

An elegant anti-disturbance control (EADC) strategy for a class of discrete-time stochastic systems with both nonlinearity and multiple disturbances, which include the disturbance with partially known information and a sequence of random vectors, is proposed in this paper. A stochastic disturbance observer is constructed to estimate the disturbance with partially known information, based on which, an EADC scheme is proposed by combining pole placement and linear matrix inequality methods. It is proved that the two different disturbances can be rejected and attenuated, and the corresponding desired performances can be guaranteed for discrete-time stochastic systems with known and unknown nonlinear dynamics, respectively. Simulation examples are given to demonstrate the effectiveness of the proposed schemes compared with some existing results.

Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

PubMed

Wang, Jun-Sheng; Yang, Guang-Hong

2017-07-25

This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

Enhancement of the Logistics Battle Command Model: Architecture Upgrades and Attrition Module Development

DTIC Science & Technology

2017-01-05

module. 15. SUBJECT TERMS Logistics, attrition, discrete event simulation, Simkit, LBC 16. SECURITY CLASSIFICATION OF: Unclassified 17. LIMITATION...stochastics, and discrete event model programmed in Java building largely on the Simkit library. The primary purpose of the LBC model is to support...equations makes them incompatible with the discrete event construct of LBC. Bullard further advances this methodology by developing a stochastic

Stochastic resetting in backtrack recovery by RNA polymerases

NASA Astrophysics Data System (ADS)

Roldán, Édgar; Lisica, Ana; Sánchez-Taltavull, Daniel; Grill, Stephan W.

2016-06-01

Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally inactive backtracked state is determined by a kinetic competition between one-dimensional diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-passage time of a random walker to reach an absorbing state. We represent RNA cleavage as a stochastic resetting process and derive exact expressions for the recovery time distributions and mean recovery times from a given initial backtrack depth for both continuous and discrete-lattice descriptions of the random walk. We show that recovery time statistics do not depend on the discreteness of the DNA lattice when the rate of one-dimensional diffusion is large compared to the rate of cleavage.

Models for discrete-time self-similar vector processes with application to network traffic

NASA Astrophysics Data System (ADS)

Lee, Seungsin; Rao, Raghuveer M.; Narasimha, Rajesh

2003-07-01

The paper defines self-similarity for vector processes by employing the discrete-time continuous-dilation operation which has successfully been used previously by the authors to define 1-D discrete-time stochastic self-similar processes. To define self-similarity of vector processes, it is required to consider the cross-correlation functions between different 1-D processes as well as the autocorrelation function of each constituent 1-D process in it. System models to synthesize self-similar vector processes are constructed based on the definition. With these systems, it is possible to generate self-similar vector processes from white noise inputs. An important aspect of the proposed models is that they can be used to synthesize various types of self-similar vector processes by choosing proper parameters. Additionally, the paper presents evidence of vector self-similarity in two-channel wireless LAN data and applies the aforementioned systems to simulate the corresponding network traffic traces.

Waiting time distribution for continuous stochastic systems

NASA Astrophysics Data System (ADS)

Gernert, Robert; Emary, Clive; Klapp, Sabine H. L.

2014-12-01

The waiting time distribution (WTD) is a common tool for analyzing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers. In the present paper we propose a consistent generalization of the WTD from the discrete case to situations where the particles perform continuous barrier crossing characterized by a finite duration. To this end, we introduce a recipe to calculate the WTD from the Fokker-Planck (Smoluchowski) equation. In contrast to the closely related first passage time distribution (FPTD), which is frequently used to describe continuous processes, the WTD contains information about the direction of motion. As an application, we consider the paradigmatic example of an overdamped particle diffusing through a washboard potential. To verify the approach and to elucidate its numerical implications, we compare the WTD defined via the Smoluchowski equation with data from direct simulation of the underlying Langevin equation and find full consistency provided that the jumps in the Langevin approach are defined properly. Moreover, for sufficiently large energy barriers, the WTD defined via the Smoluchowski equation becomes consistent with that resulting from the analytical solution of a (two-state) master equation model for the short-time dynamics developed previously by us [Phys. Rev. E 86, 061135 (2012), 10.1103/PhysRevE.86.061135]. Thus, our approach "interpolates" between these two types of stochastic motion. We illustrate our approach for both symmetric systems and systems under constant force.

An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping.

PubMed

Koh, Wonryull; Blackwell, Kim T

2011-04-21

Stochastic simulation of reaction-diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies.

Pricing European option with transaction costs under the fractional long memory stochastic volatility model

NASA Astrophysics Data System (ADS)

Wang, Xiao-Tian; Wu, Min; Zhou, Ze-Min; Jing, Wei-Shu

2012-02-01

This paper deals with the problem of discrete time option pricing using the fractional long memory stochastic volatility model with transaction costs. Through the 'anchoring and adjustment' argument in a discrete time setting, a European call option pricing formula is obtained.

Reconstruction of the modified discrete Langevin equation from persistent time series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Czechowski, Zbigniew

The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived. For an exemplary meteorological time series, an appropriate Langevin equation, which constitutes a stochastic macroscopic model of the phenomenon, was reconstructed.

Control Improvement for Jump-Diffusion Processes with Applications to Finance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baeuerle, Nicole, E-mail: nicole.baeuerle@kit.edu; Rieder, Ulrich, E-mail: ulrich.rieder@uni-ulm.de

2012-02-15

We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control {pi}, a new control with a better value. If no improvement is possible, then {pi} is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard's policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting results in financial portfolio optimization.

Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009)

PubMed Central

2011-01-01

Background Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. Methods A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. Results The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Conclusions Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance. PMID:21324153

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Stochastic differential equation (SDE) model of opening gold share price of bursa saham malaysia

NASA Astrophysics Data System (ADS)

Hussin, F. N.; Rahman, H. A.; Bahar, A.

2017-09-01

Black and Scholes option pricing model is one of the most recognized stochastic differential equation model in mathematical finance. Two parameter estimation methods have been utilized for the Geometric Brownian model (GBM); historical and discrete method. The historical method is a statistical method which uses the property of independence and normality logarithmic return, giving out the simplest parameter estimation. Meanwhile, discrete method considers the function of density of transition from the process of diffusion normal log which has been derived from maximum likelihood method. These two methods are used to find the parameter estimates samples of Malaysians Gold Share Price data such as: Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas, and Financial Times and Stock Exchange (FTSE) Bursa Malaysia Emas Shariah. Modelling of gold share price is essential since fluctuation of gold affects worldwide economy nowadays, including Malaysia. It is found that discrete method gives the best parameter estimates than historical method due to the smallest Root Mean Square Error (RMSE) value.

Stochastic approach to equilibrium and nonequilibrium thermodynamics.

PubMed

Tomé, Tânia; de Oliveira, Mário J

2015-04-01

We develop the stochastic approach to thermodynamics based on stochastic dynamics, which can be discrete (master equation) and continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second the definition of entropy production rate, which is non-negative and vanishes in thermodynamic equilibrium. Based on these assumptions, we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasiequilibrium processes; the convexity of the equilibrium surface; the monotonic time behavior of thermodynamic potentials, including entropy; the bilinear form of the entropy production rate; the Onsager coefficients and reciprocal relations; and the nonequilibrium steady states of chemical reactions.

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks.

PubMed

Rathinam, Muruhan; Sheppard, Patrick W; Khammash, Mustafa

2010-01-21

Parametric sensitivity of biochemical networks is an indispensable tool for studying system robustness properties, estimating network parameters, and identifying targets for drug therapy. For discrete stochastic representations of biochemical networks where Monte Carlo methods are commonly used, sensitivity analysis can be particularly challenging, as accurate finite difference computations of sensitivity require a large number of simulations for both nominal and perturbed values of the parameters. In this paper we introduce the common random number (CRN) method in conjunction with Gillespie's stochastic simulation algorithm, which exploits positive correlations obtained by using CRNs for nominal and perturbed parameters. We also propose a new method called the common reaction path (CRP) method, which uses CRNs together with the random time change representation of discrete state Markov processes due to Kurtz to estimate the sensitivity via a finite difference approximation applied to coupled reaction paths that emerge naturally in this representation. While both methods reduce the variance of the estimator significantly compared to independent random number finite difference implementations, numerical evidence suggests that the CRP method achieves a greater variance reduction. We also provide some theoretical basis for the superior performance of CRP. The improved accuracy of these methods allows for much more efficient sensitivity estimation. In two example systems reported in this work, speedup factors greater than 300 and 10,000 are demonstrated.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

Structured population dynamics: continuous size and discontinuous stage structures.

PubMed

Buffoni, Giuseppe; Pasquali, Sara

2007-04-01

A nonlinear stochastic model for the dynamics of a population with either a continuous size structure or a discontinuous stage structure is formulated in the Eulerian formalism. It takes into account dispersion effects due to stochastic variability of the development process of the individuals. The discrete equations of the numerical approximation are derived, and an analysis of the existence and stability of the equilibrium states is performed. An application to a copepod population is illustrated; numerical results of Eulerian and Lagrangian models are compared.

Retrospective estimation of breeding phenology of American Goldfinch (Carduelis tristis) using pattern oriented modeling

EPA Science Inventory

Avian seasonal productivity is often modeled as a time-limited stochastic process. Many mathematical formulations have been proposed, including individual based models, continuous-time differential equations, and discrete Markov models. All such models typically include paramete...

Multifractal analysis of time series generated by discrete Ito equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Telesca, Luciano; Czechowski, Zbigniew; Lovallo, Michele

2015-06-15

In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.

Multithreaded Stochastic PDES for Reactions and Diffusions in Neurons.

PubMed

Lin, Zhongwei; Tropper, Carl; Mcdougal, Robert A; Patoary, Mohammand Nazrul Ishlam; Lytton, William W; Yao, Yiping; Hines, Michael L

2017-07-01

Cells exhibit stochastic behavior when the number of molecules is small. Hence a stochastic reaction-diffusion simulator capable of working at scale can provide a more accurate view of molecular dynamics within the cell. This paper describes a parallel discrete event simulator, Neuron Time Warp-Multi Thread (NTW-MT), developed for the simulation of reaction diffusion models of neurons. To the best of our knowledge, this is the first parallel discrete event simulator oriented towards stochastic simulation of chemical reactions in a neuron. The simulator was developed as part of the NEURON project. NTW-MT is optimistic and thread-based, which attempts to capitalize on multi-core architectures used in high performance machines. It makes use of a multi-level queue for the pending event set and a single roll-back message in place of individual anti-messages to disperse contention and decrease the overhead of processing rollbacks. Global Virtual Time is computed asynchronously both within and among processes to get rid of the overhead for synchronizing threads. Memory usage is managed in order to avoid locking and unlocking when allocating and de-allocating memory and to maximize cache locality. We verified our simulator on a calcium buffer model. We examined its performance on a calcium wave model, comparing it to the performance of a process based optimistic simulator and a threaded simulator which uses a single priority queue for each thread. Our multi-threaded simulator is shown to achieve superior performance to these simulators. Finally, we demonstrated the scalability of our simulator on a larger CICR model and a more detailed CICR model.

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

PubMed

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.

The exact fundamental solution for the Benes tracking problem

NASA Astrophysics Data System (ADS)

Balaji, Bhashyam

2009-05-01

The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.

Explore Stochastic Instabilities of Periodic Points by Transition Path Theory

NASA Astrophysics Data System (ADS)

Cao, Yu; Lin, Ling; Zhou, Xiang

2016-06-01

We consider the noise-induced transitions from a linearly stable periodic orbit consisting of T periodic points in randomly perturbed discrete logistic map. Traditional large deviation theory and asymptotic analysis at small noise limit cannot distinguish the quantitative difference in noise-induced stochastic instabilities among the T periodic points. To attack this problem, we generalize the transition path theory to the discrete-time continuous-space stochastic process. In our first criterion to quantify the relative instability among T periodic points, we use the distribution of the last passage location related to the transitions from the whole periodic orbit to a prescribed disjoint set. This distribution is related to individual contributions to the transition rate from each periodic points. The second criterion is based on the competency of the transition paths associated with each periodic point. Both criteria utilize the reactive probability current in the transition path theory. Our numerical results for the logistic map reveal the transition mechanism of escaping from the stable periodic orbit and identify which periodic point is more prone to lose stability so as to make successful transitions under random perturbations.

Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism

NASA Astrophysics Data System (ADS)

Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G.

2015-04-01

We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.

Hybrid Markov-mass action law model for cell activation by rare binding events: Application to calcium induced vesicular release at neuronal synapses.

PubMed

Guerrier, Claire; Holcman, David

2016-10-18

Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian. The large ensemble of particles is described by mass action laws. We use this novel model to predict the time distribution of vesicular release at neuronal synapses. Vesicular release is triggered by the binding of few calcium ions that can originate either from the synaptic bulk or from the entry through calcium channels. We report here that the distribution of release time is bimodal although it is triggered by a single fast action potential. While the first peak follows a stimulation, the second corresponds to the random arrival over much longer time of ions located in the synaptic terminal to small binding vesicular targets. To conclude, the present multiscale stochastic modeling approach allows studying cellular events based on integrating discrete molecular events over several time scales.

Analyzing a stochastic time series obeying a second-order differential equation.

PubMed

Lehle, B; Peinke, J

2015-06-01

The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in 2N dimensions from a non-Markovian signal in N dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series.

A hybrid continuous-discrete method for stochastic reaction-diffusion processes.

PubMed

Lo, Wing-Cheong; Zheng, Likun; Nie, Qing

2016-09-01

Stochastic fluctuations in reaction-diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method.

Stability of continuous-time quantum filters with measurement imperfections

NASA Astrophysics Data System (ADS)

Amini, H.; Pellegrini, C.; Rouchon, P.

2014-07-01

The fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is shown to be always a submartingale. The observed system is assumed to be governed by a continuous-time Stochastic Master Equation (SME), driven simultaneously by Wiener and Poisson processes and that takes into account incompleteness and errors in measurements. This stability result is the continuous-time counterpart of a similar stability result already established for discrete-time quantum systems and where the measurement imperfections are modelled by a left stochastic matrix.

Periodic measure for the stochastic equation of the barotropic viscous gas in a discretized one-dimensional domain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benseghir, Rym, E-mail: benseghirrym@ymail.com, E-mail: benseghirrym@ymail.com; Benchettah, Azzedine, E-mail: abenchettah@hotmail.com; Raynaud de Fitte, Paul, E-mail: prf@univ-rouen.fr

2015-11-30

A stochastic equation system corresponding to the description of the motion of a barotropic viscous gas in a discretized one-dimensional domain with a weight regularizing the density is considered. In [2], the existence of an invariant measure was established for this discretized problem in the stationary case. In this paper, applying a slightly modified version of Khas’minskii’s theorem [5], we generalize this result in the periodic case by proving the existence of a periodic measure for this problem.

Stochastic Analysis of Reaction–Diffusion Processes

PubMed Central

Hu, Jifeng; Kang, Hye-Won

2013-01-01

Reaction and diffusion processes are used to model chemical and biological processes over a wide range of spatial and temporal scales. Several routes to the diffusion process at various levels of description in time and space are discussed and the master equation for spatially discretized systems involving reaction and diffusion is developed. We discuss an estimator for the appropriate compartment size for simulating reaction–diffusion systems and introduce a measure of fluctuations in a discretized system. We then describe a new computational algorithm for implementing a modified Gillespie method for compartmental systems in which reactions are aggregated into equivalence classes and computational cells are searched via an optimized tree structure. Finally, we discuss several examples that illustrate the issues that have to be addressed in general systems. PMID:23719732

Discrete stochastic simulation methods for chemically reacting systems.

PubMed

Cao, Yang; Samuels, David C

2009-01-01

Discrete stochastic chemical kinetics describe the time evolution of a chemically reacting system by taking into account the fact that, in reality, chemical species are present with integer populations and exhibit some degree of randomness in their dynamical behavior. In recent years, with the development of new techniques to study biochemistry dynamics in a single cell, there are increasing studies using this approach to chemical kinetics in cellular systems, where the small copy number of some reactant species in the cell may lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. This chapter reviews the fundamental theory related to stochastic chemical kinetics and several simulation methods based on that theory. We focus on nonstiff biochemical systems and the two most important discrete stochastic simulation methods: Gillespie's stochastic simulation algorithm (SSA) and the tau-leaping method. Different implementation strategies of these two methods are discussed. Then we recommend a relatively simple and efficient strategy that combines the strengths of the two methods: the hybrid SSA/tau-leaping method. The implementation details of the hybrid strategy are given here and a related software package is introduced. Finally, the hybrid method is applied to simple biochemical systems as a demonstration of its application.

Fluid Stochastic Petri Nets: Theory, Applications, and Solution

NASA Technical Reports Server (NTRS)

Horton, Graham; Kulkarni, Vidyadhar G.; Nicol, David M.; Trivedi, Kishor S.

1996-01-01

In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.

Mean-Potential Law in Evolutionary Games

NASA Astrophysics Data System (ADS)

Nałecz-Jawecki, Paweł; Miekisz, Jacek

2018-01-01

The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of a potential function for discrete-space stochastic systems. It is based on a correspondence between one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state spaces. Our method is useful for computation of fixation probabilities in discrete stochastic dynamical systems with two absorbing states. We apply it to evolutionary games, formulating two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in finite populations. In particular, we show that the 1 /3 law of evolutionary games, introduced by Nowak et al. [Nature, 2004], follows from a more general mean-potential law.

Critical thresholds for eventual extinction in randomly disturbed population growth models.

PubMed

Peckham, Scott D; Waymire, Edward C; De Leenheer, Patrick

2018-02-16

This paper considers several single species growth models featuring a carrying capacity, which are subject to random disturbances that lead to instantaneous population reduction at the disturbance times. This is motivated in part by growing concerns about the impacts of climate change. Our main goal is to understand whether or not the species can persist in the long run. We consider the discrete-time stochastic process obtained by sampling the system immediately after the disturbances, and find various thresholds for several modes of convergence of this discrete process, including thresholds for the absence or existence of a positively supported invariant distribution. These thresholds are given explicitly in terms of the intensity and frequency of the disturbances on the one hand, and the population's growth characteristics on the other. We also perform a similar threshold analysis for the original continuous-time stochastic process, and obtain a formula that allows us to express the invariant distribution for this continuous-time process in terms of the invariant distribution of the discrete-time process, and vice versa. Examples illustrate that these distributions can differ, and this sends a cautionary message to practitioners who wish to parameterize these and related models using field data. Our analysis relies heavily on a particular feature shared by all the deterministic growth models considered here, namely that their solutions exhibit an exponentially weighted averaging property between a function of the initial condition, and the same function applied to the carrying capacity. This property is due to the fact that these systems can be transformed into affine systems.

A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall

NASA Astrophysics Data System (ADS)

Lombardo, F.; Volpi, E.; Koutsoyiannis, D.; Serinaldi, F.

2017-06-01

Generating fine-scale time series of intermittent rainfall that are fully consistent with any given coarse-scale totals is a key and open issue in many hydrological problems. We propose a stationary disaggregation method that simulates rainfall time series with given dependence structure, wet/dry probability, and marginal distribution at a target finer (lower-level) time scale, preserving full consistency with variables at a parent coarser (higher-level) time scale. We account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths. This approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean, variance, and autocorrelation function (ACF) for a mixed-type stochastic process in terms of mean, variance, and ACFs of both continuous and discrete components, respectively. To achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse-scale totals, the generated lower-level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model. To assess model performance, we study rainfall process as intermittent with both independent and dependent occurrences, where dependence is quantified by the probability that two consecutive time intervals are dry. In either case, we provide analytical formulations of main statistics of our mixed-type disaggregation model and show their clear accordance with Monte Carlo simulations. An application to rainfall time series from real world is shown as a proof of concept.

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions.

PubMed

Salis, Howard; Kaznessis, Yiannis

2005-02-01

The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.

Parallel Stochastic discrete event simulation of calcium dynamics in neuron.

PubMed

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.

Stochastic modeling of the hypothalamic pulse generator activity.

PubMed

Camproux, A C; Thalabard, J C; Thomas, G

1994-11-01

Luteinizing hormone (LH) is released by the pituitary in discrete pulses. In the monkey, the appearance of LH pulses in the plasma is invariably associated with sharp increases (i.e, volleys) in the frequency of the hypothalamic pulse generator electrical activity, so that continuous monitoring of this activity by telemetry provides a unique means to study the temporal structure of the mechanism generating the pulses. To assess whether the times of occurrence and durations of previous volleys exert significant influence on the timing of the next volley, we used a class of periodic counting process models that specify the stochastic intensity of the process as the product of two factors: 1) a periodic baseline intensity and 2) a stochastic regression function with covariates representing the influence of the past. This approach allows the characterization of circadian modulation and memory range of the process underlying hypothalamic pulse generator activity, as illustrated by fitting the model to experimental data from two ovariectomized rhesus monkeys.

Hybrid modeling in biochemical systems theory by means of functional petri nets.

PubMed

Wu, Jialiang; Voit, Eberhard

2009-02-01

Many biological systems are genuinely hybrids consisting of interacting discrete and continuous components and processes that often operate at different time scales. It is therefore desirable to create modeling frameworks capable of combining differently structured processes and permitting their analysis over multiple time horizons. During the past 40 years, Biochemical Systems Theory (BST) has been a very successful approach to elucidating metabolic, gene regulatory, and signaling systems. However, its foundation in ordinary differential equations has precluded BST from directly addressing problems containing switches, delays, and stochastic effects. In this study, we extend BST to hybrid modeling within the framework of Hybrid Functional Petri Nets (HFPN). First, we show how the canonical GMA and S-system models in BST can be directly implemented in a standard Petri Net framework. In a second step we demonstrate how to account for different types of time delays as well as for discrete, stochastic, and switching effects. Using representative test cases, we validate the hybrid modeling approach through comparative analyses and simulations with other approaches and highlight the feasibility, quality, and efficiency of the hybrid method.

Ensemble-type numerical uncertainty information from single model integrations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rauser, Florian, E-mail: florian.rauser@mpimet.mpg.de; Marotzke, Jochem; Korn, Peter

2015-07-01

We suggest an algorithm that quantifies the discretization error of time-dependent physical quantities of interest (goals) for numerical models of geophysical fluid dynamics. The goal discretization error is estimated using a sum of weighted local discretization errors. The key feature of our algorithm is that these local discretization errors are interpreted as realizations of a random process. The random process is determined by the model and the flow state. From a class of local error random processes we select a suitable specific random process by integrating the model over a short time interval at different resolutions. The weights of themore » influences of the local discretization errors on the goal are modeled as goal sensitivities, which are calculated via automatic differentiation. The integration of the weighted realizations of local error random processes yields a posterior ensemble of goal approximations from a single run of the numerical model. From the posterior ensemble we derive the uncertainty information of the goal discretization error. This algorithm bypasses the requirement of detailed knowledge about the models discretization to generate numerical error estimates. The algorithm is evaluated for the spherical shallow-water equations. For two standard test cases we successfully estimate the error of regional potential energy, track its evolution, and compare it to standard ensemble techniques. The posterior ensemble shares linear-error-growth properties with ensembles of multiple model integrations when comparably perturbed. The posterior ensemble numerical error estimates are of comparable size as those of a stochastic physics ensemble.« less

On the physical realizability of quantum stochastic walks

NASA Astrophysics Data System (ADS)

Taketani, Bruno; Govia, Luke; Schuhmacher, Peter; Wilhelm, Frank

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The recently developed quantum stochastic walk combines the concepts of a quantum walk and a classical random walk through open system evolution of a quantum system, and have been shown to have applications in as far reaching fields as artificial intelligence. However, nature puts significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution, and the physical assumptions underpinning them. We then introduce a way to circumvent some of these restrictions, and simulate a more general quantum stochastic walk on a quantum computer, using a technique we call quantum trajectories on a quantum computer. We finally describe a circuit QED approach to implement discrete time quantum stochastic walks.

Application of the Cluster Expansion to a Mathematical Model of the Long Memory Phenomenon in a Financial Market

NASA Astrophysics Data System (ADS)

Kuroda, Koji; Maskawa, Jun-ichi; Murai, Joshin

2013-08-01

Empirical studies of the high frequency data in stock markets show that the time series of trade signs or signed volumes has a long memory property. In this paper, we present a discrete time stochastic process for polymer model which describes trader's trading strategy, and show that a scale limit of the process converges to superposition of fractional Brownian motions with Hurst exponents and Brownian motion, provided that the index γ of the time scale about the trader's investment strategy coincides with the index δ of the interaction range in the discrete time process. The main tool for the investigation is the method of cluster expansion developed in the mathematical study of statistical mechanics.

Mean-Potential Law in Evolutionary Games.

PubMed

Nałęcz-Jawecki, Paweł; Miękisz, Jacek

2018-01-12

The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of a potential function for discrete-space stochastic systems. It is based on a correspondence between one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state spaces. Our method is useful for computation of fixation probabilities in discrete stochastic dynamical systems with two absorbing states. We apply it to evolutionary games, formulating two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in finite populations. In particular, we show that the 1/3 law of evolutionary games, introduced by Nowak et al. [Nature, 2004], follows from a more general mean-potential law.

Algorithm refinement for stochastic partial differential equations: II. Correlated systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexander, Francis J.; Garcia, Alejandro L.; Tartakovsky, Daniel M.

2005-08-10

We analyze a hybrid particle/continuum algorithm for a hydrodynamic system with long ranged correlations. Specifically, we consider the so-called train model for viscous transport in gases, which is based on a generalization of the random walk process for the diffusion of momentum. This discrete model is coupled with its continuous counterpart, given by a pair of stochastic partial differential equations. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass and momentum conservation. This methodology is an extension of our stochastic Algorithm Refinement (AR) hybrid for simple diffusion [F. Alexander, A. Garcia,more » D. Tartakovsky, Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, J. Comput. Phys. 182 (2002) 47-66]. Results from a variety of numerical experiments are presented for steady-state scenarios. In all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.« less

Improved result on stability analysis of discrete stochastic neural networks with time delay

NASA Astrophysics Data System (ADS)

Wu, Zhengguang; Su, Hongye; Chu, Jian; Zhou, Wuneng

2009-04-01

This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.

A hybrid continuous-discrete method for stochastic reaction–diffusion processes

PubMed Central

Zheng, Likun; Nie, Qing

2016-01-01

Stochastic fluctuations in reaction–diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method. PMID:27703710

A Learning Framework for Winner-Take-All Networks with Stochastic Synapses.

PubMed

Mostafa, Hesham; Cauwenberghs, Gert

2018-06-01

Many recent generative models make use of neural networks to transform the probability distribution of a simple low-dimensional noise process into the complex distribution of the data. This raises the question of whether biological networks operate along similar principles to implement a probabilistic model of the environment through transformations of intrinsic noise processes. The intrinsic neural and synaptic noise processes in biological networks, however, are quite different from the noise processes used in current abstract generative networks. This, together with the discrete nature of spikes and local circuit interactions among the neurons, raises several difficulties when using recent generative modeling frameworks to train biologically motivated models. In this letter, we show that a biologically motivated model based on multilayer winner-take-all circuits and stochastic synapses admits an approximate analytical description. This allows us to use the proposed networks in a variational learning setting where stochastic backpropagation is used to optimize a lower bound on the data log likelihood, thereby learning a generative model of the data. We illustrate the generality of the proposed networks and learning technique by using them in a structured output prediction task and a semisupervised learning task. Our results extend the domain of application of modern stochastic network architectures to networks where synaptic transmission failure is the principal noise mechanism.

Superior memory efficiency of quantum devices for the simulation of continuous-time stochastic processes

NASA Astrophysics Data System (ADS)

Elliott, Thomas J.; Gu, Mile

2018-03-01

Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of information about past behaviour, even for relatively simple models, enforcing limits on precision due to the finite memory of the machine. However, quantum machines can require less information about the past than even their optimal classical counterparts to simulate the future of discrete-time processes, and we demonstrate that this advantage extends to the continuous-time regime. Moreover, we show that this reduction in the memory requirement can be unboundedly large, allowing for arbitrary precision even with a finite quantum memory. We provide a systematic method for finding superior quantum constructions, and a protocol for analogue simulation of continuous-time renewal processes with a quantum machine.

3D discrete angiogenesis dynamic model and stochastic simulation for the assessment of blood perfusion coefficient and impact on heat transfer between nanoparticles and malignant tumors.

PubMed

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.

Optimal Stochastic Modeling and Control of Flexible Structures

DTIC Science & Technology

1988-09-01

1.37] and McLane [1.18] considered multivariable systems and derived their optimal control characteristics. Kleinman, Gorman and Zaborsky considered...Leondes [1.72,1.73] studied various aspects of multivariable linear stochastic, discrete-time systems that are partly deterministic, and partly stochastic...June 1966. 1.8. A.V. Balaknishnan, Applied Functional Analaysis , 2nd ed., New York, N.Y.: Springer-Verlag, 1981 1.9. Peter S. Maybeck, Stochastic

Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

DTIC Science & Technology

2014-10-09

problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...linear systems with Brownian motion or a discrete time linear system with a white Gaussian noise and costs 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 stochastic optimal control, fractional Brownian motion , stochastic

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

PubMed

García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G

2017-08-01

The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

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

PubMed

Adalsteinsson, David; McMillen, David; Elston, Timothy C

2004-03-08

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. We have developed the software package Biochemical Network Stochastic Simulator (BioNetS) for efficiently and 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 solves the 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. 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.

Stochastic theory of nonequilibrium steady states and its applications. Part I

NASA Astrophysics Data System (ADS)

Zhang, Xue-Juan; Qian, Hong; Qian, Min

2012-01-01

The concepts of equilibrium and nonequilibrium steady states are introduced in the present review as mathematical concepts associated with stationary Markov processes. For both discrete stochastic systems with master equations and continuous diffusion processes with Fokker-Planck equations, the nonequilibrium steady state (NESS) is characterized in terms of several key notions which are originated from nonequilibrium physics: time irreversibility, breakdown of detailed balance, free energy dissipation, and positive entropy production rate. After presenting this NESS theory in pedagogically accessible mathematical terms that require only a minimal amount of prerequisites in nonlinear differential equations and the theory of probability, it is applied, in Part I, to two widely studied problems: the stochastic resonance (also known as coherent resonance) and molecular motors (also known as Brownian ratchet). Although both areas have advanced rapidly on their own with a vast amount of literature, the theory of NESS provides them with a unifying mathematical foundation. Part II of this review contains applications of the NESS theory to processes from cellular biochemistry, ranging from enzyme catalyzed reactions, kinetic proofreading, to zeroth-order ultrasensitivity.

Using Markov Models of Fault Growth Physics and Environmental Stresses to Optimize Control Actions

NASA Technical Reports Server (NTRS)

Bole, Brian; Goebel, Kai; Vachtsevanos, George

2012-01-01

A generalized Markov chain representation of fault dynamics is presented for the case that available modeling of fault growth physics and future environmental stresses can be represented by two independent stochastic process models. A contrived but representatively challenging example will be presented and analyzed, in which uncertainty in the modeling of fault growth physics is represented by a uniformly distributed dice throwing process, and a discrete random walk is used to represent uncertain modeling of future exogenous loading demands to be placed on the system. A finite horizon dynamic programming algorithm is used to solve for an optimal control policy over a finite time window for the case that stochastic models representing physics of failure and future environmental stresses are known, and the states of both stochastic processes are observable by implemented control routines. The fundamental limitations of optimization performed in the presence of uncertain modeling information are examined by comparing the outcomes obtained from simulations of an optimizing control policy with the outcomes that would be achievable if all modeling uncertainties were removed from the system.

Stochastic Set-Based Particle Swarm Optimization Based on Local Exploration for Solving the Carpool Service Problem.

PubMed

Chou, Sheng-Kai; Jiau, Ming-Kai; Huang, Shih-Chia

2016-08-01

The growing ubiquity of vehicles has led to increased concerns about environmental issues. These concerns can be mitigated by implementing an effective carpool service. In an intelligent carpool system, an automated service process assists carpool participants in determining routes and matches. It is a discrete optimization problem that involves a system-wide condition as well as participants' expectations. In this paper, we solve the carpool service problem (CSP) to provide satisfactory ride matches. To this end, we developed a particle swarm carpool algorithm based on stochastic set-based particle swarm optimization (PSO). Our method introduces stochastic coding to augment traditional particles, and uses three terminologies to represent a particle: 1) particle position; 2) particle view; and 3) particle velocity. In this way, the set-based PSO (S-PSO) can be realized by local exploration. In the simulation and experiments, two kind of discrete PSOs-S-PSO and binary PSO (BPSO)-and a genetic algorithm (GA) are compared and examined using tested benchmarks that simulate a real-world metropolis. We observed that the S-PSO outperformed the BPSO and the GA thoroughly. Moreover, our method yielded the best result in a statistical test and successfully obtained numerical results for meeting the optimization objectives of the CSP.

The stochastic system approach for estimating dynamic treatments effect.

PubMed

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.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

PubMed

Kalantzis, Georgios

2009-06-01

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Multiple coupled landscapes and non-adiabatic dynamics with applications to self-activating genes.

PubMed

Chen, Cong; Zhang, Kun; Feng, Haidong; Sasai, Masaki; Wang, Jin

2015-11-21

Many physical, chemical and biochemical systems (e.g. electronic dynamics and gene regulatory networks) are governed by continuous stochastic processes (e.g. electron dynamics on a particular electronic energy surface and protein (gene product) synthesis) coupled with discrete processes (e.g. hopping among different electronic energy surfaces and on and off switching of genes). One can also think of the underlying dynamics as the continuous motion on a particular landscape and discrete hoppings among different landscapes. The main difference of such systems from the intra-landscape dynamics alone is the emergence of the timescale involved in transitions among different landscapes in addition to the timescale involved in a particular landscape. The adiabatic limit when inter-landscape hoppings are fast compared to continuous intra-landscape dynamics has been studied both analytically and numerically, but the analytical treatment of the non-adiabatic regime where the inter-landscape hoppings are slow or comparable to continuous intra-landscape dynamics remains challenging. In this study, we show that there exists mathematical mapping of the dynamics on 2(N) discretely coupled N continuous dimensional landscapes onto one single landscape in 2N dimensional extended continuous space. On this 2N dimensional landscape, eddy current emerges as a sign of non-equilibrium non-adiabatic dynamics and plays an important role in system evolution. Many interesting physical effects such as the enhancement of fluctuations, irreversibility, dissipation and optimal kinetics emerge due to non-adiabaticity manifested by the eddy current illustrated for an N = 1 self-activator. We further generalize our theory to the N-gene network with multiple binding sites and multiple synthesis rates for discretely coupled non-equilibrium stochastic physical and biological systems.

Recurrence plots of discrete-time Gaussian stochastic processes

NASA Astrophysics Data System (ADS)

Ramdani, Sofiane; Bouchara, Frédéric; Lagarde, Julien; Lesne, Annick

2016-09-01

We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1. These results allow us to obtain theoretical values of three measures: (i) the recurrence rate (REC) (ii) the percent determinism (DET) and (iii) RP-based estimation of the ε-entropy κ(ε) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.

The adaptation rate of a quantitative trait in an environmental gradient

NASA Astrophysics Data System (ADS)

Hermsen, R.

2016-12-01

The spatial range of a species habitat is generally determined by the ability of the species to cope with biotic and abiotic variables that vary in space. Therefore, the species range is itself an evolvable property. Indeed, environmental gradients permit a mode of evolution in which range expansion and adaptation go hand in hand. This process can contribute to rapid evolution of drug resistant bacteria and viruses, because drug concentrations in humans and livestock treated with antibiotics are far from uniform. Here, we use a minimal stochastic model of discrete, interacting organisms evolving in continuous space to study how the rate of adaptation of a quantitative trait depends on the steepness of the gradient and various population parameters. We discuss analytical results for the mean-field limit as well as extensive stochastic simulations. These simulations were performed using an exact, event-driven simulation scheme that can deal with continuous time-, density- and coordinate-dependent reaction rates and could be used for a wide variety of stochastic systems. The results reveal two qualitative regimes. If the gradient is shallow, the rate of adaptation is limited by dispersion and increases linearly with the gradient slope. If the gradient is steep, the adaptation rate is limited by mutation. In this regime, the mean-field result is highly misleading: it predicts that the adaptation rate continues to increase with the gradient slope, whereas stochastic simulations show that it in fact decreases with the square root of the slope. This discrepancy underscores the importance of discreteness and stochasticity even at high population densities; mean-field results, including those routinely used in quantitative genetics, should be interpreted with care.

The adaptation rate of a quantitative trait in an environmental gradient.

PubMed

Hermsen, R

2016-11-30

The spatial range of a species habitat is generally determined by the ability of the species to cope with biotic and abiotic variables that vary in space. Therefore, the species range is itself an evolvable property. Indeed, environmental gradients permit a mode of evolution in which range expansion and adaptation go hand in hand. This process can contribute to rapid evolution of drug resistant bacteria and viruses, because drug concentrations in humans and livestock treated with antibiotics are far from uniform. Here, we use a minimal stochastic model of discrete, interacting organisms evolving in continuous space to study how the rate of adaptation of a quantitative trait depends on the steepness of the gradient and various population parameters. We discuss analytical results for the mean-field limit as well as extensive stochastic simulations. These simulations were performed using an exact, event-driven simulation scheme that can deal with continuous time-, density- and coordinate-dependent reaction rates and could be used for a wide variety of stochastic systems. The results reveal two qualitative regimes. If the gradient is shallow, the rate of adaptation is limited by dispersion and increases linearly with the gradient slope. If the gradient is steep, the adaptation rate is limited by mutation. In this regime, the mean-field result is highly misleading: it predicts that the adaptation rate continues to increase with the gradient slope, whereas stochastic simulations show that it in fact decreases with the square root of the slope. This discrepancy underscores the importance of discreteness and stochasticity even at high population densities; mean-field results, including those routinely used in quantitative genetics, should be interpreted with care.

Development of morphogen gradient: The role of dimension and discreteness

DOE Office of Scientific and Technical Information (OSTI.GOV)

Teimouri, Hamid; Kolomeisky, Anatoly B.

2014-02-28

The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as local accumulation times, variances, and mean first-passage times. The role of discreteness in developing of morphogen gradients is analyzed by comparing with available continuummore » descriptions. It is found that the continuum models prediction about multiple time scales near the source region in two-dimensional and three-dimensional systems is not supported in our analysis. Using ideas that view the degradation process as an effective potential, the effect of dimensionality on establishment of morphogen gradients is also discussed. In addition, we investigated how these reaction-diffusion processes are modified with changing the size of the source region.« less

Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz

NASA Astrophysics Data System (ADS)

Vanicat, Matthieu

2018-04-01

We present a general method for constructing integrable stochastic processes, with two-step discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can be applied for both periodic and open boundary conditions. We also show how the stationary distribution can be built as a matrix product state. As an illustration we construct parallel discrete time dynamics associated with the R-matrix of the SSEP and of the ASEP, and provide the associated stationary distributions in a matrix product form. We use this general framework to introduce new integrable generalized exclusion processes, where a fixed number of particles is allowed on each lattice site in opposition to the (single particle) exclusion process models. They are constructed using the fusion procedure of R-matrices (and K-matrices for open boundary conditions) for the SSEP and ASEP. We develop a new method, that we named "fused" matrix ansatz, to build explicitly the stationary distribution in a matrix product form. We use this algebraic structure to compute physical observables such as the correlation functions and the mean particle current.

Distributed delays in a hybrid model of tumor-immune system interplay.

PubMed

Caravagna, Giulio; Graudenzi, Alex; d'Onofrio, Alberto

2013-02-01

A tumor is kinetically characterized by the presence of multiple spatio-temporal scales in which its cells interplay with, for instance, endothelial cells or Immune system effectors, exchanging various chemical signals. By its nature, tumor growth is an ideal object of hybrid modeling where discrete stochastic processes model low-numbers entities, and mean-field equations model abundant chemical signals. Thus, we follow this approach to model tumor cells, effector cells and Interleukin-2, in order to capture the Immune surveillance effect. We here present a hybrid model with a generic delay kernel accounting that, due to many complex phenomena such as chemical transportation and cellular differentiation, the tumor-induced recruitment of effectors exhibits a lag period. This model is a Stochastic Hybrid Automata and its semantics is a Piecewise Deterministic Markov process where a two-dimensional stochastic process is interlinked to a multi-dimensional mean-field system. We instantiate the model with two well-known weak and strong delay kernels and perform simulations by using an algorithm to generate trajectories of this process. Via simulations and parametric sensitivity analysis techniques we (i) relate tumor mass growth with the two kernels, we (ii) measure the strength of the Immune surveillance in terms of probability distribution of the eradication times, and (iii) we prove, in the oscillatory regime, the existence of a stochastic bifurcation resulting in delay-induced tumor eradication.

A Stochastic Dynamic Programming Model With Fuzzy Storage States Applied to Reservoir Operation Optimization

NASA Astrophysics Data System (ADS)

Mousavi, Seyed Jamshid; Mahdizadeh, Kourosh; Afshar, Abbas

2004-08-01

Application of stochastic dynamic programming (SDP) models to reservoir optimization calls for state variables discretization. As an important variable discretization of reservoir storage volume has a pronounced effect on the computational efforts. The error caused by storage volume discretization is examined by considering it as a fuzzy state variable. In this approach, the point-to-point transitions between storage volumes at the beginning and end of each period are replaced by transitions between storage intervals. This is achieved by using fuzzy arithmetic operations with fuzzy numbers. In this approach, instead of aggregating single-valued crisp numbers, the membership functions of fuzzy numbers are combined. Running a simulated model with optimal release policies derived from fuzzy and non-fuzzy SDP models shows that a fuzzy SDP with a coarse discretization scheme performs as well as a classical SDP having much finer discretized space. It is believed that this advantage in the fuzzy SDP model is due to the smooth transitions between storage intervals which benefit from soft boundaries.

Stochastic Dual Algorithm for Voltage Regulation in Distribution Networks with Discrete Loads: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhou, Xinyang; Liu, Zhiyuan

This paper considers distribution networks with distributed energy resources and discrete-rate loads, and designs an incentive-based algorithm that allows the network operator and the customers to pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. Four major challenges include: (1) the non-convexity from discrete decision variables, (2) the non-convexity due to a Stackelberg game structure, (3) unavailable private information from customers, and (4) different update frequency from two types of devices. In this paper, we first make convex relaxation for discrete variables, then reformulate the non-convex structure into a convex optimization problem together withmore » pricing/reward signal design, and propose a distributed stochastic dual algorithm for solving the reformulated problem while restoring feasible power rates for discrete devices. By doing so, we are able to statistically achieve the solution of the reformulated problem without exposure of any private information from customers. Stability of the proposed schemes is analytically established and numerically corroborated.« less

Optimization of Operations Resources via Discrete Event Simulation Modeling

NASA Technical Reports Server (NTRS)

Joshi, B.; Morris, D.; White, N.; Unal, R.

1996-01-01

The resource levels required for operation and support of reusable launch vehicles are typically defined through discrete event simulation modeling. Minimizing these resources constitutes an optimization problem involving discrete variables and simulation. Conventional approaches to solve such optimization problems involving integer valued decision variables are the pattern search and statistical methods. However, in a simulation environment that is characterized by search spaces of unknown topology and stochastic measures, these optimization approaches often prove inadequate. In this paper, we have explored the applicability of genetic algorithms to the simulation domain. Genetic algorithms provide a robust search strategy that does not require continuity and differentiability of the problem domain. The genetic algorithm successfully minimized the operation and support activities for a space vehicle, through a discrete event simulation model. The practical issues associated with simulation optimization, such as stochastic variables and constraints, were also taken into consideration.

Hybrid discrete/continuum algorithms for stochastic reaction networks

DOE PAGES

Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; ...

2014-10-22

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discretemore » and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.« less

Discreteness-induced concentration inversion in mesoscopic chemical systems.

PubMed

Ramaswamy, Rajesh; González-Segredo, Nélido; Sbalzarini, Ivo F; Grima, Ramon

2012-04-10

Molecular discreteness is apparent in small-volume chemical systems, such as biological cells, leading to stochastic kinetics. Here we present a theoretical framework to understand the effects of discreteness on the steady state of a monostable chemical reaction network. We consider independent realizations of the same chemical system in compartments of different volumes. Rate equations ignore molecular discreteness and predict the same average steady-state concentrations in all compartments. However, our theory predicts that the average steady state of the system varies with volume: if a species is more abundant than another for large volumes, then the reverse occurs for volumes below a critical value, leading to a concentration inversion effect. The addition of extrinsic noise increases the size of the critical volume. We theoretically predict the critical volumes and verify, by exact stochastic simulations, that rate equations are qualitatively incorrect in sub-critical volumes.

Theory of relativistic Brownian motion: the (1+3) -dimensional case.

PubMed

Dunkel, Jörn; Hänggi, Peter

2005-09-01

A theory for (1+3) -dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but multiplicative Langevin equations we describe the relativistic stochastic dynamics of a forced Brownian particle. The corresponding Fokker-Planck equations are studied in the laboratory frame coordinates. In particular, the stochastic integration prescription--i.e., the discretization rule dilemma--is elucidated (prepoint discretization rule versus midpoint discretization rule versus postpoint discretization rule). Remarkably, within our relativistic scheme we find that the postpoint rule (or the transport form) yields the only Fokker-Planck dynamics from which the relativistic Maxwell-Boltzmann statistics is recovered as the stationary solution. The relativistic velocity effects become distinctly more pronounced by going from one to three spatial dimensions. Moreover, we present numerical results for the asymptotic mean-square displacement of a free relativistic Brownian particle moving in 1+3 dimensions.

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Luoping; Zheng, Bin; Lin, Guang

In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse meshmore » $$\\mathcal{T}_H$$ with a low level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_{P}$$) and solve linearized equations on a fine mesh $$\\mathcal{T}_h$$ using high level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_p$$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $$\\mathcal{T}_h$$ and $$\\mathcal{P}_p$$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.« less

Appropriate Domain Size for Groundwater Flow Modeling with a Discrete Fracture Network Model.

PubMed

Ji, Sung-Hoon; Koh, Yong-Kwon

2017-01-01

When a discrete fracture network (DFN) is constructed from statistical conceptualization, uncertainty in simulating the hydraulic characteristics of a fracture network can arise due to the domain size. In this study, the appropriate domain size, where less significant uncertainty in the stochastic DFN model is expected, was suggested for the Korea Atomic Energy Research Institute Underground Research Tunnel (KURT) site. The stochastic DFN model for the site was established, and the appropriate domain size was determined with the density of the percolating cluster and the percolation probability using the stochastically generated DFNs for various domain sizes. The applicability of the appropriate domain size to our study site was evaluated by comparing the statistical properties of stochastically generated fractures of varying domain sizes and estimating the uncertainty in the equivalent permeability of the generated DFNs. Our results show that the uncertainty of the stochastic DFN model is acceptable when the modeling domain is larger than the determined appropriate domain size, and the appropriate domain size concept is applicable to our study site. © 2016, National Ground Water Association.

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

PubMed Central

Weinberg, Seth H.; Smith, Gregory D.

2012-01-01

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

Input reconstruction for networked control systems subject to deception attacks and data losses on control signals

NASA Astrophysics Data System (ADS)

Keller, J. Y.; Chabir, K.; Sauter, D.

2016-03-01

State estimation of stochastic discrete-time linear systems subject to unknown inputs or constant biases has been widely studied but no work has been dedicated to the case where a disturbance switches between unknown input and constant bias. We show that such disturbance can affect a networked control system subject to deception attacks and data losses on the control signals transmitted by the controller to the plant. This paper proposes to estimate the switching disturbance from an augmented state version of the intermittent unknown input Kalman filter recently developed by the authors. Sufficient stochastic stability conditions are established when the arrival binary sequence of data losses follows a Bernoulli random process.

Discrete diffusion models to study the effects of Mg2+ concentration on the PhoPQ signal transduction system

PubMed Central

2010-01-01

Background The challenge today is to develop a modeling and simulation paradigm that integrates structural, molecular and genetic data for a quantitative understanding of physiology and behavior of biological processes at multiple scales. This modeling method requires techniques that maintain a reasonable accuracy of the biological process and also reduces the computational overhead. This objective motivates the use of new methods that can transform the problem from energy and affinity based modeling to information theory based modeling. To achieve this, we transform all dynamics within the cell into a random event time, which is specified through an information domain measure like probability distribution. This allows us to use the “in silico” stochastic event based modeling approach to find the molecular dynamics of the system. Results In this paper, we present the discrete event simulation concept using the example of the signal transduction cascade triggered by extra-cellular Mg2+ concentration in the two component PhoPQ regulatory system of Salmonella Typhimurium. We also present a model to compute the information domain measure of the molecular transport process by estimating the statistical parameters of inter-arrival time between molecules/ions coming to a cell receptor as external signal. This model transforms the diffusion process into the information theory measure of stochastic event completion time to get the distribution of the Mg2+ departure events. Using these molecular transport models, we next study the in-silico effects of this external trigger on the PhoPQ system. Conclusions Our results illustrate the accuracy of the proposed diffusion models in explaining the molecular/ionic transport processes inside the cell. Also, the proposed simulation framework can incorporate the stochasticity in cellular environments to a certain degree of accuracy. We expect that this scalable simulation platform will be able to model more complex biological systems with reasonable accuracy to understand their temporal dynamics. PMID:21143785

Discrete diffusion models to study the effects of Mg2+ concentration on the PhoPQ signal transduction system.

PubMed

Ghosh, Preetam; Ghosh, Samik; Basu, Kalyan; Das, Sajal K; Zhang, Chaoyang

2010-12-01

The challenge today is to develop a modeling and simulation paradigm that integrates structural, molecular and genetic data for a quantitative understanding of physiology and behavior of biological processes at multiple scales. This modeling method requires techniques that maintain a reasonable accuracy of the biological process and also reduces the computational overhead. This objective motivates the use of new methods that can transform the problem from energy and affinity based modeling to information theory based modeling. To achieve this, we transform all dynamics within the cell into a random event time, which is specified through an information domain measure like probability distribution. This allows us to use the "in silico" stochastic event based modeling approach to find the molecular dynamics of the system. In this paper, we present the discrete event simulation concept using the example of the signal transduction cascade triggered by extra-cellular Mg2+ concentration in the two component PhoPQ regulatory system of Salmonella Typhimurium. We also present a model to compute the information domain measure of the molecular transport process by estimating the statistical parameters of inter-arrival time between molecules/ions coming to a cell receptor as external signal. This model transforms the diffusion process into the information theory measure of stochastic event completion time to get the distribution of the Mg2+ departure events. Using these molecular transport models, we next study the in-silico effects of this external trigger on the PhoPQ system. Our results illustrate the accuracy of the proposed diffusion models in explaining the molecular/ionic transport processes inside the cell. Also, the proposed simulation framework can incorporate the stochasticity in cellular environments to a certain degree of accuracy. We expect that this scalable simulation platform will be able to model more complex biological systems with reasonable accuracy to understand their temporal dynamics.

Robust stochastic stability of discrete-time fuzzy Markovian jump neural networks.

PubMed

Arunkumar, A; Sakthivel, R; Mathiyalagan, K; Park, Ju H

2014-07-01

This paper focuses the issue of robust stochastic stability for a class of uncertain fuzzy Markovian jumping discrete-time neural networks (FMJDNNs) with various activation functions and mixed time delay. By employing the Lyapunov technique and linear matrix inequality (LMI) approach, a new set of delay-dependent sufficient conditions are established for the robust stochastic stability of uncertain FMJDNNs. More precisely, the parameter uncertainties are assumed to be time varying, unknown and norm bounded. The obtained stability conditions are established in terms of LMIs, which can be easily checked by using the efficient MATLAB-LMI toolbox. Finally, numerical examples with simulation result are provided to illustrate the effectiveness and less conservativeness of the obtained results. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Mesoscopic and continuum modelling of angiogenesis

PubMed Central

Spill, F.; Guerrero, P.; Alarcon, T.; Maini, P. K.; Byrne, H. M.

2016-01-01

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells. PMID:24615007

Investment portfolio of a pension fund: Stochastic model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bosch-Princep, M.; Fontanals-Albiol, H.

1994-12-31

This paper presents a stochastic programming model that aims at getting the optimal investment portfolio of a Pension Funds. The model has been designed bearing in mind the liabilities of the Funds to its members. The essential characteristic of the objective function and the constraints is the randomness of the coefficients and the right hand side of the constraints, so it`s necessary to use techniques of stochastic mathematical programming to get information about the amount of money that should be assigned to each sort of investment. It`s important to know the risky attitude of the person that has to takemore » decisions towards running risks. It incorporates the relation between the different coefficients of the objective function and constraints of each period of temporal horizon, through lineal and discrete random processes. Likewise, it includes the hypotheses that are related to Spanish law concerning the subject of Pension Funds.« less

Stochastic fire-diffuse-fire model with realistic cluster dynamics.

PubMed

Calabrese, Ana; Fraiman, Daniel; Zysman, Daniel; Ponce Dawson, Silvina

2010-09-01

Living organisms use waves that propagate through excitable media to transport information. Ca2+ waves are a paradigmatic example of this type of processes. A large hierarchy of Ca2+ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, Ca2+ release occurs trough inositol 1,4,5-trisphosphate receptors (IP3Rs) which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of IP3R 's that replicates the experimental observations reported in [D. Fraiman, Biophys. J. 90, 3897 (2006)]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the IP3 concentration is increased.

Modelling and simulation techniques for membrane biology.

PubMed

Burrage, Kevin; Hancock, John; Leier, André; Nicolau, Dan V

2007-07-01

One of the most important aspects of Computational Cell Biology is the understanding of the complicated dynamical processes that take place on plasma membranes. These processes are often so complicated that purely temporal models cannot always adequately capture the dynamics. On the other hand, spatial models can have large computational overheads. In this article, we review some of these issues with respect to chemistry, membrane microdomains and anomalous diffusion and discuss how to select appropriate modelling and simulation paradigms based on some or all the following aspects: discrete, continuous, stochastic, delayed and complex spatial processes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duncan, Andrew, E-mail: a.duncan@imperial.ac.uk; Erban, Radek, E-mail: erban@maths.ox.ac.uk; Zygalakis, Konstantinos, E-mail: k.zygalakis@ed.ac.uk

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 onemore » 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.« less

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

PubMed Central

2018-01-01

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the properties of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Last, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site. PMID:29386401

Stochastic cellular automata model of cell migration, proliferation and differentiation: validation with in vitro cultures of muscle satellite cells.

PubMed

Garijo, N; Manzano, R; Osta, R; Perez, M A

2012-12-07

Cell migration and proliferation has been modelled in the literature as a process similar to diffusion. However, using diffusion models to simulate the proliferation and migration of cells tends to create a homogeneous distribution in the cell density that does not correlate to empirical observations. In fact, the mechanism of cell dispersal is not diffusion. Cells disperse by crawling or proliferation, or are transported in a moving fluid. The use of cellular automata, particle models or cell-based models can overcome this limitation. This paper presents a stochastic cellular automata model to simulate the proliferation, migration and differentiation of cells. These processes are considered as completely stochastic as well as discrete. The model developed was applied to predict the behaviour of in vitro cell cultures performed with adult muscle satellite cells. Moreover, non homogeneous distribution of cells has been observed inside the culture well and, using the above mentioned stochastic cellular automata model, we have been able to predict this heterogeneous cell distribution and compute accurate quantitative results. Differentiation was also incorporated into the computational simulation. The results predicted the myotube formation that typically occurs with adult muscle satellite cells. In conclusion, we have shown how a stochastic cellular automata model can be implemented and is capable of reproducing the in vitro behaviour of adult muscle satellite cells. Copyright © 2012 Elsevier Ltd. All rights reserved.

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Continuum and discrete approach in modeling biofilm development and structure: a review.

PubMed

Mattei, M R; Frunzo, L; D'Acunto, B; Pechaud, Y; Pirozzi, F; Esposito, G

2018-03-01

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

Approximation of optimal filter for Ornstein-Uhlenbeck process with quantised discrete-time observation

NASA Astrophysics Data System (ADS)

Bania, Piotr; Baranowski, Jerzy

2018-02-01

Quantisation of signals is a ubiquitous property of digital processing. In many cases, it introduces significant difficulties in state estimation and in consequence control. Popular approaches either do not address properly the problem of system disturbances or lead to biased estimates. Our intention was to find a method for state estimation for stochastic systems with quantised and discrete observation, that is free of the mentioned drawbacks. We have formulated a general form of the optimal filter derived by a solution of Fokker-Planck equation. We then propose the approximation method based on Galerkin projections. We illustrate the approach for the Ornstein-Uhlenbeck process, and derive analytic formulae for the approximated optimal filter, also extending the results for the variant with control. Operation is illustrated with numerical experiments and compared with classical discrete-continuous Kalman filter. Results of comparison are substantially in favour of our approach, with over 20 times lower mean squared error. The proposed filter is especially effective for signal amplitudes comparable to the quantisation thresholds. Additionally, it was observed that for high order of approximation, state estimate is very close to the true process value. The results open the possibilities of further analysis, especially for more complex processes.

Review of stochastic hybrid systems with applications in biological systems modeling and analysis.

PubMed

Li, Xiangfang; Omotere, Oluwaseyi; Qian, Lijun; Dougherty, Edward R

2017-12-01

Stochastic hybrid systems (SHS) have attracted a lot of research interests in recent years. In this paper, we review some of the recent applications of SHS to biological systems modeling and analysis. Due to the nature of molecular interactions, many biological processes can be conveniently described as a mixture of continuous and discrete phenomena employing SHS models. With the advancement of SHS theory, it is expected that insights can be obtained about biological processes such as drug effects on gene regulation. Furthermore, combining with advanced experimental methods, in silico simulations using SHS modeling techniques can be carried out for massive and rapid verification or falsification of biological hypotheses. The hope is to substitute costly and time-consuming in vitro or in vivo experiments or provide guidance for those experiments and generate better hypotheses.

Modeling the evolution space of breakage fusion bridge cycles with a stochastic folding process.

PubMed

Greenman, C D; Cooke, S L; Marshall, J; Stratton, M R; Campbell, P J

2016-01-01

Breakage-fusion-bridge cycles in cancer arise when a broken segment of DNA is duplicated and an end from each copy joined together. This structure then 'unfolds' into a new piece of palindromic DNA. This is one mechanism responsible for the localised amplicons observed in cancer genome data. Here we study the evolution space of breakage-fusion-bridge structures in detail. We firstly consider discrete representations of this space with 2-d trees to demonstrate that there are [Formula: see text] qualitatively distinct evolutions involving [Formula: see text] breakage-fusion-bridge cycles. Secondly we consider the stochastic nature of the process to show these evolutions are not equally likely, and also describe how amplicons become localized. Finally we highlight these methods by inferring the evolution of breakage-fusion-bridge cycles with data from primary tissue cancer samples.

Stochastic nonlinear time series forecasting using time-delay reservoir computers: performance and universality.

PubMed

Grigoryeva, Lyudmila; Henriques, Julie; Larger, Laurent; Ortega, Juan-Pablo

2014-07-01

Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs. Copyright © 2014 Elsevier Ltd. All rights reserved.

Stochastic Model of Seasonal Runoff Forecasts

NASA Astrophysics Data System (ADS)

Krzysztofowicz, Roman; Watada, Leslie M.

1986-03-01

Each year the National Weather Service and the Soil Conservation Service issue a monthly sequence of five (or six) categorical forecasts of the seasonal snowmelt runoff volume. To describe uncertainties in these forecasts for the purposes of optimal decision making, a stochastic model is formulated. It is a discrete-time, finite, continuous-space, nonstationary Markov process. Posterior densities of the actual runoff conditional upon a forecast, and transition densities of forecasts are obtained from a Bayesian information processor. Parametric densities are derived for the process with a normal prior density of the runoff and a linear model of the forecast error. The structure of the model and the estimation procedure are motivated by analyses of forecast records from five stations in the Snake River basin, from the period 1971-1983. The advantages of supplementing the current forecasting scheme with a Bayesian analysis are discussed.

Projection scheme for a reflected stochastic heat equation with additive noise

NASA Astrophysics Data System (ADS)

Higa, Arturo Kohatsu; Pettersson, Roger

2005-02-01

We consider a projection scheme as a numerical solution of a reflected stochastic heat equation driven by a space-time white noise. Convergence is obtained via a discrete contraction principle and known convergence results for numerical solutions of parabolic variational inequalities.

Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

Collective behavior of coupled nonuniform stochastic oscillators

NASA Astrophysics Data System (ADS)

Assis, Vladimir R. V.; Copelli, Mauro

2012-02-01

Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the literature, with equal transition rates among the states. Here we start from the model recently introduced by Wood et al. [K. Wood, C. Van den Broeck, R. Kawai, K. Lindenberg, Universality of synchrony: critical behavior in a discrete model of stochastic phase-coupled oscillators, Phys. Rev. Lett. 96 (2006) 145701], which has a collectively synchronized phase, and parametrically modify the phase-coupled oscillators to render them (stochastically) nonuniform. We show that, depending on the nonuniformity parameter 0≤α≤1, a mean field analysis predicts the occurrence of several phase transitions. In particular, the phase with collective oscillations is stable for the complete graph only for α≤α‧<1. At α=1 the oscillators become excitable elements and the system has an absorbing state. In the excitable regime, no collective oscillations were found in the model.

Investigation for improving Global Positioning System (GPS) orbits using a discrete sequential estimator and stochastic models of selected physical processes

NASA Technical Reports Server (NTRS)

Goad, Clyde C.; Chadwell, C. David

1993-01-01

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

A stochastic discrete optimization model for designing container terminal facilities

NASA Astrophysics Data System (ADS)

Zukhruf, Febri; Frazila, Russ Bona; Burhani, Jzolanda Tsavalista

2017-11-01

As uncertainty essentially affect the total transportation cost, it remains important in the container terminal that incorporates several modes and transshipments process. This paper then presents a stochastic discrete optimization model for designing the container terminal, which involves the decision of facilities improvement action. The container terminal operation model is constructed by accounting the variation of demand and facilities performance. In addition, for illustrating the conflicting issue that practically raises in the terminal operation, the model also takes into account the possible increment delay of facilities due to the increasing number of equipment, especially the container truck. Those variations expectantly reflect the uncertainty issue in the container terminal operation. A Monte Carlo simulation is invoked to propagate the variations by following the observed distribution. The problem is constructed within the framework of the combinatorial optimization problem for investigating the optimal decision of facilities improvement. A new variant of glow-worm swarm optimization (GSO) is thus proposed for solving the optimization, which is rarely explored in the transportation field. The model applicability is tested by considering the actual characteristics of the container terminal.

Biochemical simulations: stochastic, approximate stochastic and hybrid approaches.

PubMed

Pahle, Jürgen

2009-01-01

Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem.

Biochemical simulations: stochastic, approximate stochastic and hybrid approaches

PubMed Central

2009-01-01

Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem. PMID:19151097

Ecological invasion, roughened fronts, and a competitor's extreme advance: integrating stochastic spatial-growth models.

PubMed

O'Malley, Lauren; Korniss, G; Caraco, Thomas

2009-07-01

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a "roughened" front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner's relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front's mean position. We find that a class of models with different assumptions about neighborhood interactions exhibits universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.

Persistent Surveillance of Transient Events with Unknown Statistics

DTIC Science & Technology

2016-12-18

different bird species by a documentary maker is shown in Fig. 1. Additional examples of scenarios following this setting include robots patrolling the...persistent monitoring application in which a documentary maker would like to monitor three different species of birds appearing in three discrete, species...specific locations. Bird sightings at each location follow a stochastic process with a rate that is initially unknown to the documentary maker and must

The secular evolution of discrete quasi-Keplerian systems. II. Application to a multi-mass axisymmetric disc around a supermassive black hole

NASA Astrophysics Data System (ADS)

Fouvry, J.-B.; Pichon, C.; Chavanis, P.-H.

2018-01-01

A discrete self-gravitating quasi-Keplerian razor-thin axisymmetric stellar disc orbiting a massive black hole sees its orbital structure diffuse on secular timescales as a result of a self-induced resonant relaxation. In the absence of collective effects, such a process is described by the recently derived inhomogeneous multi-mass degenerate Landau equation. Relying on Gauss' method, we computed the associated drift and diffusion coefficients to characterise the properties of the resonant relaxation of razor-thin discs. For a disc-like configuration in our Galactic centre, we showed how this secular diffusion induces an adiabatic distortion of orbits and estimate the typical timescale of resonant relaxation. When considering a disc composed of multiple masses similarly distributed, we have illustrated how the population of lighter stars will gain eccentricity, driving it closer to the central black hole, provided the distribution function increases with angular momentum. The kinetic equation recovers as well the quenching of the resonant diffusion of a test star in the vicinity of the black hole (the "Schwarzschild barrier") as a result of the divergence of the relativistic precessions. The dual stochastic Langevin formulation yields consistent results and offers a versatile framework in which to incorporate other stochastic processes.

Spectral simplicity of apparent complexity. II. Exact complexities and complexity spectra

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-03-01

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior. Using the resulting spectral decomposition, we derive closed-form expressions for correlation functions, finite-length Shannon entropy-rate approximates, asymptotic entropy rate, excess entropy, transient information, transient and asymptotic state uncertainties, and synchronization information of stochastic processes generated by finite-state hidden Markov models. This introduces analytical tractability to investigating information processing in discrete-event stochastic processes, symbolic dynamics, and chaotic dynamical systems. Comparisons reveal mathematical similarities between complexity measures originally thought to capture distinct informational and computational properties. We also introduce a new kind of spectral analysis via coronal spectrograms and the frequency-dependent spectra of past-future mutual information. We analyze a number of examples to illustrate the methods, emphasizing processes with multivariate dependencies beyond pairwise correlation. This includes spectral decomposition calculations for one representative example in full detail.

On the origins of approximations for stochastic chemical kinetics.

PubMed

Haseltine, Eric L; Rawlings, James B

2005-10-22

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems

NASA Astrophysics Data System (ADS)

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems.

PubMed

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

Space-Time Discrete KPZ Equation

NASA Astrophysics Data System (ADS)

Cannizzaro, G.; Matetski, K.

2018-03-01

We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn

We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.

On Nash Equilibria in Stochastic Games

DTIC Science & Technology

2003-10-01

Traditionally automata theory and veri cation has considered zero sum or strictly competitive versions of stochastic games . In these games there are two players...zero- sum discrete-time stochastic dynamic games . SIAM J. Control and Optimization, 19(5):617{634, 1981. 18. R.J. Lipton, E . Markakis, and A. Mehta...Playing large games using simple strate- gies. In EC 03: Electronic Commerce, pages 36{41. ACM Press, 2003. 19. A. Maitra and W. Sudderth. Finitely

On modeling animal movements using Brownian motion with measurement error.

PubMed

Pozdnyakov, Vladimir; Meyer, Thomas; Wang, Yu-Bo; Yan, Jun

2014-02-01

Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation.

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

NASA Technical Reports Server (NTRS)

Menga, G.

1975-01-01

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

Stochastic Dynamics through Hierarchically Embedded Markov Chains

NASA Astrophysics Data System (ADS)

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

2017-02-01

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.

Stochastic Dynamics through Hierarchically Embedded Markov Chains.

PubMed

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.

SOME DISCRETE PROCESSES IN THE THEORY OF STOCHASTIC DUELS,

DTIC Science & Technology

By limiting the time between rounds to a constant, certain duels in which each side has a fixed kill probability in which strong interactions occur...are investigated. The models investigated here are (1) the fundamental (one versus one) duel in which firing times are fixed and their ratio is a...rational number; (2) the duel with displacements in which two contestants fire simultaneously at fixed intervals and a near miss causes a contestant to

Computational Cellular Dynamics Based on the Chemical Master Equation: A Challenge for Understanding Complexity

PubMed Central

Liang, Jie; Qian, Hong

2010-01-01

Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology. Twenty-five years ago, the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics. In this paper, we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume (i.e., mesoscopic) in terms of a stochastic, discrete-state continuous-time formulation, called the chemical master equation (CME). Similar to the wavefunction in quantum mechanics, the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system. The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm. In contrast to the Metropolis algorithm, this Monte Carlo sampling technique does not follow a process with detailed balance. We shall show several examples how CMEs are used to model cellular biochemical systems. We shall also illustrate the computational challenges involved: multiscale phenomena, the interplay between stochasticity and nonlinearity, and how macroscopic determinism arises from mesoscopic dynamics. We point out recent advances in computing solutions to the CME, including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm. We argue that the CME is an ideal system from which one can learn to understand “complex behavior” and complexity theory, and from which important biological insight can be gained. PMID:24999297

Computational Cellular Dynamics Based on the Chemical Master Equation: A Challenge for Understanding Complexity.

PubMed

Liang, Jie; Qian, Hong

2010-01-01

Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology. Twenty-five years ago, the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics. In this paper, we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume (i.e., mesoscopic) in terms of a stochastic, discrete-state continuous-time formulation, called the chemical master equation (CME). Similar to the wavefunction in quantum mechanics, the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system. The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm. In contrast to the Metropolis algorithm, this Monte Carlo sampling technique does not follow a process with detailed balance. We shall show several examples how CMEs are used to model cellular biochemical systems. We shall also illustrate the computational challenges involved: multiscale phenomena, the interplay between stochasticity and nonlinearity, and how macroscopic determinism arises from mesoscopic dynamics. We point out recent advances in computing solutions to the CME, including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm. We argue that the CME is an ideal system from which one can learn to understand "complex behavior" and complexity theory, and from which important biological insight can be gained.

Revisiting Temporal Markov Chains for Continuum modeling of Transport in Porous Media

NASA Astrophysics Data System (ADS)

Delgoshaie, A. H.; Jenny, P.; Tchelepi, H.

2017-12-01

The transport of fluids in porous media is dominated by flow­-field heterogeneity resulting from the underlying permeability field. Due to the high uncertainty in the permeability field, many realizations of the reference geological model are used to describe the statistics of the transport phenomena in a Monte Carlo (MC) framework. There has been strong interest in working with stochastic formulations of the transport that are different from the standard MC approach. Several stochastic models based on a velocity process for tracer particle trajectories have been proposed. Previous studies have shown that for high variances of the log-conductivity, the stochastic models need to account for correlations between consecutive velocity transitions to predict dispersion accurately. The correlated velocity models proposed in the literature can be divided into two general classes of temporal and spatial Markov models. Temporal Markov models have been applied successfully to tracer transport in both the longitudinal and transverse directions. These temporal models are Stochastic Differential Equations (SDEs) with very specific drift and diffusion terms tailored for a specific permeability correlation structure. The drift and diffusion functions devised for a certain setup would not necessarily be suitable for a different scenario, (e.g., a different permeability correlation structure). The spatial Markov models are simple discrete Markov chains that do not require case specific assumptions. However, transverse spreading of contaminant plumes has not been successfully modeled with the available correlated spatial models. Here, we propose a temporal discrete Markov chain to model both the longitudinal and transverse dispersion in a two-dimensional domain. We demonstrate that these temporal Markov models are valid for different correlation structures without modification. Similar to the temporal SDEs, the proposed model respects the limited asymptotic transverse spreading of the plume in two-dimensional problems.

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Yen Ting; Buchler, Nicolas E.

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the propertiesmore » of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Finally, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site.« less

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes

DOE PAGES

Lin, Yen Ting; Buchler, Nicolas E.

2018-01-31

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the propertiesmore » of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Finally, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site.« less

State-and-transition simulation models: a framework for forecasting landscape change

USGS Publications Warehouse

Daniel, Colin; Frid, Leonardo; Sleeter, Benjamin M.; Fortin, Marie-Josée

2016-01-01

SummaryA wide range of spatially explicit simulation models have been developed to forecast landscape dynamics, including models for projecting changes in both vegetation and land use. While these models have generally been developed as separate applications, each with a separate purpose and audience, they share many common features.We present a general framework, called a state-and-transition simulation model (STSM), which captures a number of these common features, accompanied by a software product, called ST-Sim, to build and run such models. The STSM method divides a landscape into a set of discrete spatial units and simulates the discrete state of each cell forward as a discrete-time-inhomogeneous stochastic process. The method differs from a spatially interacting Markov chain in several important ways, including the ability to add discrete counters such as age and time-since-transition as state variables, to specify one-step transition rates as either probabilities or target areas, and to represent multiple types of transitions between pairs of states.We demonstrate the STSM method using a model of land-use/land-cover (LULC) change for the state of Hawai'i, USA. Processes represented in this example include expansion/contraction of agricultural lands, urbanization, wildfire, shrub encroachment into grassland and harvest of tree plantations; the model also projects shifts in moisture zones due to climate change. Key model output includes projections of the future spatial and temporal distribution of LULC classes and moisture zones across the landscape over the next 50 years.State-and-transition simulation models can be applied to a wide range of landscapes, including questions of both land-use change and vegetation dynamics. Because the method is inherently stochastic, it is well suited for characterizing uncertainty in model projections. When combined with the ST-Sim software, STSMs offer a simple yet powerful means for developing a wide range of models of landscape dynamics.

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem.

PubMed

Pandiselvi, S; Raja, R; Cao, Jinde; Rajchakit, G; Ahmad, Bashir

2018-01-01

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.

Entropy production of doubly stochastic quantum channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Müller-Hermes, Alexander, E-mail: muellerh@posteo.net; Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen; Stilck França, Daniel, E-mail: dsfranca@mytum.de

2016-02-15

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an applicationmore » we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.« less

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp; Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610

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 realisticmore » 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.« less

Noise in Nonlinear Dynamical Systems 3 Volume Paperback Set

NASA Astrophysics Data System (ADS)

Moss, Frank; McClintock, P. V. E.

2011-11-01

Volume 1: List of contributors; Preface; Introduction to volume one; 1. Noise-activated escape from metastable states: an historical view Rolf Landauer; 2. Some Markov methods in the theory of stochastic processes in non-linear dynamical systems R. L. Stratonovich; 3. Langevin equations with coloured noise J. M. Sancho and M. San Miguel; 4. First passage time problems for non-Markovian processes Katja Lindenberg, Bruce J. West and Jaume Masoliver; 5. The projection approach to the Fokker-Planck equation: applications to phenomenological stochastic equations with coloured noises Paolo Grigolini; 6. Methods for solving Fokker-Planck equations with applications to bistable and periodic potentials H. Risken and H. D. Vollmer; 7. Macroscopic potentials, bifurcations and noise in dissipative systems Robert Graham; 8. Transition phenomena in multidimensional systems - models of evolution W. Ebeling and L. Schimansky-Geier; 9. Coloured noise in continuous dynamical systems: a functional calculus approach Peter Hanggi; Appendix. On the statistical treatment of dynamical systems L. Pontryagin, A. Andronov and A. Vitt; Index. Volume 2: List of contributors; Preface; Introduction to volume two; 1. Stochastic processes in quantum mechanical settings Ronald F. Fox; 2. Self-diffusion in non-Markovian condensed-matter systems Toyonori Munakata; 3. Escape from the underdamped potential well M. Buttiker; 4. Effect of noise on discrete dynamical systems with multiple attractors Edgar Knobloch and Jeffrey B. Weiss; 5. Discrete dynamics perturbed by weak noise Peter Talkner and Peter Hanggi; 6. Bifurcation behaviour under modulated control parameters M. Lucke; 7. Period doubling bifurcations: what good are they? Kurt Wiesenfeld; 8. Noise-induced transitions Werner Horsthemke and Rene Lefever; 9. Mechanisms for noise-induced transitions in chemical systems Raymond Kapral and Edward Celarier; 10. State selection dynamics in symmetry-breaking transitions Dilip K. Kondepudi; 11. Noise in a ring-laser gyroscope K. Vogel, H. Risken and W. Schleich; 12. Control of noise and applications to optical systems L. A. Lugiato, G. Broggi, M. Merri and M. A. Pernigo; 13. Transition probabilities and spectral density of fluctuations of noise driven bistable systems M. I. Dykman, M. A. Krivoglaz and S. M. Soskin; Index. Volume 3: List of contributors; Preface; Introduction to volume three; 1. The effects of coloured quadratic noise on a turbulent transition in liquid He II J. T. Tough; 2. Electrohydrodynamic instability of nematic liquid crystals: growth process and influence of noise S. Kai; 3. Suppression of electrohydrodynamic instabilities by external noise Helmut R. Brand; 4. Coloured noise in dye laser fluctuations R. Roy, A. W. Yu and S. Zhu; 5. Noisy dynamics in optically bistable systems E. Arimondo, D. Hennequin and P. Glorieux; 6. Use of an electronic model as a guideline in experiments on transient optical bistability W. Lange; 7. Computer experiments in nonlinear stochastic physics Riccardo Mannella; 8. Analogue simulations of stochastic processes by means of minimum component electronic devices Leone Fronzoni; 9. Analogue techniques for the study of problems in stochastic nonlinear dynamics P. V. E. McClintock and Frank Moss; Index.

A well-posed and stable stochastic Galerkin formulation of the incompressible Navier–Stokes equations with random data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pettersson, Per, E-mail: per.pettersson@uib.no; Nordström, Jan, E-mail: jan.nordstrom@liu.se; Doostan, Alireza, E-mail: alireza.doostan@colorado.edu

2016-02-01

We present a well-posed stochastic Galerkin formulation of the incompressible Navier–Stokes equations with uncertainty in model parameters or the initial and boundary conditions. The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations. A relatively low-order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered. We derive boundary conditions for the continuous form of the stochastic Galerkin formulation of the velocity and pressure equations. The resulting problem formulation leads to an energy estimatemore » for the divergence. With suitable boundary data on the pressure and velocity, the energy estimate implies zero divergence of the velocity field. Based on the analysis of the continuous equations, we present a semi-discretized system where the spatial derivatives are approximated using finite difference operators with a summation-by-parts property. With a suitable choice of dissipative boundary conditions imposed weakly through penalty terms, the semi-discrete scheme is shown to be stable. Numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high-order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined.« less

How input fluctuations reshape the dynamics of a biological switching system

NASA Astrophysics Data System (ADS)

Hu, Bo; Kessler, David A.; Rappel, Wouter-Jan; Levine, Herbert

2012-12-01

An important task in quantitative biology is to understand the role of stochasticity in biochemical regulation. Here, as an extension of our recent work [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.148101 107, 148101 (2011)], we study how input fluctuations affect the stochastic dynamics of a simple biological switch. In our model, the on transition rate of the switch is directly regulated by a noisy input signal, which is described as a non-negative mean-reverting diffusion process. This continuous process can be a good approximation of the discrete birth-death process and is much more analytically tractable. Within this setup, we apply the Feynman-Kac theorem to investigate the statistical features of the output switching dynamics. Consistent with our previous findings, the input noise is found to effectively suppress the input-dependent transitions. We show analytically that this effect becomes significant when the input signal fluctuates greatly in amplitude and reverts slowly to its mean.

Inversion of Robin coefficient by a spectral stochastic finite element approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yunlong; Wang, Aiping; Guo, Lei

This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic system. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization criterion is compared with the mean-square-error minimization in the simulation results.

Integrating discrete stochastic models and single-cell experiments to infer predictive models of MAPK-induced transcription dynamics

NASA Astrophysics Data System (ADS)

Munsky, Brian

2015-03-01

MAPK signal-activated transcription plays central roles in myriad biological processes including stress adaptation responses and cell fate decisions. Recent single-cell and single-molecule experiments have advanced our ability to quantify the spatial, temporal, and stochastic fluctuations for such signals and their downstream effects on transcription regulation. This talk explores how integrating such experiments with discrete stochastic computational analyses can yield quantitative and predictive understanding of transcription regulation in both space and time. We use single-molecule mRNA fluorescence in situ hybridization (smFISH) experiments to reveal locations and numbers of multiple endogenous mRNA species in 100,000's of individual cells, at different times and under different genetic and environmental perturbations. We use finite state projection methods to precisely and efficiently compute the full joint probability distributions of these mRNA, which capture measured spatial, temporal and correlative fluctuations. By combining these experimental and computational tools with uncertainty quantification, we systematically compare models of varying complexity and select those which give optimally precise and accurate predictions in new situations. We use these tools to explore two MAPK-activated gene regulation pathways. In yeast adaptation to osmotic shock, we analyze Hog1 kinase activation of transcription for three different genes STL1 (osmotic stress), CTT1 (oxidative stress) and HSP12 (heat shock). In human osteosarcoma cells under serum induction, we analyze ERK activation of c-Fos transcription.

Monte-Carlo Simulations of Drug Delivery on Biofilms

NASA Astrophysics Data System (ADS)

Buldum, Alper; Simpson, Andrew

2013-03-01

The focus of this work is on biofilms that grow in the lungs of cystic fibrosis (CF) patients. A discrete model which describes the nutrient and biomass as discrete particles is created. Diffusion of the nutrient, consumption of the nutrient by microbial particles, and growth and decay of microbial particles are simulated using stochastic processes. Our model extends the complexity of the biofilm system by including the conversion and reversion of living bacteria into a hibernated state, known as persister bacteria. Another new contribution is the inclusion of antimicrobial in two forms: an aqueous solution and encapsulated in biodegradable nanoparticles. The bacteria population growth and spatial variation of drugs and their effectiveness are investigated in this work. Supported by NIH

Nonlinear Estimation of Discrete-Time Signals Under Random Observation Delay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caballero-Aguila, R.; Jimenez-Lopez, J. D.; Hermoso-Carazo, A.

2008-11-06

This paper presents an approximation to the nonlinear least-squares estimation problem of discrete-time stochastic signals using nonlinear observations with additive white noise which can be randomly delayed by one sampling time. The observation delay is modelled by a sequence of independent Bernoulli random variables whose values, zero or one, indicate that the real observation arrives on time or it is delayed and, hence, the available measurement to estimate the signal is not up-to-date. Assuming that the state-space model generating the signal is unknown and only the covariance functions of the processes involved in the observation equation are ready for use,more » a filtering algorithm based on linear approximations of the real observations is proposed.« less

Modelling uncertainty in incompressible flow simulation using Galerkin based generalized ANOVA

NASA Astrophysics Data System (ADS)

Chakraborty, Souvik; Chowdhury, Rajib

2016-11-01

This paper presents a new algorithm, referred to here as Galerkin based generalized analysis of variance decomposition (GG-ANOVA) for modelling input uncertainties and its propagation in incompressible fluid flow. The proposed approach utilizes ANOVA to represent the unknown stochastic response. Further, the unknown component functions of ANOVA are represented using the generalized polynomial chaos expansion (PCE). The resulting functional form obtained by coupling the ANOVA and PCE is substituted into the stochastic Navier-Stokes equation (NSE) and Galerkin projection is employed to decompose it into a set of coupled deterministic 'Navier-Stokes alike' equations. Temporal discretization of the set of coupled deterministic equations is performed by employing Adams-Bashforth scheme for convective term and Crank-Nicolson scheme for diffusion term. Spatial discretization is performed by employing finite difference scheme. Implementation of the proposed approach has been illustrated by two examples. In the first example, a stochastic ordinary differential equation has been considered. This example illustrates the performance of proposed approach with change in nature of random variable. Furthermore, convergence characteristics of GG-ANOVA has also been demonstrated. The second example investigates flow through a micro channel. Two case studies, namely the stochastic Kelvin-Helmholtz instability and stochastic vortex dipole, have been investigated. For all the problems results obtained using GG-ANOVA are in excellent agreement with benchmark solutions.

Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model

PubMed Central

Zheng, Wendong; Zeng, Pingping

2016-01-01

ABSTRACT Most of the empirical studies on stochastic volatility dynamics favour the 3/2 specification over the square-root (CIR) process in the Heston model. In the context of option pricing, the 3/2 stochastic volatility model (SVM) is reported to be able to capture the volatility skew evolution better than the Heston model. In this article, we make a thorough investigation on the analytic tractability of the 3/2 SVM by proposing a closed-form formula for the partial transform of the triple joint transition density which stand for the log asset price, the quadratic variation (continuous realized variance) and the instantaneous variance, respectively. Two distinct formulations are provided for deriving the main result. The closed-form partial transform enables us to deduce a variety of marginal partial transforms and characteristic functions and plays a crucial role in pricing discretely sampled variance derivatives and exotic options that depend on both the asset price and quadratic variation. Various applications and numerical examples on pricing moment swaps and timer options with discrete monitoring feature are given to demonstrate the versatility of the partial transform under the 3/2 model. PMID:28706460

Distributed fault detection over sensor networks with Markovian switching topologies

NASA Astrophysics Data System (ADS)

Ge, Xiaohua; Han, Qing-Long

2014-05-01

This paper deals with the distributed fault detection for discrete-time Markov jump linear systems over sensor networks with Markovian switching topologies. The sensors are scatteredly deployed in the sensor field and the fault detectors are physically distributed via a communication network. The system dynamics changes and sensing topology variations are modeled by a discrete-time Markov chain with incomplete mode transition probabilities. Each of these sensor nodes firstly collects measurement outputs from its all underlying neighboring nodes, processes these data in accordance with the Markovian switching topologies, and then transmits the processed data to the remote fault detector node. Network-induced delays and accumulated data packet dropouts are incorporated in the data transmission between the sensor nodes and the distributed fault detector nodes through the communication network. To generate localized residual signals, mode-independent distributed fault detection filters are proposed. By means of the stochastic Lyapunov functional approach, the residual system performance analysis is carried out such that the overall residual system is stochastically stable and the error between each residual signal and the fault signal is made as small as possible. Furthermore, a sufficient condition on the existence of the mode-independent distributed fault detection filters is derived in the simultaneous presence of incomplete mode transition probabilities, Markovian switching topologies, network-induced delays, and accumulated data packed dropouts. Finally, a stirred-tank reactor system is given to show the effectiveness of the developed theoretical results.

Stochastic dynamic modeling of regular and slow earthquakes

NASA Astrophysics Data System (ADS)

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 diffusion appears much slower than the particle velocity of each molecule. The concept of stochastic triggering originates in the Brownian walk model [Ide, 2008], and the present study introduces the stochastic dynamics into dynamic simulations. The stochastic dynamic model has the potential to explain both regular and slow earthquakes more realistically.

Phenotypic switching of populations of cells in a stochastic environment

NASA Astrophysics Data System (ADS)

Hufton, Peter G.; Lin, Yen Ting; Galla, Tobias

2018-02-01

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response. We focus on the case in which the environment switches randomly between discrete states. Starting from an individual-based model we derive stochastic differential equations to describe the dynamics, and obtain analytical expressions for the mean instantaneous growth rates based on the theory of piecewise-deterministic Markov processes. We show that optimal phenotypic responses are non-trivial for slow and intermediate environmental processes, and systematically compare the cases of periodic and random environments. The best response to random switching is more likely to be heterogeneity than in the case of deterministic periodic environments, net growth rates tend to be higher under stochastic environmental dynamics. The combined system of environment and population of cells can be interpreted as host-pathogen interaction, in which the host tries to choose environmental switching so as to minimise growth of the pathogen, and in which the pathogen employs a phenotypic switching optimised to increase its growth rate. We discuss the existence of Nash-like mutual best-response scenarios for such host-pathogen games.

Fixation, transient landscape, and diffusion dilemma in stochastic evolutionary game dynamics

NASA Astrophysics Data System (ADS)

Zhou, Da; Qian, Hong

2011-09-01

Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical “device” that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.

Analytical Models of Cross-Layer Protocol Optimization in Real-Time Wireless Sensor Ad Hoc Networks

NASA Astrophysics Data System (ADS)

Hortos, William S.

The real-time interactions among the nodes of a wireless sensor network (WSN) to cooperatively process data from multiple sensors are modeled. Quality-of-service (QoS) metrics are associated with the quality of fused information: throughput, delay, packet error rate, etc. Multivariate point process (MVPP) models of discrete random events in WSNs establish stochastic characteristics of optimal cross-layer protocols. Discrete-event, cross-layer interactions in mobile ad hoc network (MANET) protocols have been modeled using a set of concatenated design parameters and associated resource levels by the MVPPs. Characterization of the "best" cross-layer designs for a MANET is formulated by applying the general theory of martingale representations to controlled MVPPs. Performance is described in terms of concatenated protocol parameters and controlled through conditional rates of the MVPPs. Modeling limitations to determination of closed-form solutions versus explicit iterative solutions for ad hoc WSN controls are examined.

Noise in Neuronal and Electronic Circuits: A General Modeling Framework and Non-Monte Carlo Simulation Techniques.

PubMed

Kilinc, Deniz; Demir, Alper

2017-08-01

The brain is extremely energy efficient and remarkably robust in what it does despite the considerable variability and noise caused by the stochastic mechanisms in neurons and synapses. Computational modeling is a powerful tool that can help us gain insight into this important aspect of brain mechanism. A deep understanding and computational design tools can help develop robust neuromorphic electronic circuits and hybrid neuroelectronic systems. In this paper, we present a general modeling framework for biological neuronal circuits that systematically captures the nonstationary stochastic behavior of ion channels and synaptic processes. In this framework, fine-grained, discrete-state, continuous-time Markov chain models of both ion channels and synaptic processes are treated in a unified manner. Our modeling framework features a mechanism for the automatic generation of the corresponding coarse-grained, continuous-state, continuous-time stochastic differential equation models for neuronal variability and noise. Furthermore, we repurpose non-Monte Carlo noise analysis techniques, which were previously developed for analog electronic circuits, for the stochastic characterization of neuronal circuits both in time and frequency domain. We verify that the fast non-Monte Carlo analysis methods produce results with the same accuracy as computationally expensive Monte Carlo simulations. We have implemented the proposed techniques in a prototype simulator, where both biological neuronal and analog electronic circuits can be simulated together in a coupled manner.

Mimicking Nonequilibrium Steady States with Time-Periodic Driving

DTIC Science & Technology

2016-08-29

nonequilibrium steady states, and vice versa, within the theoretical framework of discrete-state stochastic thermodynamics . Nonequilibrium steady states...equilibrium [2], spontaneous relaxation towards equilibrium [3], nonequilibrium steady states generated by fixed thermodynamic forces [4], and stochastic pumps...paradigm, a system driven by fixed thermodynamic forces—such as temperature gradients or chemical potential differences— reaches a steady state in

Persistence of non-Markovian Gaussian stationary processes in discrete time

NASA Astrophysics Data System (ADS)

Nyberg, Markus; Lizana, Ludvig

2018-04-01

The persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval. Although persistence is a simple concept to understand, it is in general hard to calculate. Here we consider zero mean Gaussian stationary processes in discrete time n . Few results are known for the persistence P0(n ) in discrete time, except the large time behavior which is characterized by the nontrivial constant θ through P0(n ) ˜θn . Using a modified version of the independent interval approximation (IIA) that we developed before, we are able to calculate P0(n ) analytically in z -transform space in terms of the autocorrelation function A (n ) . If A (n )→0 as n →∞ , we extract θ numerically, while if A (n )=0 , for finite n >N , we find θ exactly (within the IIA). We apply our results to three special cases: the nearest-neighbor-correlated "first order moving average process", where A (n )=0 for n >1 , the double exponential-correlated "second order autoregressive process", where A (n ) =c1λ1n+c2λ2n , and power-law-correlated variables, where A (n ) ˜n-μ . Apart from the power-law case when μ <5 , we find excellent agreement with simulations.

A Discrete Probability Function Method for the Equation of Radiative Transfer

NASA Technical Reports Server (NTRS)

Sivathanu, Y. R.; Gore, J. P.

1993-01-01

A discrete probability function (DPF) method for the equation of radiative transfer is derived. The DPF is defined as the integral of the probability density function (PDF) over a discrete interval. The derivation allows the evaluation of the PDF of intensities leaving desired radiation paths including turbulence-radiation interactions without the use of computer intensive stochastic methods. The DPF method has a distinct advantage over conventional PDF methods since the creation of a partial differential equation from the equation of transfer is avoided. Further, convergence of all moments of intensity is guaranteed at the basic level of simulation unlike the stochastic method where the number of realizations for convergence of higher order moments increases rapidly. The DPF method is described for a representative path with approximately integral-length scale-sized spatial discretization. The results show good agreement with measurements in a propylene/air flame except for the effects of intermittency resulting from highly correlated realizations. The method can be extended to the treatment of spatial correlations as described in the Appendix. However, information regarding spatial correlations in turbulent flames is needed prior to the execution of this extension.

A Framework for the Optimization of Discrete-Event Simulation Models

NASA Technical Reports Server (NTRS)

Joshi, B. D.; Unal, R.; White, N. H.; Morris, W. D.

1996-01-01

With the growing use of computer modeling and simulation, in all aspects of engineering, the scope of traditional optimization has to be extended to include simulation models. Some unique aspects have to be addressed while optimizing via stochastic simulation models. The optimization procedure has to explicitly account for the randomness inherent in the stochastic measures predicted by the model. This paper outlines a general purpose framework for optimization of terminating discrete-event simulation models. The methodology combines a chance constraint approach for problem formulation, together with standard statistical estimation and analyses techniques. The applicability of the optimization framework is illustrated by minimizing the operation and support resources of a launch vehicle, through a simulation model.

Kalman filters for fractional discrete-time stochastic systems along with time-delay in the observation signal

NASA Astrophysics Data System (ADS)

Torabi, H.; Pariz, N.; Karimpour, A.

2016-02-01

This paper investigates fractional Kalman filters when time-delay is entered in the observation signal in the discrete-time stochastic fractional order state-space representation. After investigating the common fractional Kalman filter, we try to derive a fractional Kalman filter for time-delay fractional systems. A detailed derivation is given. Fractional Kalman filters will be used to estimate recursively the states of fractional order state-space systems based on minimizing the cost function when there is a constant time delay (d) in the observation signal. The problem will be solved by converting the filtering problem to a usual d-step prediction problem for delay-free fractional systems.

An Algebraic Construction of Duality Functions for the Stochastic {U_q( A_n^{(1)})} Vertex Model and Its Degenerations

NASA Astrophysics Data System (ADS)

Kuan, Jeffrey

2018-03-01

A recent paper (Kuniba in Nucl Phys B 913:248-277, 2016) introduced the stochastic U}_q(A_n^{(1)})} vertex model. The stochastic S-matrix is related to the R-matrix of the quantum group {U_q(A_n^{(1)})} by a gauge transformation. We will show that a certain function {D^+_{m intertwines with the transfer matrix and its space reversal. When interpreting the transfer matrix as the transition matrix of a discrete-time totally asymmetric particle system on the one-dimensional lattice Z , the function {D^+m} becomes a Markov duality function {Dm} which only depends on q and the vertical spin parameters μ_x. By considering degenerations in the spectral parameter, the duality results also hold on a finite lattice with closed boundary conditions, and for a continuous-time degeneration. This duality function had previously appeared in a multi-species ASEP(q, j) process (Kuan in A multi-species ASEP(q, j) and q-TAZRP with stochastic duality, 2017). The proof here uses that the R-matrix intertwines with the co-product, but does not explicitly use the Yang-Baxter equation. It will also be shown that the stochastic U}_q(A_n^{(1)})} is a multi-species version of a stochastic vertex model studied in Borodin and Petrov (Higher spin six vertex model and symmetric rational functions, 2016) and Corwin and Petrov (Commun Math Phys 343:651-700, 2016). This will be done by generalizing the fusion process of Corwin and Petrov (2016) and showing that it matches the fusion of Kulish and yu (Lett Math Phys 5:393-403, 1981) up to the gauge transformation. We also show, by direct computation, that the multi-species q-Hahn Boson process (which arises at a special value of the spectral parameter) also satisfies duality with respect to D_∞, generalizing the single-species result of Corwin (Int Math Res Not 2015:5577-5603, 2015).

Stochastic maps, continuous approximation, and stable distribution

NASA Astrophysics Data System (ADS)

Kessler, David A.; Burov, Stanislav

2017-10-01

A continuous approximation framework for general nonlinear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the Itô lemma, we obtain a Langevin type of equation. Specifically, we show how nonlinear maps give rise to a Langevin description that involves multiplicative noise. The multiplicative nature of the noise induces an additional effective force, not present in the absence of noise. We further exploit the continuum description and provide an explicit formula for the stable distribution of the stochastic map and conditions for its existence. Our results are in good agreement with numerical simulations of several maps.

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vidal-Codina, F., E-mail: fvidal@mit.edu; Nguyen, N.C., E-mail: cuongng@mit.edu; Giles, M.B., E-mail: mike.giles@maths.ox.ac.uk

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basismore » approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.« less

Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays

NASA Astrophysics Data System (ADS)

Wan, Li; Zhou, Qinghua

2007-10-01

The stability property of stochastic hybrid bidirectional associate memory (BAM) neural networks with discrete delays is considered. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the delay-independent sufficient conditions to guarantee the exponential stability of the equilibrium solution for such networks are given by using the nonnegative semimartingale convergence theorem.

Mimicking Nonequilibrium Steady States with Time-Periodic Driving (Open Source)

DTIC Science & Technology

2016-05-18

nonequilibrium steady states, and vice versa, within the theoretical framework of discrete-state stochastic thermodynamics . Nonequilibrium steady states...equilibrium [2], spontaneous relaxation towards equilibrium [3], nonequilibrium steady states generated by fixed thermodynamic forces [4], and stochastic pumps...paradigm, a system driven by fixed thermodynamic forces—such as temperature gradients or chemical potential differences— reaches a steady state in

Intermittency inhibited by transport: An exactly solvable model

NASA Astrophysics Data System (ADS)

Zanette, Damián H.

1994-04-01

Transport is incorporated in a discrete-time stochastic model of a system undergoing autocatalytic reactions of the type A-->2A and A-->0, whose population field is known to exhibit spatiotemporal intermittency. The temporal evolution is exactly solved, and it is shown that if the transport process is strong enough, intermittency is inhibited. This inhibition is nonuniform, in the sense that, as transport is strengthened, low-order population moments are affected before the high-order ones. Numerical simulations are presented to support the analytical results.

On the Computational Complexity of Stochastic Scheduling Problems,

DTIC Science & Technology

1981-09-01

Survey": 1979, Ann. Discrete Math . 5, pp. 287-326. i I (.4) Karp, R.M., "Reducibility Among Combinatorial Problems": 1972, R.E. Miller and J.W...Weighted Completion Time Subject to Precedence Constraints": 1978, Ann. Discrete Math . 2, pp. 75-90. (8) Lawler, E.L. and J.W. Moore, "A Functional

Likelihood-based inference for discretely observed birth-death-shift processes, with applications to evolution of mobile genetic elements.

PubMed

Xu, Jason; Guttorp, Peter; Kato-Maeda, Midori; Minin, Vladimir N

2015-12-01

Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements-important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a multi-type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low-dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply broadly to multi-type branching processes whose rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections. © 2015, The International Biometric Society.

On orthogonality preserving quadratic stochastic operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-05-15

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

State-dependent biasing method for importance sampling in the weighted stochastic simulation algorithm.

PubMed

Roh, Min K; Gillespie, Dan T; Petzold, Linda R

2010-11-07

The weighted stochastic simulation algorithm (wSSA) was developed by Kuwahara and Mura [J. Chem. Phys. 129, 165101 (2008)] to efficiently estimate the probabilities of rare events in discrete stochastic systems. The wSSA uses importance sampling to enhance the statistical accuracy in the estimation of the probability of the rare event. The original algorithm biases the reaction selection step with a fixed importance sampling parameter. In this paper, we introduce a novel method where the biasing parameter is state-dependent. The new method features improved accuracy, efficiency, and robustness.

Adaptive Microwave Staring Correlated Imaging for Targets Appearing in Discrete Clusters.

PubMed

Tian, Chao; Jiang, Zheng; Chen, Weidong; Wang, Dongjin

2017-10-21

Microwave staring correlated imaging (MSCI) can achieve ultra-high resolution in real aperture staring radar imaging using the correlated imaging process (CIP) under all-weather and all-day circumstances. The CIP must combine the received echo signal with the temporal-spatial stochastic radiation field. However, a precondition of the CIP is that the continuous imaging region must be discretized to a fine grid, and the measurement matrix should be accurately computed, which makes the imaging process highly complex when the MSCI system observes a wide area. This paper proposes an adaptive imaging approach for the targets in discrete clusters to reduce the complexity of the CIP. The approach is divided into two main stages. First, as discrete clustered targets are distributed in different range strips in the imaging region, the transmitters of the MSCI emit narrow-pulse waveforms to separate the echoes of the targets in different strips in the time domain; using spectral entropy, a modified method robust against noise is put forward to detect the echoes of the discrete clustered targets, based on which the strips with targets can be adaptively located. Second, in a strip with targets, the matched filter reconstruction algorithm is used to locate the regions with targets, and only the regions of interest are discretized to a fine grid; sparse recovery is used, and the band exclusion is used to maintain the non-correlation of the dictionary. Simulation results are presented to demonstrate that the proposed approach can accurately and adaptively locate the regions with targets and obtain high-quality reconstructed images.

Delay chemical master equation: direct and closed-form solutions

PubMed Central

Leier, Andre; Marquez-Lago, Tatiana T.

2015-01-01

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived. PMID:26345616

Delay chemical master equation: direct and closed-form solutions.

PubMed

Leier, Andre; Marquez-Lago, Tatiana T

2015-07-08

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.

Small-scale plasticity critically needs a new mechanics description

NASA Astrophysics Data System (ADS)

Ngan, Alfonso H. W.

2013-06-01

Continuum constitutive laws describe the plastic deformation of materials as a smooth, continuously differentiable process. However, provided that the measurement is done with a fine enough resolution, the plastic deformation of real materials is often found to comprise discrete events usually nanometric in size. For bulk-sized specimens, such nanoscale events are minute compared with the specimen size, and so their associated strain changes are negligibly small, and this is why the continuum laws work well. However, when the specimen size is in the micrometer scale or smaller, the strain changes due to the discrete events could be significant, and the continuum description would be highly unsatisfactory. Yet, because of the advent of microtechnology and nanotechnolgy, small-sized materials will be increasingly used, and so there is a strong need to develop suitable replacement descriptions for plasticity of small materials. As the occurrence of the discrete plastic events is also strongly stochastic, their satisfactory description should also be one of a probabilistic, rather than deterministic, nature.

Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems

NASA Astrophysics Data System (ADS)

Mahdi Alavi, S. M.; Saif, Mehrdad

2013-12-01

This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.

Nonstationary stochastic charge fluctuations of a dust particle in plasmas.

PubMed

Shotorban, B

2011-06-01

Stochastic charge fluctuations of a dust particle that are due to discreteness of electrons and ions in plasmas can be described by a one-step process master equation [T. Matsoukas and M. Russell, J. Appl. Phys. 77, 4285 (1995)] with no exact solution. In the present work, using the system size expansion method of Van Kampen along with the linear noise approximation, a Fokker-Planck equation with an exact Gaussian solution is developed by expanding the master equation. The Gaussian solution has time-dependent mean and variance governed by two ordinary differential equations modeling the nonstationary process of dust particle charging. The model is tested via the comparison of its results to the results obtained by solving the master equation numerically. The electron and ion currents are calculated through the orbital motion limited theory. At various times of the nonstationary process of charging, the model results are in a very good agreement with the master equation results. The deviation is more significant when the standard deviation of the charge is comparable to the mean charge in magnitude.

A stochastic estimation procedure for intermittently-observed semi-Markov multistate models with back transitions.

PubMed

Aralis, Hilary; Brookmeyer, Ron

2017-01-01

Multistate models provide an important method for analyzing a wide range of life history processes including disease progression and patient recovery following medical intervention. Panel data consisting of the states occupied by an individual at a series of discrete time points are often used to estimate transition intensities of the underlying continuous-time process. When transition intensities depend on the time elapsed in the current state and back transitions between states are possible, this intermittent observation process presents difficulties in estimation due to intractability of the likelihood function. In this manuscript, we present an iterative stochastic expectation-maximization algorithm that relies on a simulation-based approximation to the likelihood function and implement this algorithm using rejection sampling. In a simulation study, we demonstrate the feasibility and performance of the proposed procedure. We then demonstrate application of the algorithm to a study of dementia, the Nun Study, consisting of intermittently-observed elderly subjects in one of four possible states corresponding to intact cognition, impaired cognition, dementia, and death. We show that the proposed stochastic expectation-maximization algorithm substantially reduces bias in model parameter estimates compared to an alternative approach used in the literature, minimal path estimation. We conclude that in estimating intermittently observed semi-Markov models, the proposed approach is a computationally feasible and accurate estimation procedure that leads to substantial improvements in back transition estimates.

MARKOV: A methodology for the solution of infinite time horizon MARKOV decision processes

USGS Publications Warehouse

Williams, B.K.

1988-01-01

Algorithms are described for determining optimal policies for finite state, finite action, infinite discrete time horizon Markov decision processes. Both value-improvement and policy-improvement techniques are used in the algorithms. Computing procedures are also described. The algorithms are appropriate for processes that are either finite or infinite, deterministic or stochastic, discounted or undiscounted, in any meaningful combination of these features. Computing procedures are described in terms of initial data processing, bound improvements, process reduction, and testing and solution. Application of the methodology is illustrated with an example involving natural resource management. Management implications of certain hypothesized relationships between mallard survival and harvest rates are addressed by applying the optimality procedures to mallard population models.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

PubMed Central

Chevalier, Michael W.; El-Samad, Hana

2014-01-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled. PMID:25481130

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

NASA Astrophysics Data System (ADS)

Chevalier, Michael W.; El-Samad, Hana

2014-12-01

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.

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

NASA Astrophysics Data System (ADS)

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 partitioning for hybrid simulation of the bistable HIV-1 transactivation network.

PubMed

Griffith, Mark; Courtney, Tod; Peccoud, Jean; Sanders, William H

2006-11-15

The stochastic kinetics of a well-mixed chemical system, governed by the chemical Master equation, can be simulated using the exact methods of Gillespie. However, these methods do not scale well as systems become more complex and larger models are built to include reactions with widely varying rates, since the computational burden of simulation increases with the number of reaction events. Continuous models may provide an approximate solution and are computationally less costly, but they fail to capture the stochastic behavior of small populations of macromolecules. In this article we present a hybrid simulation algorithm that dynamically partitions the system into subsets of continuous and discrete reactions, approximates the continuous reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte Carlo method for generating discrete reaction events according to a time-dependent propensity. Our approach to partitioning is improved such that we dynamically partition the system of reactions, based on a threshold relative to the distribution of propensities in the discrete subset. We have implemented the hybrid algorithm in an extensible framework, utilizing two rigorous ODE solvers to approximate the continuous reactions, and use an example model to illustrate the accuracy and potential speedup of the algorithm when compared with exact stochastic simulation. Software and benchmark models used for this publication can be made available upon request from the authors.

Delay-distribution-dependent H∞ state estimation for delayed neural networks with (x,v)-dependent noises and fading channels.

PubMed

Sheng, Li; Wang, Zidong; Tian, Engang; Alsaadi, Fuad E

2016-12-01

This paper deals with the H ∞ state estimation problem for a class of discrete-time neural networks with stochastic delays subject to state- and disturbance-dependent noises (also called (x,v)-dependent noises) and fading channels. The time-varying stochastic delay takes values on certain intervals with known probability distributions. The system measurement is transmitted through fading channels described by the Rice fading model. The aim of the addressed problem is to design a state estimator such that the estimation performance is guaranteed in the mean-square sense against admissible stochastic time-delays, stochastic noises as well as stochastic fading signals. By employing the stochastic analysis approach combined with the Kronecker product, several delay-distribution-dependent conditions are derived to ensure that the error dynamics of the neuron states is stochastically stable with prescribed H ∞ performance. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Fluctuation Induced Almost Invariant Sets

DTIC Science & Technology

2006-12-28

Planck) for the probability density function [15], discrete dynamical systems benefit from using the Frobenius - Perron operator (FP) formalism [12] to...from epidemiology. Conclusions are summarized in Section 4. II. GENERAL THEORY A. Stochastic Frobenius - Perron operator We define the Frobenius - Perron ...function ν(x). The stochastic Frobenius - 3 Perron (SFP) operator is defined to be PF [ρ(x)] = ∫ M ν(x− F (y))ρ(y)dy. (4) For our applications, we will

A new computer code for discrete fracture network modelling

NASA Astrophysics Data System (ADS)

Xu, Chaoshui; Dowd, Peter

2010-03-01

The authors describe a comprehensive software package for two- and three-dimensional stochastic rock fracture simulation using marked point processes. Fracture locations can be modelled by a Poisson, a non-homogeneous, a cluster or a Cox point process; fracture geometries and properties are modelled by their respective probability distributions. Virtual sampling tools such as plane, window and scanline sampling are included in the software together with a comprehensive set of statistical tools including histogram analysis, probability plots, rose diagrams and hemispherical projections. The paper describes in detail the theoretical basis of the implementation and provides a case study in rock fracture modelling to demonstrate the application of the software.

Parallel discrete-event simulation schemes with heterogeneous processing elements.

PubMed

Kim, Yup; Kwon, Ikhyun; Chae, Huiseung; Yook, Soon-Hyung

2014-07-01

To understand the effects of nonidentical processing elements (PEs) on parallel discrete-event simulation (PDES) schemes, two stochastic growth models, the restricted solid-on-solid (RSOS) model and the Family model, are investigated by simulations. The RSOS model is the model for the PDES scheme governed by the Kardar-Parisi-Zhang equation (KPZ scheme). The Family model is the model for the scheme governed by the Edwards-Wilkinson equation (EW scheme). Two kinds of distributions for nonidentical PEs are considered. In the first kind computing capacities of PEs are not much different, whereas in the second kind the capacities are extremely widespread. The KPZ scheme on the complex networks shows the synchronizability and scalability regardless of the kinds of PEs. The EW scheme never shows the synchronizability for the random configuration of PEs of the first kind. However, by regularizing the arrangement of PEs of the first kind, the EW scheme is made to show the synchronizability. In contrast, EW scheme never shows the synchronizability for any configuration of PEs of the second kind.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Hang, E-mail: hangchen@mit.edu; Thill, Peter; Cao, Jianshu

In biochemical systems, intrinsic noise may drive the system switch from one stable state to another. We investigate how kinetic switching between stable states in a bistable network is influenced by dynamic disorder, i.e., fluctuations in the rate coefficients. Using the geometric minimum action method, we first investigate the optimal transition paths and the corresponding minimum actions based on a genetic toggle switch model in which reaction coefficients draw from a discrete probability distribution. For the continuous probability distribution of the rate coefficient, we then consider two models of dynamic disorder in which reaction coefficients undergo different stochastic processes withmore » the same stationary distribution. In one, the kinetic parameters follow a discrete Markov process and in the other they follow continuous Langevin dynamics. We find that regulation of the parameters modulating the dynamic disorder, as has been demonstrated to occur through allosteric control in bistable networks in the immune system, can be crucial in shaping the statistics of optimal transition paths, transition probabilities, and the stationary probability distribution of the network.« less

Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases

NASA Astrophysics Data System (ADS)

Lundengârd, Karl; Ogutu, Carolyne; Silvestrov, Sergei; Ni, Ying; Weke, Patrick

2017-01-01

In order to describe and analyze the quantitative behavior of stochastic processes, such as the process followed by a financial asset, various discretization methods are used. One such set of methods are lattice models where a time interval is divided into equal time steps and the rate of change for the process is restricted to a particular set of values in each time step. The well-known binomial- and trinomial models are the most commonly used in applications, although several kinds of higher order models have also been examined. Here we will examine various ways of designing higher order lattice schemes with different node placements in order to guarantee moment-matching with the process.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavlou, A. T.; Betzler, B. R.; Burke, T. P.

Uncertainties in the composition and fabrication of fuel compacts for the Fort St. Vrain (FSV) high temperature gas reactor have been studied by performing eigenvalue sensitivity studies that represent the key uncertainties for the FSV neutronic analysis. The uncertainties for the TRISO fuel kernels were addressed by developing a suite of models for an 'average' FSV fuel compact that models the fuel as (1) a mixture of two different TRISO fuel particles representing fissile and fertile kernels, (2) a mixture of four different TRISO fuel particles representing small and large fissile kernels and small and large fertile kernels and (3)more » a stochastic mixture of the four types of fuel particles where every kernel has its diameter sampled from a continuous probability density function. All of the discrete diameter and continuous diameter fuel models were constrained to have the same fuel loadings and packing fractions. For the non-stochastic discrete diameter cases, the MCNP compact model arranged the TRISO fuel particles on a hexagonal honeycomb lattice. This lattice-based fuel compact was compared to a stochastic compact where the locations (and kernel diameters for the continuous diameter cases) of the fuel particles were randomly sampled. Partial core configurations were modeled by stacking compacts into fuel columns containing graphite. The differences in eigenvalues between the lattice-based and stochastic models were small but the runtime of the lattice-based fuel model was roughly 20 times shorter than with the stochastic-based fuel model. (authors)« less

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

PubMed Central

Müller, Eike H.; Scheichl, Rob; Shardlow, Tony

2015-01-01

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy. PMID:27547075

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

PubMed

Müller, Eike H; Scheichl, Rob; Shardlow, Tony

2015-04-08

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

Acceleration of discrete stochastic biochemical simulation using GPGPU.

PubMed

Sumiyoshi, Kei; Hirata, Kazuki; Hiroi, Noriko; Funahashi, Akira

2015-01-01

For systems made up of a small number of molecules, such as a biochemical network in a single cell, a simulation requires a stochastic approach, instead of a deterministic approach. The stochastic simulation algorithm (SSA) simulates the stochastic behavior of a spatially homogeneous system. Since stochastic approaches produce different results each time they are used, multiple runs are required in order to obtain statistical results; this results in a large computational cost. We have implemented a parallel method for using SSA to simulate a stochastic model; the method uses a graphics processing unit (GPU), which enables multiple realizations at the same time, and thus reduces the computational time and cost. During the simulation, for the purpose of analysis, each time course is recorded at each time step. A straightforward implementation of this method on a GPU is about 16 times faster than a sequential simulation on a CPU with hybrid parallelization; each of the multiple simulations is run simultaneously, and the computational tasks within each simulation are parallelized. We also implemented an improvement to the memory access and reduced the memory footprint, in order to optimize the computations on the GPU. We also implemented an asynchronous data transfer scheme to accelerate the time course recording function. To analyze the acceleration of our implementation on various sizes of model, we performed SSA simulations on different model sizes and compared these computation times to those for sequential simulations with a CPU. When used with the improved time course recording function, our method was shown to accelerate the SSA simulation by a factor of up to 130.

Acceleration of discrete stochastic biochemical simulation using GPGPU

PubMed Central

Sumiyoshi, Kei; Hirata, Kazuki; Hiroi, Noriko; Funahashi, Akira

2015-01-01

For systems made up of a small number of molecules, such as a biochemical network in a single cell, a simulation requires a stochastic approach, instead of a deterministic approach. The stochastic simulation algorithm (SSA) simulates the stochastic behavior of a spatially homogeneous system. Since stochastic approaches produce different results each time they are used, multiple runs are required in order to obtain statistical results; this results in a large computational cost. We have implemented a parallel method for using SSA to simulate a stochastic model; the method uses a graphics processing unit (GPU), which enables multiple realizations at the same time, and thus reduces the computational time and cost. During the simulation, for the purpose of analysis, each time course is recorded at each time step. A straightforward implementation of this method on a GPU is about 16 times faster than a sequential simulation on a CPU with hybrid parallelization; each of the multiple simulations is run simultaneously, and the computational tasks within each simulation are parallelized. We also implemented an improvement to the memory access and reduced the memory footprint, in order to optimize the computations on the GPU. We also implemented an asynchronous data transfer scheme to accelerate the time course recording function. To analyze the acceleration of our implementation on various sizes of model, we performed SSA simulations on different model sizes and compared these computation times to those for sequential simulations with a CPU. When used with the improved time course recording function, our method was shown to accelerate the SSA simulation by a factor of up to 130. PMID:25762936

Discrete-event system simulation on small and medium enterprises productivity improvement

NASA Astrophysics Data System (ADS)

Sulistio, J.; Hidayah, N. A.

2017-12-01

Small and medium industries in Indonesia is currently developing. The problem faced by SMEs is the difficulty of meeting growing demand coming into the company. Therefore, SME need an analysis and evaluation on its production process in order to meet all orders. The purpose of this research is to increase the productivity of SMEs production floor by applying discrete-event system simulation. This method preferred because it can solve complex problems die to the dynamic and stochastic nature of the system. To increase the credibility of the simulation, model validated by cooperating the average of two trials, two trials of variance and chi square test. Afterwards, Benferroni method applied to development several alternatives. The article concludes that, the productivity of SMEs production floor increased up to 50% by adding the capacity of dyeing and drying machines.

Cross-Paradigm Simulation Modeling: Challenges and Successes

DTIC Science & Technology

2011-12-01

is also highlighted. 2.1 Discrete-Event Simulation Discrete-event simulation ( DES ) is a modeling method for stochastic, dynamic models where...which almost anything can be coded; models can be incredibly detailed. Most commercial DES software has a graphical interface which allows the user to...results. Although the above definition is the commonly accepted definition of DES , there are two different worldviews that dominate DES modeling today: a

Adaptive Decision Making Using Probabilistic Programming and Stochastic Optimization

DTIC Science & Technology

2018-01-01

world optimization problems (and hence 16 Approved for Public Release (PA); Distribution Unlimited Pred. demand (uncertain; discrete ...simplify the setting, we further assume that the demands are discrete , taking on values d1, . . . , dk with probabilities (conditional on x) (pθ)i ≡ p...Tyrrell Rockafellar. Implicit functions and solution mappings. Springer Monogr. Math ., 2009. Anthony V Fiacco and Yo Ishizuka. Sensitivity and stability

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

On the Probability of Error and Stochastic Resonance in Discrete Memoryless Channels

DTIC Science & Technology

2013-12-01

Information - Driven Doppler Shift Estimation and Compensation Methods for Underwater Wireless Sensor Networks ”, which is to analyze and develop... underwater wireless sensor networks . We formulated an analytic relationship that relates the average probability of error to the systems parameters, the...thesis, we studied the performance of Discrete Memoryless Channels (DMC), arising in the context of cooperative underwater wireless sensor networks

Discrete and continuous models for tissue growth and shrinkage.

PubMed

Yates, Christian A

2014-06-07

The incorporation of domain growth into stochastic models of biological processes is of increasing interest to mathematical modellers and biologists alike. In many situations, especially in developmental biology, the growth of the underlying tissue domain plays an important role in the redistribution of particles (be they cells or molecules) which may move and react atop the domain. Although such processes have largely been modelled using deterministic, continuum models there is an increasing appetite for individual-based stochastic models which can capture the fine details of the biological movement processes which are being elucidated by modern experimental techniques, and also incorporate the inherent stochasticity of such systems. In this work we study a simple stochastic model of domain growth. From a basic version of this model, Hywood et al. (2013) were able to derive a Fokker-Plank equation (FPE) (in this case an advection-diffusion partial differential equation on a growing domain) which describes the evolution of the probability density of some tracer particles on the domain. We extend their work so that a variety of different domain growth mechanisms can be incorporated and demonstrate a good agreement between the mean tracer density and the solution of the FPE in each case. In addition we incorporate domain shrinkage (via element death) into our individual-level model and demonstrate that we are able to derive coefficients for the FPE in this case as well. For situations in which the drift and diffusion coefficients are not readily available we introduce a numerical coefficient estimation approach and demonstrate the accuracy of this approach by comparing it with situations in which an analytical solution is obtainable. Copyright © 2014 Elsevier Ltd. All rights reserved.

A scalable moment-closure approximation for large-scale biochemical reaction networks

PubMed Central

Kazeroonian, Atefeh; Theis, Fabian J.; Hasenauer, Jan

2017-01-01

Abstract Motivation: Stochastic molecular processes are a leading cause of cell-to-cell variability. Their dynamics are often described by continuous-time discrete-state Markov chains and simulated using stochastic simulation algorithms. As these stochastic simulations are computationally demanding, ordinary differential equation models for the dynamics of the statistical moments have been developed. The number of state variables of these approximating models, however, grows at least quadratically with the number of biochemical species. This limits their application to small- and medium-sized processes. Results: In this article, we present a scalable moment-closure approximation (sMA) for the simulation of statistical moments of large-scale stochastic processes. The sMA exploits the structure of the biochemical reaction network to reduce the covariance matrix. We prove that sMA yields approximating models whose number of state variables depends predominantly on local properties, i.e. the average node degree of the reaction network, instead of the overall network size. The resulting complexity reduction is assessed by studying a range of medium- and large-scale biochemical reaction networks. To evaluate the approximation accuracy and the improvement in computational efficiency, we study models for JAK2/STAT5 signalling and NFκB signalling. Our method is applicable to generic biochemical reaction networks and we provide an implementation, including an SBML interface, which renders the sMA easily accessible. Availability and implementation: The sMA is implemented in the open-source MATLAB toolbox CERENA and is available from https://github.com/CERENADevelopers/CERENA. Contact: jan.hasenauer@helmholtz-muenchen.de or atefeh.kazeroonian@tum.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:28881983

Species survival emerge from rare events of individual migration

NASA Astrophysics Data System (ADS)

Zelnik, Yuval R.; Solomon, Sorin; Yaari, Gur

2015-01-01

Ecosystems greatly vary in their species composition and interactions, yet they all show remarkable resilience to external influences. Recent experiments have highlighted the significant effects of spatial structure and connectivity on the extinction and survival of species. It has also been emphasized lately that in order to study extinction dynamics reliably, it is essential to incorporate stochasticity, and in particular the discrete nature of populations, into the model. Accordingly, we applied a bottom-up modeling approach that includes both spatial features and stochastic interactions to study survival mechanisms of species. Using the simplest spatial extension of the Lotka-Volterra predator-prey model with competition, subject to demographic and environmental noise, we were able to systematically study emergent properties of this rich system. By scanning the relevant parameter space, we show that both survival and extinction processes often result from a combination of habitat fragmentation and individual rare events of recolonization.

Species survival emerge from rare events of individual migration.

PubMed

Zelnik, Yuval R; Solomon, Sorin; Yaari, Gur

2015-01-19

Ecosystems greatly vary in their species composition and interactions, yet they all show remarkable resilience to external influences. Recent experiments have highlighted the significant effects of spatial structure and connectivity on the extinction and survival of species. It has also been emphasized lately that in order to study extinction dynamics reliably, it is essential to incorporate stochasticity, and in particular the discrete nature of populations, into the model. Accordingly, we applied a bottom-up modeling approach that includes both spatial features and stochastic interactions to study survival mechanisms of species. Using the simplest spatial extension of the Lotka-Volterra predator-prey model with competition, subject to demographic and environmental noise, we were able to systematically study emergent properties of this rich system. By scanning the relevant parameter space, we show that both survival and extinction processes often result from a combination of habitat fragmentation and individual rare events of recolonization.

Networked iterative learning control design for discrete-time systems with stochastic communication delay in input and output channels

NASA Astrophysics Data System (ADS)

Liu, Jian; Ruan, Xiaoe

2017-07-01

This paper develops two kinds of derivative-type networked iterative learning control (NILC) schemes for repetitive discrete-time systems with stochastic communication delay occurred in input and output channels and modelled as 0-1 Bernoulli-type stochastic variable. In the two schemes, the delayed signal of the current control input is replaced by the synchronous input utilised at the previous iteration, whilst for the delayed signal of the system output the one scheme substitutes it by the synchronous predetermined desired trajectory and the other takes it by the synchronous output at the previous operation, respectively. In virtue of the mathematical expectation, the tracking performance is analysed which exhibits that for both the linear time-invariant and nonlinear affine systems the two kinds of NILCs are convergent under the assumptions that the probabilities of communication delays are adequately constrained and the product of the input-output coupling matrices is full-column rank. Last, two illustrative examples are presented to demonstrate the effectiveness and validity of the proposed NILC schemes.

Stochastic flux analysis of chemical reaction networks

PubMed Central

2013-01-01

Background Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. Results We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. Conclusions We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network. PMID:24314153

Stochastic flux analysis of chemical reaction networks.

PubMed

Kahramanoğulları, Ozan; Lynch, James F

2013-12-07

Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network.

Estimating rare events in biochemical systems using conditional sampling.

PubMed

Sundar, V S

2017-01-28

The paper focuses on development of variance reduction strategies to estimate rare events in biochemical systems. Obtaining this probability using brute force Monte Carlo simulations in conjunction with the stochastic simulation algorithm (Gillespie's method) is computationally prohibitive. To circumvent this, important sampling tools such as the weighted stochastic simulation algorithm and the doubly weighted stochastic simulation algorithm have been proposed. However, these strategies require an additional step of determining the important region to sample from, which is not straightforward for most of the problems. In this paper, we apply the subset simulation method, developed as a variance reduction tool in the context of structural engineering, to the problem of rare event estimation in biochemical systems. The main idea is that the rare event probability is expressed as a product of more frequent conditional probabilities. These conditional probabilities are estimated with high accuracy using Monte Carlo simulations, specifically the Markov chain Monte Carlo method with the modified Metropolis-Hastings algorithm. Generating sample realizations of the state vector using the stochastic simulation algorithm is viewed as mapping the discrete-state continuous-time random process to the standard normal random variable vector. This viewpoint opens up the possibility of applying more sophisticated and efficient sampling schemes developed elsewhere to problems in stochastic chemical kinetics. The results obtained using the subset simulation method are compared with existing variance reduction strategies for a few benchmark problems, and a satisfactory improvement in computational time is demonstrated.

A mathematical approach for evaluating Markov models in continuous time without discrete-event simulation.

PubMed

van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F

2013-08-01

Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.

THE DISTRIBUTION OF ROUNDS FIRED IN STOCHASTIC DUELS

DTIC Science & Technology

This paper continues the development of the theory of Stochastic Duels to include the distribution of the number of rounds fired. Most generally...the duel between two contestants who fire at each other with constant kill probabilities per round is considered. The time between rounds fired may be...at the beginning of the duel may be limited and is a discrete random variable. Besides the distribution of rounds fired, its first two moments and

A Combined Remote Sensing-Numerical Modelling Approach to the Stability Analysis of Delabole Slate Quarry, Cornwall, UK

NASA Astrophysics Data System (ADS)

Havaej, Mohsen; Coggan, John; Stead, Doug; Elmo, Davide

2016-04-01

Rock slope geometry and discontinuity properties are among the most important factors in realistic rock slope analysis yet they are often oversimplified in numerical simulations. This is primarily due to the difficulties in obtaining accurate structural and geometrical data as well as the stochastic representation of discontinuities. Recent improvements in both digital data acquisition and incorporation of discrete fracture network data into numerical modelling software have provided better tools to capture rock mass characteristics, slope geometries and digital terrain models allowing more effective modelling of rock slopes. Advantages of using improved data acquisition technology include safer and faster data collection, greater areal coverage, and accurate data geo-referencing far exceed limitations due to orientation bias and occlusion. A key benefit of a detailed point cloud dataset is the ability to measure and evaluate discontinuity characteristics such as orientation, spacing/intensity and persistence. This data can be used to develop a discrete fracture network which can be imported into the numerical simulations to study the influence of the stochastic nature of the discontinuities on the failure mechanism. We demonstrate the application of digital terrestrial photogrammetry in discontinuity characterization and distinct element simulations within a slate quarry. An accurately geo-referenced photogrammetry model is used to derive the slope geometry and to characterize geological structures. We first show how a discontinuity dataset, obtained from a photogrammetry model can be used to characterize discontinuities and to develop discrete fracture networks. A deterministic three-dimensional distinct element model is then used to investigate the effect of some key input parameters (friction angle, spacing and persistence) on the stability of the quarry slope model. Finally, adopting a stochastic approach, discrete fracture networks are used as input for 3D distinct element simulations to better understand the stochastic nature of the geological structure and its effect on the quarry slope failure mechanism. The numerical modelling results highlight the influence of discontinuity characteristics and kinematics on the slope failure mechanism and the variability in the size and shape of the failed blocks.

Accounting for stimulus-specific variation in precision reveals a discrete capacity limit in visual working memory

PubMed Central

Pratte, Michael S.; Park, Young Eun; Rademaker, Rosanne L.; Tong, Frank

2016-01-01

If we view a visual scene that contains many objects, then momentarily close our eyes, some details persist while others seem to fade. Discrete models of visual working memory (VWM) assume that only a few items can be actively maintained in memory, beyond which pure guessing will emerge. Alternatively, continuous resource models assume that all items in a visual scene can be stored with some precision. Distinguishing between these competing models is challenging, however, as resource models that allow for stochastically variable precision (across items and trials) can produce error distributions that resemble random guessing behavior. Here, we evaluated the hypothesis that a major source of variability in VWM performance arises from systematic variation in precision across the stimuli themselves; such stimulus-specific variability can be incorporated into both discrete-capacity and variable-precision resource models. Participants viewed multiple oriented gratings, and then reported the orientation of a cued grating from memory. When modeling the overall distribution of VWM errors, we found that the variable-precision resource model outperformed the discrete model. However, VWM errors revealed a pronounced “oblique effect”, with larger errors for oblique than cardinal orientations. After this source of variability was incorporated into both models, we found that the discrete model provided a better account of VWM errors. Our results demonstrate that variable precision across the stimulus space can lead to an unwarranted advantage for resource models that assume stochastically variable precision. When these deterministic sources are adequately modeled, human working memory performance reveals evidence of a discrete capacity limit. PMID:28004957

Accounting for stimulus-specific variation in precision reveals a discrete capacity limit in visual working memory.

PubMed

Pratte, Michael S; Park, Young Eun; Rademaker, Rosanne L; Tong, Frank

2017-01-01

If we view a visual scene that contains many objects, then momentarily close our eyes, some details persist while others seem to fade. Discrete models of visual working memory (VWM) assume that only a few items can be actively maintained in memory, beyond which pure guessing will emerge. Alternatively, continuous resource models assume that all items in a visual scene can be stored with some precision. Distinguishing between these competing models is challenging, however, as resource models that allow for stochastically variable precision (across items and trials) can produce error distributions that resemble random guessing behavior. Here, we evaluated the hypothesis that a major source of variability in VWM performance arises from systematic variation in precision across the stimuli themselves; such stimulus-specific variability can be incorporated into both discrete-capacity and variable-precision resource models. Participants viewed multiple oriented gratings, and then reported the orientation of a cued grating from memory. When modeling the overall distribution of VWM errors, we found that the variable-precision resource model outperformed the discrete model. However, VWM errors revealed a pronounced "oblique effect," with larger errors for oblique than cardinal orientations. After this source of variability was incorporated into both models, we found that the discrete model provided a better account of VWM errors. Our results demonstrate that variable precision across the stimulus space can lead to an unwarranted advantage for resource models that assume stochastically variable precision. When these deterministic sources are adequately modeled, human working memory performance reveals evidence of a discrete capacity limit. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Diffusion of multiple species with excluded-volume effects.

PubMed

Bruna, Maria; Chapman, S Jonathan

2012-11-28

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results.

Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2018-05-01

In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics. This result provides a new perspective for a better understanding of how environmental fluctuations may contribute to the evolution of behavioral diversity.

Zonostrophic instability driven by discrete particle noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

St-Onge, D. A.; Krommes, J. A.

The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just below the threshold for linear instability. The scenario provides a new interpretation of the random forcing that is ubiquitously invoked in stochastic models such as the second-order cumulant expansion or stochastic structural instability theory; neither intrinsic turbulence nor coupling to extrinsic turbulence is required. A representative calculation of the zonostrophic neutral curve is made for a simple two-field model of toroidal ion-temperature-gradient-driven modes. To themore » extent that the damping of zonal flows is controlled by the ion-ion collision rate, the point of zonostrophic instability is independent of that rate. Published by AIP Publishing.« less

H∞ filtering for discrete-time systems subject to stochastic missing measurements: a decomposition approach

NASA Astrophysics Data System (ADS)

Gu, Zhou; Fei, Shumin; Yue, Dong; Tian, Engang

2014-07-01

This paper deals with the problem of H∞ filtering for discrete-time systems with stochastic missing measurements. A new missing measurement model is developed by decomposing the interval of the missing rate into several segments. The probability of the missing rate in each subsegment is governed by its corresponding random variables. We aim to design a linear full-order filter such that the estimation error converges to zero exponentially in the mean square with a less conservatism while the disturbance rejection attenuation is constrained to a given level by means of an H∞ performance index. Based on Lyapunov theory, the reliable filter parameters are characterised in terms of the feasibility of a set of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.

Zonostrophic instability driven by discrete particle noise

DOE PAGES

St-Onge, D. A.; Krommes, J. A.

2017-04-01

The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just below the threshold for linear instability. The scenario provides a new interpretation of the random forcing that is ubiquitously invoked in stochastic models such as the second-order cumulant expansion or stochastic structural instability theory; neither intrinsic turbulence nor coupling to extrinsic turbulence is required. A representative calculation of the zonostrophic neutral curve is made for a simple two-field model of toroidal ion-temperature-gradient-driven modes. To themore » extent that the damping of zonal flows is controlled by the ion-ion collision rate, the point of zonostrophic instability is independent of that rate. Published by AIP Publishing.« less

Stochastic effects in a discretized kinetic model of economic exchange

NASA Astrophysics Data System (ADS)

Bertotti, M. L.; Chattopadhyay, A. K.; Modanese, G.

2017-04-01

Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker-Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.

Generation of Complex Karstic Conduit Networks with a Hydro-chemical Model

NASA Astrophysics Data System (ADS)

De Rooij, R.; Graham, W. D.

2016-12-01

The discrete-continuum approach is very well suited to simulate flow and solute transport within karst aquifers. Using this approach, discrete one-dimensional conduits are embedded within a three-dimensional continuum representative of the porous limestone matrix. Typically, however, little is known about the geometry of the karstic conduit network. As such the discrete-continuum approach is rarely used for practical applications. It may be argued, however, that the uncertainty associated with the geometry of the network could be handled by modeling an ensemble of possible karst conduit networks within a stochastic framework. We propose to generate stochastically realistic karst conduit networks by simulating the widening of conduits as caused by the dissolution of limestone over geological relevant timescales. We illustrate that advanced numerical techniques permit to solve the non-linear and coupled hydro-chemical processes efficiently, such that relatively large and complex networks can be generated in acceptable time frames. Instead of specifying flow boundary conditions on conduit cells to recharge the network as is typically done in classical speleogenesis models, we specify an effective rainfall rate over the land surface and let model physics determine the amount of water entering the network. This is advantageous since the amount of water entering the network is extremely difficult to reconstruct, whereas the effective rainfall rate may be quantified using paleoclimatic data. Furthermore, we show that poorly known flow conditions may be constrained by requiring a realistic flow field. Using our speleogenesis model we have investigated factors that influence the geometry of simulated conduit networks. We illustrate that our model generates typical branchwork, network and anastomotic conduit systems. Flow, solute transport and water ages in karst aquifers are simulated using a few illustrative networks.

Invasive advance of an advantageous mutation: nucleation theory.

PubMed

O'Malley, Lauren; Basham, James; Yasi, Joseph A; Korniss, G; Allstadt, Andrew; Caraco, Thomas

2006-12-01

For sedentary organisms with localized reproduction, spatially clustered growth drives the invasive advance of a favorable mutation. We model competition between two alleles where recurrent mutation introduces a genotype with a rate of local propagation exceeding the resident's rate. We capture ecologically important properties of the rare invader's stochastic dynamics by assuming discrete individuals and local neighborhood interactions. To understand how individual-level processes may govern population patterns, we invoke the physical theory for nucleation of spatial systems. Nucleation theory discriminates between single-cluster and multi-cluster dynamics. A sufficiently low mutation rate, or a sufficiently small environment, generates single-cluster dynamics, an inherently stochastic process; a favorable mutation advances only if the invader cluster reaches a critical radius. For this mode of invasion, we identify the probability distribution of waiting times until the favored allele advances to competitive dominance, and we ask how the critical cluster size varies as propagation or mortality rates vary. Increasing the mutation rate or system size generates multi-cluster invasion, where spatial averaging produces nearly deterministic global dynamics. For this process, an analytical approximation from nucleation theory, called Avrami's Law, describes the time-dependent behavior of the genotype densities with remarkable accuracy.

Mathematical modeling of degradation for bulk-erosive polymers: applications in tissue engineering scaffolds and drug delivery systems.

PubMed

Chen, Yuhang; Zhou, Shiwei; Li, Qing

2011-03-01

The degradation of polymeric biomaterials, which are widely exploited in tissue engineering and drug delivery systems, has drawn significant attention in recent years. This paper aims to develop a mathematical model that combines stochastic hydrolysis and mass transport to simulate the polymeric degradation and erosion process. The hydrolysis reaction is modeled in a discrete fashion by a fundamental stochastic process and an additional autocatalytic effect induced by the local carboxylic acid concentration in terms of the continuous diffusion equation. Illustrative examples of microparticles and tissue scaffolds demonstrate the applicability of the model. It is found that diffusive transport plays a critical role in determining the degradation pathway, whilst autocatalysis makes the degradation size dependent. The modeling results show good agreement with experimental data in the literature, in which the hydrolysis rate, polymer architecture and matrix size actually work together to determine the characteristics of the degradation and erosion processes of bulk-erosive polymer devices. The proposed degradation model exhibits great potential for the design optimization of drug carriers and tissue scaffolds. Copyright © 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Stochastic search in structural optimization - Genetic algorithms and simulated annealing

NASA Technical Reports Server (NTRS)

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.

Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes

NASA Astrophysics Data System (ADS)

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.

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

PubMed

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

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu

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) kineticsmore » 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.« less

Automatic mesh refinement and parallel load balancing for Fokker-Planck-DSMC algorithm

NASA Astrophysics Data System (ADS)

Küchlin, Stephan; Jenny, Patrick

2018-06-01

Recently, a parallel Fokker-Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers was developed by the authors. Fokker-Planck-DSMC (FP-DSMC) is an augmentation of the classical DSMC algorithm, which mitigates the near-continuum deficiencies in terms of computational cost of pure DSMC. At each time step, based on a local Knudsen number criterion, the discrete DSMC collision operator is dynamically switched to the Fokker-Planck operator, which is based on the integration of continuous stochastic processes in time, and has fixed computational cost per particle, rather than per collision. In this contribution, we present an extension of the previous implementation with automatic local mesh refinement and parallel load-balancing. In particular, we show how the properties of discrete approximations to space-filling curves enable an efficient implementation. Exemplary numerical studies highlight the capabilities of the new code.

Parallel discrete-event simulation of FCFS stochastic queueing networks

NASA Technical Reports Server (NTRS)

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.

Robust and irreversible development in cell society as a general consequence of intra-inter dynamics

NASA Astrophysics Data System (ADS)

Kaneko, Kunihiko; Furusawa, Chikara

2000-05-01

A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and rules for differentiation are found as a natural consequence of such a system. “Stem cells” that either proliferate or differentiate to different types stochastically are found to appear when intra-cellular dynamics are chaotic. Robustness of the developmental process against microscopic and macroscopic perturbations is shown to be a natural consequence of such intra-inter dynamics, while irreversibility in developmental process is discussed in terms of the gain of stability, loss of diversity and chaotic instability.

Complex discrete dynamics from simple continuous population models.

PubMed

Gamarra, Javier G P; Solé, Ricard V

2002-05-01

Nonoverlapping generations have been classically modelled as difference equations in order to account for the discrete nature of reproductive events. However, other events such as resource consumption or mortality are continuous and take place in the within-generation time. We have realistically assumed a hybrid ODE bidimensional model of resources and consumers with discrete events for reproduction. Numerical and analytical approaches showed that the resulting dynamics resembles a Ricker map, including the doubling route to chaos. Stochastic simulations with a handling-time parameter for indirect competition of juveniles may affect the qualitative behaviour of the model.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chevalier, Michael W., E-mail: Michael.Chevalier@ucsf.edu; El-Samad, Hana, E-mail: Hana.El-Samad@ucsf.edu

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation timesmore » of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.« less

HyDE Framework for Stochastic and Hybrid Model-Based Diagnosis

NASA Technical Reports Server (NTRS)

Narasimhan, Sriram; Brownston, Lee

2012-01-01

Hybrid Diagnosis Engine (HyDE) is a general framework for stochastic and hybrid model-based diagnosis that offers flexibility to the diagnosis application designer. The HyDE architecture supports the use of multiple modeling paradigms at the component and system level. Several alternative algorithms are available for the various steps in diagnostic reasoning. This approach is extensible, with support for the addition of new modeling paradigms as well as diagnostic reasoning algorithms for existing or new modeling paradigms. HyDE is a general framework for stochastic hybrid model-based diagnosis of discrete faults; that is, spontaneous changes in operating modes of components. HyDE combines ideas from consistency-based and stochastic approaches to model- based diagnosis using discrete and continuous models to create a flexible and extensible architecture for stochastic and hybrid diagnosis. HyDE supports the use of multiple paradigms and is extensible to support new paradigms. HyDE generates candidate diagnoses and checks them for consistency with the observations. It uses hybrid models built by the users and sensor data from the system to deduce the state of the system over time, including changes in state indicative of faults. At each time step when observations are available, HyDE checks each existing candidate for continued consistency with the new observations. If the candidate is consistent, it continues to remain in the candidate set. If it is not consistent, then the information about the inconsistency is used to generate successor candidates while discarding the candidate that was inconsistent. The models used by HyDE are similar to simulation models. They describe the expected behavior of the system under nominal and fault conditions. The model can be constructed in modular and hierarchical fashion by building component/subsystem models (which may themselves contain component/ subsystem models) and linking them through shared variables/parameters. The component model is expressed as operating modes of the component and conditions for transitions between these various modes. Faults are modeled as transitions whose conditions for transitions are unknown (and have to be inferred through the reasoning process). Finally, the behavior of the components is expressed as a set of variables/ parameters and relations governing the interaction between the variables. The hybrid nature of the systems being modeled is captured by a combination of the above transitional model and behavioral model. Stochasticity is captured as probabilities associated with transitions (indicating the likelihood of that transition being taken), as well as noise on the sensed variables.

Finite Element Aircraft Simulation of Turbulence

DOT National Transportation Integrated Search

1997-02-01

A Simulation of Rotor Blade Element Turbulence (SORBET) model has been : developed for realtime aircraft simulation that accommodates stochastic : turbulence and distributed discrete gusts as a function of the terrain. This : model is applicable to c...

The influence of planetary-wave transience on horizontal air motions in the stratosphere

NASA Technical Reports Server (NTRS)

Salby, Murry L.

1992-01-01

The influence of transience of the planetary-wave field on the horizontal air motions and tracer distributions in the stratosphere was investigated in equivalent barotropic calculations. Two classes of transience are considered: a monochromatic traveling wave, representative of discrete components such as the 5- and 16-day waves, and a second-order stochastic process representative of broadband variability. The response to each of these forms of unsteady forcing is investigated in terms of the characteristic time scale of the transience. Results are presented, and the implications these results have on stratospheric behavior are discussed.

The fundamental theorem of asset pricing under default and collateral in finite discrete time

NASA Astrophysics Data System (ADS)

Alvarez-Samaniego, Borys; Orrillo, Jaime

2006-08-01

We consider a financial market where time and uncertainty are modeled by a finite event-tree. The event-tree has a length of N, a unique initial node at the initial date, and a continuum of branches at each node of the tree. Prices and returns of J assets are modeled, respectively, by a R2JxR2J-valued stochastic process . In this framework we prove a version of the Fundamental Theorem of Asset Pricing which applies to defaultable securities backed by exogenous collateral suffering a contingent linear depreciation.

Stochastic model of cell rearrangements in convergent extension of ascidian notochord

NASA Astrophysics Data System (ADS)

Lubkin, Sharon; Backes, Tracy; Latterman, Russell; Small, Stephen

2007-03-01

We present a discrete stochastic cell based model of convergent extension of the ascidian notochord. Our work derives from research that clarifies the coupling of invagination and convergent extension in ascidian notochord morphogenesis (Odell and Munro, 2002). We have tested the roles of cell-cell adhesion, cell-extracellular matrix adhesion, random motion, and extension of individual cells, as well as the presence or absence of various tissue types, and determined which factors are necessary and/or sufficient for convergent extension.

Integrated Human Behavior Modeling and Stochastic Control (IHBMSC)

DTIC Science & Technology

2014-08-01

T after the outcome of two inspections has become available is calculated as in the Kalman filtering paradigm. First and foremost, n = 2 is adequate...output, the probability P2(T |·, ·) that the inspected object is a T is calculated—see equations (5.7, 5.8) where a discrete Kalman filtering ...information or value. The behavior of the Stochastic Controller can be usefully compared to a 2-stage screen or a 2-stage filter . The 1st stage of the

Stochastic Differential Games with Complexity Constrained Strategies.

DTIC Science & Technology

1982-03-01

Stochastic Differential Game ..... . 39 2.-1 A b.mp.C mcamp e ..... .... ................ . ..... qu CHAPTER 3 - PROBLEM OF STATE ESTDAATION IN TWO...similar to that used vith the differential game , e vould find that the optimal K has the form K T[T* + ( 2.58) This is not a surprising ansver in viev...Examle Example: Discrete-time, one-stage scalar game Transition equation: Y X + U - V P-offtfuntinl: J E + {5 2 CV Cc~ c>a> 0 Observation equations: Z x

Integrating continuous stocks and flows into state-and-transition simulation models of landscape change

USGS Publications Warehouse

Daniel, Colin J.; Sleeter, Benjamin M.; Frid, Leonardo; Fortin, Marie-Josée

2018-01-01

State-and-transition simulation models (STSMs) provide a general framework for forecasting landscape dynamics, including projections of both vegetation and land-use/land-cover (LULC) change. The STSM method divides a landscape into spatially-referenced cells and then simulates the state of each cell forward in time, as a discrete-time stochastic process using a Monte Carlo approach, in response to any number of possible transitions. A current limitation of the STSM method, however, is that all of the state variables must be discrete.Here we present a new approach for extending a STSM, in order to account for continuous state variables, called a state-and-transition simulation model with stocks and flows (STSM-SF). The STSM-SF method allows for any number of continuous stocks to be defined for every spatial cell in the STSM, along with a suite of continuous flows specifying the rates at which stock levels change over time. The change in the level of each stock is then simulated forward in time, for each spatial cell, as a discrete-time stochastic process. The method differs from the traditional systems dynamics approach to stock-flow modelling in that the stocks and flows can be spatially-explicit, and the flows can be expressed as a function of the STSM states and transitions.We demonstrate the STSM-SF method by integrating a spatially-explicit carbon (C) budget model with a STSM of LULC change for the state of Hawai'i, USA. In this example, continuous stocks are pools of terrestrial C, while the flows are the possible fluxes of C between these pools. Importantly, several of these C fluxes are triggered by corresponding LULC transitions in the STSM. Model outputs include changes in the spatial and temporal distribution of C pools and fluxes across the landscape in response to projected future changes in LULC over the next 50 years.The new STSM-SF method allows both discrete and continuous state variables to be integrated into a STSM, including interactions between them. With the addition of stocks and flows, STSMs provide a conceptually simple yet powerful approach for characterizing uncertainties in projections of a wide range of questions regarding landscape change.

Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons

PubMed Central

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

2011-01-01

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. PMID:22096452

Simulation of stochastic diffusion via first exit times

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lötstedt, Per, E-mail: perl@it.uu.se; Meinecke, Lina, E-mail: lina.meinecke@it.uu.se

2015-11-01

In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh. If the mesh is of poor quality, due to a complicated cell geometry, standard discretization methods can generate negative jump coefficients, which no longer allows the interpretation as the probability to jump between the subvolumes. We propose a methodmore » based on the mean first exit time of a molecule from a subvolume, which guarantees positive jump coefficients. Two approaches to exit times, a global and a local one, are presented and tested in simulations on meshes of different quality in two and three dimensions.« less

Simulation of stochastic diffusion via first exit times

PubMed Central

Lötstedt, Per; Meinecke, Lina

2015-01-01

In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh. If the mesh is of poor quality, due to a complicated cell geometry, standard discretization methods can generate negative jump coefficients, which no longer allows the interpretation as the probability to jump between the subvolumes. We propose a method based on the mean first exit time of a molecule from a subvolume, which guarantees positive jump coefficients. Two approaches to exit times, a global and a local one, are presented and tested in simulations on meshes of different quality in two and three dimensions. PMID:26600600

Non-fragile ?-? control for discrete-time stochastic nonlinear systems under event-triggered protocols

NASA Astrophysics Data System (ADS)

Sun, Ying; Ding, Derui; Zhang, Sunjie; Wei, Guoliang; Liu, Hongjian

2018-07-01

In this paper, the non-fragile ?-? control problem is investigated for a class of discrete-time stochastic nonlinear systems under event-triggered communication protocols, which determine whether the measurement output should be transmitted to the controller or not. The main purpose of the addressed problem is to design an event-based output feedback controller subject to gain variations guaranteeing the prescribed disturbance attenuation level described by the ?-? performance index. By utilizing the Lyapunov stability theory combined with S-procedure, a sufficient condition is established to guarantee both the exponential mean-square stability and the ?-? performance for the closed-loop system. In addition, with the help of the orthogonal decomposition, the desired controller parameter is obtained in terms of the solution to certain linear matrix inequalities. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed event-based controller design scheme.

Role of weakest links and system-size scaling in multiscale modeling of stochastic plasticity

NASA Astrophysics Data System (ADS)

Ispánovity, Péter Dusán; Tüzes, Dániel; Szabó, Péter; Zaiser, Michael; Groma, István

2017-02-01

Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where details of the microstructure evolution are statistically represented in terms of a fluctuating local yield threshold. In the present paper we propose a method for determining the corresponding yield stress distribution for the case of crystal plasticity from lower scale discrete dislocation dynamics simulations which we combine with weakest link arguments. The success of scale linking is demonstrated by comparing stress-strain curves obtained from the resulting mesoscopic and the underlying discrete dislocation models in the microplastic regime. As shown by various scaling relations they are statistically equivalent and behave identically in the thermodynamic limit. The proposed technique is expected to be applicable to different microstructures and also to amorphous materials.

Some Classes of Imperfect Information Finite State-Space Stochastic Games with Finite-Dimensional Solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

McEneaney, William M.

2004-08-15

Stochastic games under imperfect information are typically computationally intractable even in the discrete-time/discrete-state case considered here. We consider a problem where one player has perfect information.A function of a conditional probability distribution is proposed as an information state.In the problem form here, the payoff is only a function of the terminal state of the system,and the initial information state is either linear ora sum of max-plus delta functions.When the initial information state belongs to these classes, its propagation is finite-dimensional.The state feedback value function is also finite-dimensional,and obtained via dynamic programming,but has a nonstandard form due to the necessity ofmore » an expanded state variable.Under a saddle point assumption,Certainty Equivalence is obtained and the proposed function is indeed an information state.« less

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics.

PubMed

Strehl, Robert; Ilie, Silvana

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.

Mechanisms for the target patterns formation in a stochastic bistable excitable medium

NASA Astrophysics Data System (ADS)

Verisokin, Andrey Yu.; Verveyko, Darya V.; Postnov, Dmitry E.

2018-04-01

We study the features of formation and evolution of spatiotemporal chaotic regime generated by autonomous pacemakers in excitable deterministic and stochastic bistable active media using the example of the FitzHugh - Nagumo biological neuron model under discrete medium conditions. The following possible mechanisms for the formation of autonomous pacemakers have been studied: 1) a temporal external force applied to a small region of the medium, 2) geometry of the solution region (the medium contains regions with Dirichlet or Neumann boundaries). In our work we explore the conditions for the emergence of pacemakers inducing target patterns in a stochastic bistable excitable system and propose the algorithm for their analysis.

Stochastic approach and fluctuation theorem for charge transport in diodes

NASA Astrophysics Data System (ADS)

Gu, Jiayin; Gaspard, Pierre

2018-05-01

A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction stochastic partial differential equations and the electric field generated by the charges is determined with the Poisson equation. These equations are discretized in space for the numerical simulations of the mean density profiles, the mean electric potential, and the current-voltage characteristics. Moreover, the full counting statistics of the carrier current and the measured total current including the contribution of the displacement current are investigated. On the basis of local detailed balance, the fluctuation theorem is shown to hold for both currents.

H∞ state estimation for discrete-time memristive recurrent neural networks with stochastic time-delays

NASA Astrophysics Data System (ADS)

Liu, Hongjian; Wang, Zidong; Shen, Bo; Alsaadi, Fuad E.

2016-07-01

This paper deals with the robust H∞ state estimation problem for a class of memristive recurrent neural networks with stochastic time-delays. The stochastic time-delays under consideration are governed by a Bernoulli-distributed stochastic sequence. The purpose of the addressed problem is to design the robust state estimator such that the dynamics of the estimation error is exponentially stable in the mean square, and the prescribed ? performance constraint is met. By utilizing the difference inclusion theory and choosing a proper Lyapunov-Krasovskii functional, the existence condition of the desired estimator is derived. Based on it, the explicit expression of the estimator gain is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is employed to demonstrate the effectiveness and applicability of the proposed estimation approach.

Combining cellular automata and Lattice Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and immune competition.

PubMed

Alemani, Davide; Pappalardo, Francesco; Pennisi, Marzio; Motta, Santo; Brusic, Vladimir

2012-02-28

In the last decades the Lattice Boltzmann method (LB) has been successfully used to simulate a variety of processes. The LB model describes the microscopic processes occurring at the cellular level and the macroscopic processes occurring at the continuum level with a unique function, the probability distribution function. Recently, it has been tried to couple deterministic approaches with probabilistic cellular automata (probabilistic CA) methods with the aim to model temporal evolution of tumor growths and three dimensional spatial evolution, obtaining hybrid methodologies. Despite the good results attained by CA-PDE methods, there is one important issue which has not been completely solved: the intrinsic stochastic nature of the interactions at the interface between cellular (microscopic) and continuum (macroscopic) level. CA methods are able to cope with the stochastic phenomena because of their probabilistic nature, while PDE methods are fully deterministic. Even if the coupling is mathematically correct, there could be important statistical effects that could be missed by the PDE approach. For such a reason, to be able to develop and manage a model that takes into account all these three level of complexity (cellular, molecular and continuum), we believe that PDE should be replaced with a statistic and stochastic model based on the numerical discretization of the Boltzmann equation: The Lattice Boltzmann (LB) method. In this work we introduce a new hybrid method to simulate tumor growth and immune system, by applying Cellular Automata Lattice Boltzmann (CA-LB) approach. Copyright © 2011 Elsevier B.V. All rights reserved.

Mimicking Nonequilibrium Steady States with Time-Periodic Driving

NASA Astrophysics Data System (ADS)

Raz, O.; Subaşı, Y.; Jarzynski, C.

2016-04-01

Under static conditions, a system satisfying detailed balance generically relaxes to an equilibrium state in which there are no currents. To generate persistent currents, either detailed balance must be broken or the system must be driven in a time-dependent manner. A stationary system that violates detailed balance evolves to a nonequilibrium steady state (NESS) characterized by fixed currents. Conversely, a system that satisfies instantaneous detailed balance but is driven by the time-periodic variation of external parameters—also known as a stochastic pump (SP)—reaches a periodic state with nonvanishing currents. In both cases, these currents are maintained at the cost of entropy production. Are these two paradigmatic scenarios effectively equivalent? For discrete-state systems, we establish a mapping between nonequilibrium stationary states and stochastic pumps. Given a NESS characterized by a particular set of stationary probabilities, currents, and entropy production rates, we show how to construct a SP with exactly the same (time-averaged) values. The mapping works in the opposite direction as well. These results establish a proof of principle: They show that stochastic pumps are able to mimic the behavior of nonequilibrium steady states, and vice versa, within the theoretical framework of discrete-state stochastic thermodynamics. Nonequilibrium steady states and stochastic pumps are often used to model, respectively, biomolecular motors driven by chemical reactions and artificial molecular machines steered by the variation of external, macroscopic parameters. Our results loosely suggest that anything a biomolecular machine can do, an artificial molecular machine can do equally well. We illustrate this principle by showing that kinetic proofreading, a NESS mechanism that explains the low error rates in biochemical reactions, can be effectively mimicked by a constrained periodic driving.

Learning in stochastic neural networks for constraint satisfaction problems

NASA Technical Reports Server (NTRS)

Johnston, Mark D.; Adorf, Hans-Martin

1989-01-01

Researchers describe a newly-developed artificial neural network algorithm for solving constraint satisfaction problems (CSPs) which includes a learning component that can significantly improve the performance of the network from run to run. The network, referred to as the Guarded Discrete Stochastic (GDS) network, is based on the discrete Hopfield network but differs from it primarily in that auxiliary networks (guards) are asymmetrically coupled to the main network to enforce certain types of constraints. Although the presence of asymmetric connections implies that the network may not converge, it was found that, for certain classes of problems, the network often quickly converges to find satisfactory solutions when they exist. The network can run efficiently on serial machines and can find solutions to very large problems (e.g., N-queens for N as large as 1024). One advantage of the network architecture is that network connection strengths need not be instantiated when the network is established: they are needed only when a participating neural element transitions from off to on. They have exploited this feature to devise a learning algorithm, based on consistency techniques for discrete CSPs, that updates the network biases and connection strengths and thus improves the network performance.

On generic obstructions to recovering correct statistics from climate simulations: Homogenization for deterministic maps and multiplicative noise

NASA Astrophysics Data System (ADS)

Gottwald, Georg; Melbourne, Ian

2013-04-01

Whereas diffusion limits of stochastic multi-scale systems have a long and successful history, the case of constructing stochastic parametrizations of chaotic deterministic systems has been much less studied. We present rigorous results of convergence of a chaotic slow-fast system to a stochastic differential equation with multiplicative noise. Furthermore we present rigorous results for chaotic slow-fast maps, occurring as numerical discretizations of continuous time systems. This raises the issue of how to interpret certain stochastic integrals; surprisingly the resulting integrals of the stochastic limit system are generically neither of Stratonovich nor of Ito type in the case of maps. It is shown that the limit system of a numerical discretisation is different to the associated continuous time system. This has important consequences when interpreting the statistics of long time simulations of multi-scale systems - they may be very different to the one of the original continuous time system which we set out to study.

Diffusive transport in the presence of stochastically gated absorption

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; Karamched, Bhargav R.; Lawley, Sean D.; Levien, Ethan

2017-08-01

We analyze a population of Brownian particles moving in a spatially uniform environment with stochastically gated absorption. The state of the environment at time t is represented by a discrete stochastic variable k (t )∈{0 ,1 } such that the rate of absorption is γ [1 -k (t )] , with γ a positive constant. The variable k (t ) evolves according to a two-state Markov chain. We focus on how stochastic gating affects the attenuation of particle absorption with distance from a localized source in a one-dimensional domain. In the static case (no gating), the steady-state attenuation is given by an exponential with length constant √{D /γ }, where D is the diffusivity. We show that gating leads to slower, nonexponential attenuation. We also explore statistical correlations between particles due to the fact that they all diffuse in the same switching environment. Such correlations can be determined in terms of moments of the solution to a corresponding stochastic Fokker-Planck equation.

Monte Carlo algorithms for Brownian phylogenetic models.

PubMed

Horvilleur, Benjamin; Lartillot, Nicolas

2014-11-01

Brownian models have been introduced in phylogenetics for describing variation in substitution rates through time, with applications to molecular dating or to the comparative analysis of variation in substitution patterns among lineages. Thus far, however, the Monte Carlo implementations of these models have relied on crude approximations, in which the Brownian process is sampled only at the internal nodes of the phylogeny or at the midpoints along each branch, and the unknown trajectory between these sampled points is summarized by simple branchwise average substitution rates. A more accurate Monte Carlo approach is introduced, explicitly sampling a fine-grained discretization of the trajectory of the (potentially multivariate) Brownian process along the phylogeny. Generic Monte Carlo resampling algorithms are proposed for updating the Brownian paths along and across branches. Specific computational strategies are developed for efficient integration of the finite-time substitution probabilities across branches induced by the Brownian trajectory. The mixing properties and the computational complexity of the resulting Markov chain Monte Carlo sampler scale reasonably with the discretization level, allowing practical applications with up to a few hundred discretization points along the entire depth of the tree. The method can be generalized to other Markovian stochastic processes, making it possible to implement a wide range of time-dependent substitution models with well-controlled computational precision. The program is freely available at www.phylobayes.org. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Mechanisms of stochastic focusing and defocusing in biological reaction networks: insight from accurate chemical master equation (ACME) solutions.

PubMed

Gursoy, Gamze; Terebus, Anna; Youfang Cao; Jie Liang

2016-08-01

Stochasticity plays important roles in regulation of biochemical reaction networks when the copy numbers of molecular species are small. Studies based on Stochastic Simulation Algorithm (SSA) has shown that a basic reaction system can display stochastic focusing (SF) by increasing the sensitivity of the network as a result of the signal noise. Although SSA has been widely used to study stochastic networks, it is ineffective in examining rare events and this becomes a significant issue when the tails of probability distributions are relevant as is the case of SF. Here we use the ACME method to solve the exact solution of the discrete Chemical Master Equations and to study a network where SF was reported. We showed that the level of SF depends on the degree of the fluctuations of signal molecule. We discovered that signaling noise under certain conditions in the same reaction network can lead to a decrease in the system sensitivities, thus the network can experience stochastic defocusing. These results highlight the fundamental role of stochasticity in biological reaction networks and the need for exact computation of probability landscape of the molecules in the system.

Numerical methods for stochastic differential equations

NASA Astrophysics Data System (ADS)

Kloeden, Peter; Platen, Eckhard

1991-06-01

The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to the peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, both theory and applications. The main emphasise is placed on the numerical methods needed to solve such equations. It assumes an undergraduate background in mathematical methods typical of engineers and physicists, through many chapters begin with a descriptive summary which may be accessible to others who only require numerical recipes. To help the reader develop an intuitive understanding of the underlying mathematicals and hand-on numerical skills exercises and over 100 PC Exercises (PC-personal computer) are included. The stochastic Taylor expansion provides the key tool for the systematic derivation and investigation of discrete time numerical methods for stochastic differential equations. The book presents many new results on higher order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extrapolation and variance-reduction methods. Besides serving as a basic text on such methods. the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable.

Bayesian selection of Markov models for symbol sequences: application to microsaccadic eye movements.

PubMed

Bettenbühl, Mario; Rusconi, Marco; Engbert, Ralf; Holschneider, Matthias

2012-01-01

Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.

Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems.

PubMed

Wolf, Elizabeth Skubak; Anderson, David F

2015-01-21

Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations of model output quantities with respect to model parameters, are useful in this setting for a variety of applications. In this paper, we introduce a class of hybrid pathwise differentiation methods for the numerical estimation of parametric sensitivities. The new hybrid methods combine elements from the three main classes of procedures for sensitivity estimation and have a number of desirable qualities. First, the new methods are unbiased for a broad class of problems. Second, the methods are applicable to nearly any physically relevant biochemical CTMC model. Third, and as we demonstrate on several numerical examples, the new methods are quite efficient, particularly if one wishes to estimate the full gradient of parametric sensitivities. The methods are rather intuitive and utilize the multilevel Monte Carlo philosophy of splitting an expectation into separate parts and handling each in an efficient manner.

The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems.

PubMed

Lampoudi, Sotiria; Gillespie, Dan T; Petzold, Linda R

2009-03-07

The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is a variant of the stochastic simulation algorithm in which the spatially inhomogeneous volume of the system is divided into homogeneous subvolumes, and the chemical reactions in those subvolumes are augmented by diffusive transfers of molecules between adjacent subvolumes. The ISSA can be prohibitively slow when the system is such that diffusive transfers occur much more frequently than chemical reactions. In this paper we present the Multinomial Simulation Algorithm (MSA), which is designed to, on the one hand, outperform the ISSA when diffusive transfer events outnumber reaction events, and on the other, to handle small reactant populations with greater accuracy than deterministic-stochastic hybrid algorithms. The MSA treats reactions in the usual ISSA fashion, but uses appropriately conditioned binomial random variables for representing the net numbers of molecules diffusing from any given subvolume to a neighbor within a prescribed distance. Simulation results illustrate the benefits of the algorithm.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems.

PubMed

Herzallah, Randa

2013-06-01

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.

Adaptive control of stochastic linear systems with unknown parameters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ku, R. T.

1972-01-01

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Stochastic hybrid delay population dynamics: well-posed models and extinction.

PubMed

Yuan, Chenggui; Mao, Xuerong; Lygeros, John

2009-01-01

Nonlinear differential equations have been used for decades for studying fluctuations in the populations of species, interactions of species with the environment, and competition and symbiosis between species. Over the years, the original non-linear models have been embellished with delay terms, stochastic terms and more recently discrete dynamics. In this paper, we investigate stochastic hybrid delay population dynamics (SHDPD), a very general class of population dynamics that comprises all of these phenomena. For this class of systems, we provide sufficient conditions to ensure that SHDPD have global positive, ultimately bounded solutions, a minimum requirement for a realistic, well-posed model. We then study the question of extinction and establish conditions under which an ecosystem modelled by SHDPD is doomed.

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strehl, Robert; Ilie, Silvana, E-mail: silvana@ryerson.ca

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated onmore » three benchmarking systems, with special focus on approximation accuracy and efficiency.« less

Hierarchy of forward-backward stochastic Schrödinger equation

NASA Astrophysics Data System (ADS)

Ke, Yaling; Zhao, Yi

2016-07-01

Driven by the impetus to simulate quantum dynamics in photosynthetic complexes or even larger molecular aggregates, we have established a hierarchy of forward-backward stochastic Schrödinger equation in the light of stochastic unravelling of the symmetric part of the influence functional in the path-integral formalism of reduced density operator. The method is numerically exact and is suited for Debye-Drude spectral density, Ohmic spectral density with an algebraic or exponential cutoff, as well as discrete vibrational modes. The power of this method is verified by performing the calculations of time-dependent population differences in the valuable spin-boson model from zero to high temperatures. By simulating excitation energy transfer dynamics of the realistic full FMO trimer, some important features are revealed.

StochKit2: software for discrete stochastic simulation of biochemical systems with events.

PubMed

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.

First assembly times and equilibration in stochastic coagulation-fragmentation

DOE Office of Scientific and Technical Information (OSTI.GOV)

D’Orsogna, Maria R.; Department of Mathematics, CSUN, Los Angeles, California 91330-8313; Lei, Qi

2015-07-07

We develop a fully stochastic theory for coagulation and fragmentation (CF) in a finite system with a maximum cluster size constraint. The process is modeled using a high-dimensional master equation for the probabilities of cluster configurations. For certain realizations of total mass and maximum cluster sizes, we find exact analytical results for the expected equilibrium cluster distributions. If coagulation is fast relative to fragmentation and if the total system mass is indivisible by the mass of the largest allowed cluster, we find a mean cluster-size distribution that is strikingly broader than that predicted by the corresponding mass-action equations. Combinations ofmore » total mass and maximum cluster size under which equilibration is accelerated, eluding late-stage coarsening, are also delineated. Finally, we compute the mean time it takes particles to first assemble into a maximum-sized cluster. Through careful state-space enumeration, the scaling of mean assembly times is derived for all combinations of total mass and maximum cluster size. We find that CF accelerates assembly relative to monomer kinetic only in special cases. All of our results hold in the infinite system limit and can be only derived from a high-dimensional discrete stochastic model, highlighting how classical mass-action models of self-assembly can fail.« less

An application of different dioids in public key cryptography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Durcheva, Mariana I., E-mail: mdurcheva66@gmail.com

2014-11-18

Dioids provide a natural framework for analyzing a broad class of discrete event dynamical systems such as the design and analysis of bus and railway timetables, scheduling of high-throughput industrial processes, solution of combinatorial optimization problems, the analysis and improvement of flow systems in communication networks. They have appeared in several branches of mathematics such as functional analysis, optimization, stochastic systems and dynamic programming, tropical geometry, fuzzy logic. In this paper we show how to involve dioids in public key cryptography. The main goal is to create key – exchange protocols based on dioids. Additionally the digital signature scheme ismore » presented.« less

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

NASA Astrophysics Data System (ADS)

Gross, Jonathan A.; Caves, Carlton M.; Milburn, Gerard J.; Combes, Joshua

2018-04-01

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

A H-infinity Fault Detection and Diagnosis Scheme for Discrete Nonlinear System Using Output Probability Density Estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang Yumin; Lum, Kai-Yew; Wang Qingguo

In this paper, a H-infinity fault detection and diagnosis (FDD) scheme for a class of discrete nonlinear system fault using output probability density estimation is presented. Unlike classical FDD problems, the measured output of the system is viewed as a stochastic process and its square root probability density function (PDF) is modeled with B-spline functions, which leads to a deterministic space-time dynamic model including nonlinearities, uncertainties. A weighting mean value is given as an integral function of the square root PDF along space direction, which leads a function only about time and can be used to construct residual signal. Thus,more » the classical nonlinear filter approach can be used to detect and diagnose the fault in system. A feasible detection criterion is obtained at first, and a new H-infinity adaptive fault diagnosis algorithm is further investigated to estimate the fault. Simulation example is given to demonstrate the effectiveness of the proposed approaches.« less

A H-infinity Fault Detection and Diagnosis Scheme for Discrete Nonlinear System Using Output Probability Density Estimation

NASA Astrophysics Data System (ADS)

Zhang, Yumin; Wang, Qing-Guo; Lum, Kai-Yew

2009-03-01

In this paper, a H-infinity fault detection and diagnosis (FDD) scheme for a class of discrete nonlinear system fault using output probability density estimation is presented. Unlike classical FDD problems, the measured output of the system is viewed as a stochastic process and its square root probability density function (PDF) is modeled with B-spline functions, which leads to a deterministic space-time dynamic model including nonlinearities, uncertainties. A weighting mean value is given as an integral function of the square root PDF along space direction, which leads a function only about time and can be used to construct residual signal. Thus, the classical nonlinear filter approach can be used to detect and diagnose the fault in system. A feasible detection criterion is obtained at first, and a new H-infinity adaptive fault diagnosis algorithm is further investigated to estimate the fault. Simulation example is given to demonstrate the effectiveness of the proposed approaches.

The cost of conservative synchronization in parallel discrete event simulations

NASA Technical Reports Server (NTRS)

Nicol, David M.

1990-01-01

The performance of a synchronous conservative parallel discrete-event simulation protocol is analyzed. The class of simulation models considered is oriented around a physical domain and possesses a limited ability to predict future behavior. A stochastic model is used to show that as the volume of simulation activity in the model increases relative to a fixed architecture, the complexity of the average per-event overhead due to synchronization, event list manipulation, lookahead calculations, and processor idle time approach the complexity of the average per-event overhead of a serial simulation. The method is therefore within a constant factor of optimal. The analysis demonstrates that on large problems--those for which parallel processing is ideally suited--there is often enough parallel workload so that processors are not usually idle. The viability of the method is also demonstrated empirically, showing how good performance is achieved on large problems using a thirty-two node Intel iPSC/2 distributed memory multiprocessor.

Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes

NASA Astrophysics Data System (ADS)

Neri, Izaak; Roldán, Édgar; Jülicher, Frank

2017-01-01

We study the statistics of infima, stopping times, and passage probabilities of entropy production in nonequilibrium steady states, and we show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches a given state for the first time. Our main results are as follows: (i) The distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann's constant; (ii) we find exact expressions for the passage probabilities of entropy production; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production; for example, we derive a relation between the maximal excursion of a molecular motor against the direction of an external force and the infimum of the corresponding entropy-production fluctuations. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follow from our universal results for entropy-production infima.

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

NASA Astrophysics Data System (ADS)

Sadhu, Susmita; Kuehn, Christian

2018-03-01

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

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

PubMed

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.

Threshold Based Stochastic Resonance for the Binary-Input Ternary-Output Discrete Memoryless Channels

DTIC Science & Technology

2012-05-01

noise (AGN) [1] and [11]. We focus on threshold communication systems due to the underwater environment, noncoherent communication techniques are...the threshold level. In the context of the underwater communications, where noncoherent communication techniques are affected both by noise and

Stability analysis for discrete-time stochastic memristive neural networks with both leakage and probabilistic delays.

PubMed

Liu, Hongjian; Wang, Zidong; Shen, Bo; Huang, Tingwen; Alsaadi, Fuad E

2018-06-01

This paper is concerned with the globally exponential stability problem for a class of discrete-time stochastic memristive neural networks (DSMNNs) with both leakage delays as well as probabilistic time-varying delays. For the probabilistic delays, a sequence of Bernoulli distributed random variables is utilized to determine within which intervals the time-varying delays fall at certain time instant. The sector-bounded activation function is considered in the addressed DSMNN. By taking into account the state-dependent characteristics of the network parameters and choosing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are established under which the underlying DSMNN is globally exponentially stable in the mean square. The derived conditions are made dependent on both the leakage and the probabilistic delays, and are therefore less conservative than the traditional delay-independent criteria. A simulation example is given to show the effectiveness of the proposed stability criterion. Copyright © 2018 Elsevier Ltd. All rights reserved.

Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems

NASA Astrophysics Data System (ADS)

Ivanova, Violeta M.; Sousa, Rita; Murrihy, Brian; Einstein, Herbert H.

2014-06-01

This paper presents results from research conducted at MIT during 2010-2012 on modeling of natural rock fracture systems with the GEOFRAC three-dimensional stochastic model. Following a background summary of discrete fracture network models and a brief introduction of GEOFRAC, the paper provides a thorough description of the newly developed mathematical and computer algorithms for fracture intensity, aperture, and intersection representation, which have been implemented in MATLAB. The new methods optimize, in particular, the representation of fracture intensity in terms of cumulative fracture area per unit volume, P32, via the Poisson-Voronoi Tessellation of planes into polygonal fracture shapes. In addition, fracture apertures now can be represented probabilistically or deterministically whereas the newly implemented intersection algorithms allow for computing discrete pathways of interconnected fractures. In conclusion, results from a statistical parametric study, which was conducted with the enhanced GEOFRAC model and the new MATLAB-based Monte Carlo simulation program FRACSIM, demonstrate how fracture intensity, size, and orientations influence fracture connectivity.

Investigation and appreciation of optimal output feedback. Volume 1: A convergent algorithm for the stochastic infinite-time discrete optimal output feedback problem

NASA Technical Reports Server (NTRS)

Halyo, N.; Broussard, J. R.

1984-01-01

The stochastic, infinite time, discrete output feedback problem for time invariant linear systems is examined. Two sets of sufficient conditions for the existence of a stable, globally optimal solution are presented. An expression for the total change in the cost function due to a change in the feedback gain is obtained. This expression is used to show that a sequence of gains can be obtained by an algorithm, so that the corresponding cost sequence is monotonically decreasing and the corresponding sequence of the cost gradient converges to zero. The algorithm is guaranteed to obtain a critical point of the cost function. The computational steps necessary to implement the algorithm on a computer are presented. The results are applied to a digital outer loop flight control problem. The numerical results for this 13th order problem indicate a rate of convergence considerably faster than two other algorithms used for comparison.

Discrete stochastic charging of aggregate grains

NASA Astrophysics Data System (ADS)

Matthews, Lorin S.; Shotorban, Babak; Hyde, Truell W.

2018-05-01

Dust particles immersed in a plasma environment become charged through the collection of electrons and ions at random times, causing the dust charge to fluctuate about an equilibrium value. Small grains (with radii less than 1 μm) or grains in a tenuous plasma environment are sensitive to single additions of electrons or ions. Here we present a numerical model that allows examination of discrete stochastic charge fluctuations on the surface of aggregate grains and determines the effect of these fluctuations on the dynamics of grain aggregation. We show that the mean and standard deviation of charge on aggregate grains follow the same trends as those predicted for spheres having an equivalent radius, though aggregates exhibit larger variations from the predicted values. In some plasma environments, these charge fluctuations occur on timescales which are relevant for dynamics of aggregate growth. Coupled dynamics and charging models show that charge fluctuations tend to produce aggregates which are much more linear or filamentary than aggregates formed in an environment where the charge is stationary.

Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems.

PubMed

Sivak, David A; Chodera, John D; Crooks, Gavin E

2014-06-19

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

An inexact mixed risk-aversion two-stage stochastic programming model for water resources management under uncertainty.

PubMed

Li, W; Wang, B; Xie, Y L; Huang, G H; Liu, L

2015-02-01

Uncertainties exist in the water resources system, while traditional two-stage stochastic programming is risk-neutral and compares the random variables (e.g., total benefit) to identify the best decisions. To deal with the risk issues, a risk-aversion inexact two-stage stochastic programming model is developed for water resources management under uncertainty. The model was a hybrid methodology of interval-parameter programming, conditional value-at-risk measure, and a general two-stage stochastic programming framework. The method extends on the traditional two-stage stochastic programming method by enabling uncertainties presented as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. It could not only provide information on the benefits of the allocation plan to the decision makers but also measure the extreme expected loss on the second-stage penalty cost. The developed model was applied to a hypothetical case of water resources management. Results showed that that could help managers generate feasible and balanced risk-aversion allocation plans, and analyze the trade-offs between system stability and economy.

The subtle business of model reduction for stochastic chemical kinetics

NASA Astrophysics Data System (ADS)

Gillespie, Dan T.; Cao, Yang; Sanft, Kevin R.; Petzold, Linda R.

2009-02-01

This paper addresses the problem of simplifying chemical reaction networks by adroitly reducing the number of reaction channels and chemical species. The analysis adopts a discrete-stochastic point of view and focuses on the model reaction set S1⇌S2→S3, whose simplicity allows all the mathematics to be done exactly. The advantages and disadvantages of replacing this reaction set with a single S3-producing reaction are analyzed quantitatively using novel criteria for measuring simulation accuracy and simulation efficiency. It is shown that in all cases in which such a model reduction can be accomplished accurately and with a significant gain in simulation efficiency, a procedure called the slow-scale stochastic simulation algorithm provides a robust and theoretically transparent way of implementing the reduction.

The subtle business of model reduction for stochastic chemical kinetics.

PubMed

Gillespie, Dan T; Cao, Yang; Sanft, Kevin R; Petzold, Linda R

2009-02-14

This paper addresses the problem of simplifying chemical reaction networks by adroitly reducing the number of reaction channels and chemical species. The analysis adopts a discrete-stochastic point of view and focuses on the model reaction set S(1)<=>S(2)-->S(3), whose simplicity allows all the mathematics to be done exactly. The advantages and disadvantages of replacing this reaction set with a single S(3)-producing reaction are analyzed quantitatively using novel criteria for measuring simulation accuracy and simulation efficiency. It is shown that in all cases in which such a model reduction can be accomplished accurately and with a significant gain in simulation efficiency, a procedure called the slow-scale stochastic simulation algorithm provides a robust and theoretically transparent way of implementing the reduction.

A SAS-based solution to evaluate study design efficiency of phase I pediatric oncology trials via discrete event simulation.

PubMed

Barrett, Jeffrey S; Jayaraman, Bhuvana; Patel, Dimple; Skolnik, Jeffrey M

2008-06-01

Previous exploration of oncology study design efficiency has focused on Markov processes alone (probability-based events) without consideration for time dependencies. Barriers to study completion include time delays associated with patient accrual, inevaluability (IE), time to dose limiting toxicities (DLT) and administrative and review time. Discrete event simulation (DES) can incorporate probability-based assignment of DLT and IE frequency, correlated with cohort in the case of DLT, with time-based events defined by stochastic relationships. A SAS-based solution to examine study efficiency metrics and evaluate design modifications that would improve study efficiency is presented. Virtual patients are simulated with attributes defined from prior distributions of relevant patient characteristics. Study population datasets are read into SAS macros which select patients and enroll them into a study based on the specific design criteria if the study is open to enrollment. Waiting times, arrival times and time to study events are also sampled from prior distributions; post-processing of study simulations is provided within the decision macros and compared across designs in a separate post-processing algorithm. This solution is examined via comparison of the standard 3+3 decision rule relative to the "rolling 6" design, a newly proposed enrollment strategy for the phase I pediatric oncology setting.

Partial Ordering and Stochastic Resonance in Discrete Memoryless Channels

DTIC Science & Technology

2012-05-01

Methods for Underwater Wireless Sensor Networks”, which is to analyze and develop noncoherent communication methods at the physical layer for target...Capacity Behavior for Simple Models of Optical Fiber Communication,” 8 th International conf. on Communications, COMM 2010, Bucharest, pp.1-6, July 2010

Stochastic series expansion simulation of the t -V model

NASA Astrophysics Data System (ADS)

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.

Bringing consistency to simulation of population models--Poisson simulation as a bridge between micro and macro simulation.

PubMed

Gustafsson, Leif; Sternad, Mikael

2007-10-01

Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro- and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.

Combining Particle Filters and Consistency-Based Approaches for Monitoring and Diagnosis of Stochastic Hybrid Systems

NASA Technical Reports Server (NTRS)

Narasimhan, Sriram; Dearden, Richard; Benazera, Emmanuel

2004-01-01

Fault detection and isolation are critical tasks to ensure correct operation of systems. When we consider stochastic hybrid systems, diagnosis algorithms need to track both the discrete mode and the continuous state of the system in the presence of noise. Deterministic techniques like Livingstone cannot deal with the stochasticity in the system and models. Conversely Bayesian belief update techniques such as particle filters may require many computational resources to get a good approximation of the true belief state. In this paper we propose a fault detection and isolation architecture for stochastic hybrid systems that combines look-ahead Rao-Blackwellized Particle Filters (RBPF) with the Livingstone 3 (L3) diagnosis engine. In this approach RBPF is used to track the nominal behavior, a novel n-step prediction scheme is used for fault detection and L3 is used to generate a set of candidates that are consistent with the discrepant observations which then continue to be tracked by the RBPF scheme.

Stochastic Spectral Descent for Discrete Graphical Models

DOE PAGES

Carlson, David; Hsieh, Ya-Ping; Collins, Edo; ...

2015-12-14

Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted asmore » gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.« less

The influence of Stochastic perturbation of Geotechnical media On Electromagnetic tomography

NASA Astrophysics Data System (ADS)

Song, Lei; Yang, Weihao; Huangsonglei, Jiahui; Li, HaiPeng

2015-04-01

Electromagnetic tomography (CT) are commonly utilized in Civil engineering to detect the structure defects or geological anomalies. CT are generally recognized as a high precision geophysical method and the accuracy of CT are expected to be several centimeters and even to be several millimeters. Then, high frequency antenna with short wavelength are utilized commonly in Civil Engineering. As to the geotechnical media, stochastic perturbation of the EM parameters are inevitably exist in geological scales, in structure scales and in local scales, et al. In those cases, the geometric dimensionings of the target body, the EM wavelength and the accuracy expected might be of the same order. When the high frequency EM wave propagated in the stochastic geotechnical media, the GPR signal would be reflected not only from the target bodies but also from the stochastic perturbation of the background media. To detect the karst caves in dissolution fracture rock, one need to assess the influence of the stochastic distributed dissolution holes and fractures; to detect the void in a concrete structure, one should master the influence of the stochastic distributed stones, et al. In this paper, on the base of stochastic media discrete realizations, the authors try to evaluate quantificationally the influence of the stochastic perturbation of Geotechnical media by Radon/Iradon Transfer through full-combined Monte Carlo numerical simulation. It is found the stochastic noise is related with transfer angle, perturbing strength, angle interval, autocorrelation length, et al. And the quantitative formula of the accuracy of the electromagnetic tomography is also established, which could help on the precision estimation of GPR tomography in stochastic perturbation Geotechnical media. Key words: Stochastic Geotechnical Media; Electromagnetic Tomography; Radon/Iradon Transfer.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ng, B

This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.

Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolf, Elizabeth Skubak, E-mail: ewolf@saintmarys.edu; Anderson, David F., E-mail: anderson@math.wisc.edu

2015-01-21

Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations of model output quantities with respect to model parameters, are useful in this setting for a variety of applications. In this paper, we introduce a class of hybrid pathwise differentiation methods for the numerical estimation of parametric sensitivities. The new hybrid methods combine elements from the three main classes of procedures for sensitivity estimation and have a number of desirable qualities. First, the new methods are unbiased formore » a broad class of problems. Second, the methods are applicable to nearly any physically relevant biochemical CTMC model. Third, and as we demonstrate on several numerical examples, the new methods are quite efficient, particularly if one wishes to estimate the full gradient of parametric sensitivities. The methods are rather intuitive and utilize the multilevel Monte Carlo philosophy of splitting an expectation into separate parts and handling each in an efficient manner.« less

Discrete-time moment closure models for epidemic spreading in populations of interacting individuals.

PubMed

Frasca, Mattia; Sharkey, Kieran J

2016-06-21

Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks. We derive a novel set of 'discrete-time moment equations' for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

SCOUT: A Fast Monte-Carlo Modeling Tool of Scintillation Camera Output

PubMed Central

Hunter, William C. J.; Barrett, Harrison H.; Lewellen, Thomas K.; Miyaoka, Robert S.; Muzi, John P.; Li, Xiaoli; McDougald, Wendy; MacDonald, Lawrence R.

2011-01-01

We have developed a Monte-Carlo photon-tracking and readout simulator called SCOUT to study the stochastic behavior of signals output from a simplified rectangular scintillation-camera design. SCOUT models the salient processes affecting signal generation, transport, and readout. Presently, we compare output signal statistics from SCOUT to experimental results for both a discrete and a monolithic camera. We also benchmark the speed of this simulation tool and compare it to existing simulation tools. We find this modeling tool to be relatively fast and predictive of experimental results. Depending on the modeled camera geometry, we found SCOUT to be 4 to 140 times faster than other modeling tools. PMID:22072297

SCOUT: a fast Monte-Carlo modeling tool of scintillation camera output†

PubMed Central

Hunter, William C J; Barrett, Harrison H.; Muzi, John P.; McDougald, Wendy; MacDonald, Lawrence R.; Miyaoka, Robert S.; Lewellen, Thomas K.

2013-01-01

We have developed a Monte-Carlo photon-tracking and readout simulator called SCOUT to study the stochastic behavior of signals output from a simplified rectangular scintillation-camera design. SCOUT models the salient processes affecting signal generation, transport, and readout of a scintillation camera. Presently, we compare output signal statistics from SCOUT to experimental results for both a discrete and a monolithic camera. We also benchmark the speed of this simulation tool and compare it to existing simulation tools. We find this modeling tool to be relatively fast and predictive of experimental results. Depending on the modeled camera geometry, we found SCOUT to be 4 to 140 times faster than other modeling tools. PMID:23640136

A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, Xiang; Yang, Chao; State Key Laboratory of Computer Science, Chinese Academy of Sciences, Beijing 100190

2015-03-15

We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracymore » (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.« less

A framework for discrete stochastic simulation on 3D moving boundary domains

DOE PAGES

Drawert, Brian; Hellander, Stefan; Trogdon, Michael; ...

2016-11-14

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. Finally, we demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formationmore » during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.« less

Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations.

PubMed

Bell, John B; Garcia, Alejandro L; Williams, Sarah A

2007-07-01

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

DOE PAGES

Chen, Zheng; Liu, Liu; Mu, Lin

2017-05-03

In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof ofmore » the stochastic asymptotic-preserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.« less

Differential form representation of stochastic electromagnetic fields

NASA Astrophysics Data System (ADS)

Haider, Michael; Russer, Johannes A.

2017-09-01

In this work, we revisit the theory of stochastic electromagnetic fields using exterior differential forms. We present a short overview as well as a brief introduction to the application of differential forms in electromagnetic theory. Within the framework of exterior calculus we derive equations for the second order moments, describing stochastic electromagnetic fields. Since the resulting objects are continuous quantities in space, a discretization scheme based on the Method of Moments (MoM) is introduced for numerical treatment. The MoM is applied in such a way, that the notation of exterior calculus is maintained while we still arrive at the same set of algebraic equations as obtained for the case of formulating the theory using the traditional notation of vector calculus. We conclude with an analytic calculation of the radiated electric field of two Hertzian dipole, excited by uncorrelated random currents.

Stochastic simulation in systems biology

PubMed Central

Székely, Tamás; Burrage, Kevin

2014-01-01

Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest. PMID:25505503

The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations

PubMed Central

Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R.

2014-01-01

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales. PMID:25099817

Multiscale Hy3S: hybrid stochastic simulation for supercomputers.

PubMed

Salis, Howard; Sotiropoulos, Vassilios; Kaznessis, Yiannis N

2006-02-24

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. 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 create biological systems and analyze data. We demonstrate the accuracy and efficiency of Hy3S with examples, including a large-scale system benchmark and a complex bistable biochemical network with positive feedback. The software itself is open-sourced under the GPL license and is modular, allowing users to modify it for their own purposes. Hy3S is a powerful suite of simulation programs for simulating the stochastic dynamics of networks of biochemical reactions. Its first public version enables computational biologists to more efficiently investigate the dynamics of realistic biological systems.

Neutral dynamics and cell renewal of colonic crypts in homeostatic regime

NASA Astrophysics Data System (ADS)

Fendrik, A. J.; Romanelli, L.; Rotondo, E.

2018-05-01

The self renewal process in colonic crypts is the object of several studies. We present here a new compartment model with the following characteristics: (a) we distinguish different classes of cells: stem cells, six generations of transit amplifying cells and the differentiated cells; (b) in order to take into account the monoclonal character of crypts in homeostatic regimes we include symmetric divisions of the stem cells. We first consider the dynamic differential equations that describe the evolution of the mean values of the populations, but the small observed value of the total number of cells involved plus the huge dispersion of experimental data found in the literature leads us to study the stochastic discrete process. This analysis allows us to study fluctuations, the neutral drift that leads to monoclonality, and the effects of the fixation of mutant clones.

Sublinear Upper Bounds for Stochastic Programs with Recourse. Revision.

DTIC Science & Technology

1987-06-01

approximation procedures for (1.1) generally rely on discretizations of E (Huang, Ziemba , and Ben-Tal (1977), Kall and Stoyan (1982), Birge and Wets...Wright, Practical optimization (Academic Press, London and New York,1981). C.C. Huang, W. Ziemba , and A. Ben-Tal, "Bounds on the expectation of a con

Activating clinical trials: a process improvement approach.

PubMed

Martinez, Diego A; Tsalatsanis, Athanasios; Yalcin, Ali; Zayas-Castro, José L; Djulbegovic, Benjamin

2016-02-24

The administrative process associated with clinical trial activation has been criticized as costly, complex, and time-consuming. Prior research has concentrated on identifying administrative barriers and proposing various solutions to reduce activation time, and consequently associated costs. Here, we expand on previous research by incorporating social network analysis and discrete-event simulation to support process improvement decision-making. We searched for all operational data associated with the administrative process of activating industry-sponsored clinical trials at the Office of Clinical Research of the University of South Florida in Tampa, Florida. We limited the search to those trials initiated and activated between July 2011 and June 2012. We described the process using value stream mapping, studied the interactions of the various process participants using social network analysis, and modeled potential process modifications using discrete-event simulation. The administrative process comprised 5 sub-processes, 30 activities, 11 decision points, 5 loops, and 8 participants. The mean activation time was 76.6 days. Rate-limiting sub-processes were those of contract and budget development. Key participants during contract and budget development were the Office of Clinical Research, sponsors, and the principal investigator. Simulation results indicate that slight increments on the number of trials, arriving to the Office of Clinical Research, would increase activation time by 11 %. Also, incrementing the efficiency of contract and budget development would reduce the activation time by 28 %. Finally, better synchronization between contract and budget development would reduce time spent on batching documentation; however, no improvements would be attained in total activation time. The presented process improvement analytic framework not only identifies administrative barriers, but also helps to devise and evaluate potential improvement scenarios. The strength of our framework lies in its system analysis approach that recognizes the stochastic duration of the activation process and the interdependence between process activities and entities.

State estimation of stochastic non-linear hybrid dynamic system using an interacting multiple model algorithm.

PubMed

Elenchezhiyan, M; Prakash, J

2015-09-01

In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

A robust nonparametric framework for reconstruction of stochastic differential equation models

NASA Astrophysics Data System (ADS)

Rajabzadeh, Yalda; Rezaie, Amir Hossein; Amindavar, Hamidreza

2016-05-01

In this paper, we employ a nonparametric framework to robustly estimate the functional forms of drift and diffusion terms from discrete stationary time series. The proposed method significantly improves the accuracy of the parameter estimation. In this framework, drift and diffusion coefficients are modeled through orthogonal Legendre polynomials. We employ the least squares regression approach along with the Euler-Maruyama approximation method to learn coefficients of stochastic model. Next, a numerical discrete construction of mean squared prediction error (MSPE) is established to calculate the order of Legendre polynomials in drift and diffusion terms. We show numerically that the new method is robust against the variation in sample size and sampling rate. The performance of our method in comparison with the kernel-based regression (KBR) method is demonstrated through simulation and real data. In case of real dataset, we test our method for discriminating healthy electroencephalogram (EEG) signals from epilepsy ones. We also demonstrate the efficiency of the method through prediction in the financial data. In both simulation and real data, our algorithm outperforms the KBR method.

Finite Element Aircraft Simulation of Turbulence

NASA Technical Reports Server (NTRS)

McFarland, R. E.

1997-01-01

A turbulence model has been developed for realtime aircraft simulation that accommodates stochastic turbulence and distributed discrete gusts as a function of the terrain. This model is applicable to conventional aircraft, V/STOL aircraft, and disc rotor model helicopter simulations. Vehicle angular activity in response to turbulence is computed from geometrical and temporal relationships rather than by using the conventional continuum approximations that assume uniform gust immersion and low frequency responses. By using techniques similar to those recently developed for blade-element rotor models, the angular-rate filters of conventional turbulence models are not required. The model produces rotational rates as well as air mass translational velocities in response to both stochastic and deterministic disturbances, where the discrete gusts and turbulence magnitudes may be correlated with significant terrain features or ship models. Assuming isotropy, a two-dimensional vertical turbulence field is created. A novel Gaussian interpolation technique is used to distribute vertical turbulence on the wing span or lateral rotor disc, and this distribution is used to compute roll responses. Air mass velocities are applied at significant centers of pressure in the computation of the aircraft's pitch and roll responses.

Numerical Error Estimation with UQ

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Korn, Peter; Marotzke, Jochem

2014-05-01

Ocean models are still in need of means to quantify model errors, which are inevitably made when running numerical experiments. The total model error can formally be decomposed into two parts, the formulation error and the discretization error. The formulation error arises from the continuous formulation of the model not fully describing the studied physical process. The discretization error arises from having to solve a discretized model instead of the continuously formulated model. Our work on error estimation is concerned with the discretization error. Given a solution of a discretized model, our general problem statement is to find a way to quantify the uncertainties due to discretization in physical quantities of interest (diagnostics), which are frequently used in Geophysical Fluid Dynamics. The approach we use to tackle this problem is called the "Goal Error Ensemble method". The basic idea of the Goal Error Ensemble method is that errors in diagnostics can be translated into a weighted sum of local model errors, which makes it conceptually based on the Dual Weighted Residual method from Computational Fluid Dynamics. In contrast to the Dual Weighted Residual method these local model errors are not considered deterministically but interpreted as local model uncertainty and described stochastically by a random process. The parameters for the random process are tuned with high-resolution near-initial model information. However, the original Goal Error Ensemble method, introduced in [1], was successfully evaluated only in the case of inviscid flows without lateral boundaries in a shallow-water framework and is hence only of limited use in a numerical ocean model. Our work consists in extending the method to bounded, viscous flows in a shallow-water framework. As our numerical model, we use the ICON-Shallow-Water model. In viscous flows our high-resolution information is dependent on the viscosity parameter, making our uncertainty measures viscosity-dependent. We will show that we can choose a sensible parameter by using the Reynolds-number as a criteria. Another topic, we will discuss is the choice of the underlying distribution of the random process. This is especially of importance in the scope of lateral boundaries. We will present resulting error estimates for different height- and velocity-based diagnostics applied to the Munk gyre experiment. References [1] F. RAUSER: Error Estimation in Geophysical Fluid Dynamics through Learning; PhD Thesis, IMPRS-ESM, Hamburg, 2010 [2] F. RAUSER, J. MAROTZKE, P. KORN: Ensemble-type numerical uncertainty quantification from single model integrations; SIAM/ASA Journal on Uncertainty Quantification, submitted

Signal Propagation in Proteins and Relation to Equilibrium Fluctuations

PubMed Central

Chennubhotla, Chakra; Bahar, Ivet

2007-01-01

Elastic network (EN) models have been widely used in recent years for describing protein dynamics, based on the premise that the motions naturally accessible to native structures are relevant to biological function. We posit that equilibrium motions also determine communication mechanisms inherent to the network architecture. To this end, we explore the stochastics of a discrete-time, discrete-state Markov process of information transfer across the network of residues. We measure the communication abilities of residue pairs in terms of hit and commute times, i.e., the number of steps it takes on an average to send and receive signals. Functionally active residues are found to possess enhanced communication propensities, evidenced by their short hit times. Furthermore, secondary structural elements emerge as efficient mediators of communication. The present findings provide us with insights on the topological basis of communication in proteins and design principles for efficient signal transduction. While hit/commute times are information-theoretic concepts, a central contribution of this work is to rigorously show that they have physical origins directly relevant to the equilibrium fluctuations of residues predicted by EN models. PMID:17892319

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Lu, Hanqing, E-mail: hanqing@math.wisc.edu

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (inmore » the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.« less

Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist

PubMed Central

Banerjee, Debjani; Bellesia, Giovanni; Daigle, Bernie J.; Douglas, Geoffrey; Gu, Mengyuan; Gupta, Anand; Hellander, Stefan; Horuk, Chris; Nath, Dibyendu; Takkar, Aviral; Lötstedt, Per; Petzold, Linda R.

2016-01-01

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. PMID:27930676

Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist

DOE PAGES

Drawert, Brian; Hellander, Andreas; Bales, Ben; ...

2016-12-08

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 andmore » exchange models via a public model repository. We also demonstrate the capabilities and ease of use of StochSS with an example of model development and simulation at increasing levels of complexity.« less

Cyto-Sim: a formal language model and stochastic simulator of membrane-enclosed biochemical processes.

PubMed

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.

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

State space truncation with quantified errors for accurate solutions to discrete Chemical Master Equation

PubMed Central

Cao, Youfang; Terebus, Anna; Liang, Jie

2016-01-01

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEG), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of 1) the birth and death model, 2) the single gene expression model, 3) the genetic toggle switch model, and 4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate out theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks. PMID:27105653

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cao, Youfang; Terebus, Anna; Liang, Jie

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. Wemore » further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.« less

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation

DOE PAGES

Cao, Youfang; Terebus, Anna; Liang, Jie

2016-04-22

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. Wemore » further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.« less

Discrete-element simulation of sea-ice mechanics: Contact mechanics and granular jamming

NASA Astrophysics Data System (ADS)

Damsgaard, A.; Adcroft, A.; Sergienko, O. V.; Stern, A. A.

2017-12-01

Lagrangian models of sea-ice dynamics offer several advantages to Eulerian continuum methods. Spatial discretization on the ice-floe scale is natural for Lagrangian models, which additionally offer the convenience of being able to handle arbitrary sea-ice concentrations. This is likely to improve model performance in ice-marginal zones with strong advection. Furthermore, phase transitions in granular rheology around the jamming limit, such as observed when sea ice moves through geometric confinements, includes sharp thresholds in effective viscosity which are typically ignored in Eulerian models. Granular jamming is a stochastic process dependent on having the right grains in the right place at the right time, and the jamming likelihood over time can be described by a probabilistic model. Difficult to parameterize in continuum formulations, jamming occurs naturally in dense granular systems simulated in a Lagrangian framework, and is a very relevant process controlling sea-ice transport through narrow straits. We construct a flexible discrete-element framework for simulating Lagrangian sea-ice dynamics at the ice-floe scale, forced by ocean and atmosphere velocity fields. Using this framework, we demonstrate that frictionless contact models based on compressive stiffness alone are unlikely to jam, and describe two different approaches based on friction and tensile strength which both result in increased bulk shear strength of the granular assemblage. The frictionless but cohesive contact model, with certain tensile strength values, can display jamming behavior which on the large scale is very similar to a more complex and realistic model with contact friction and ice-floe rotation.

Stochastic-Strength-Based Damage Simulation Tool for Ceramic Matrix and Polymer Matrix Composite Structures

NASA Technical Reports Server (NTRS)

Nemeth, Noel N.; Bednarcyk, Brett A.; Pineda, Evan J.; Walton, Owen J.; Arnold, Steven M.

2016-01-01

Stochastic-based, discrete-event progressive damage simulations of ceramic-matrix composite and polymer matrix composite material structures have been enabled through the development of a unique multiscale modeling tool. This effort involves coupling three independently developed software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/ Life), and (3) the Abaqus finite element analysis (FEA) program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating unit cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC. Abaqus is used at the global scale to model the overall composite structure. An Abaqus user-defined material (UMAT) interface, referred to here as "FEAMAC/CARES," was developed that enables MAC/GMC and CARES/Life to operate seamlessly with the Abaqus FEA code. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events, which incrementally progress and lead to ultimate structural failure. This report describes the FEAMAC/CARES methodology and discusses examples that illustrate the performance of the tool. A comprehensive example problem, simulating the progressive damage of laminated ceramic matrix composites under various off-axis loading conditions and including a double notched tensile specimen geometry, is described in a separate report.

Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements.

PubMed

Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats

2014-05-01

In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Stochastic entrainment of a stochastic oscillator.

PubMed

Wang, Guanyu; Peskin, Charles S

2015-01-01

In this work, we consider a stochastic oscillator described by a discrete-state continuous-time Markov chain, in which the states are arranged in a circle, and there is a constant probability per unit time of jumping from one state to the next in a specified direction around the circle. At each of a sequence of equally spaced times, the oscillator has a specified probability of being reset to a particular state. The focus of this work is the entrainment of the oscillator by this periodic but stochastic stimulus. We consider a distinguished limit, in which (i) the number of states of the oscillator approaches infinity, as does the probability per unit time of jumping from one state to the next, so that the natural mean period of the oscillator remains constant, (ii) the resetting probability approaches zero, and (iii) the period of the resetting signal approaches a multiple, by a ratio of small integers, of the natural mean period of the oscillator. In this distinguished limit, we use analytic and numerical methods to study the extent to which entrainment occurs.

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method

PubMed Central

Cao, Youfang; Liang, Jie

2013-01-01

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape. PMID:23862966

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method

NASA Astrophysics Data System (ADS)

Cao, Youfang; Liang, Jie

2013-07-01

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape.

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method.

PubMed

Cao, Youfang; Liang, Jie

2013-07-14

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape.

Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sarıkaya, Mehmet Zeki, E-mail: sarikayamz@gmail.com; Kiriş, Mehmet Eyüp, E-mail: kiris@aku.edu.tr; Çelik, Nuri, E-mail: ncelik@bartin.edu.tr

2016-04-18

The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.

FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.

PubMed

Li, Pu; Chen, Bing

2011-04-01

Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk. Copyright © 2010 Elsevier Ltd. All rights reserved.

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines.

PubMed

Neftci, Emre O; Pedroni, Bruno U; Joshi, Siddharth; Al-Shedivat, Maruan; Cauwenberghs, Gert

2016-01-01

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware.

Stochastic Switching Induced Adaptation in a Starved Escherichia coli Population

PubMed Central

Ito, Yoichiro; Ying, Bei-Wen; Yomo, Tetsuya

2011-01-01

Population adaptation can be determined by stochastic switching in living cells. To examine how stochastic switching contributes to the fate decision for a population under severe stress, we constructed an Escherichia coli strain crucially dependent on the expression of a rewired gene. The gene essential for tryptophan biosynthesis, trpC, was removed from the native regulatory unit, the Trp operon, and placed under the extraneous control of the lactose utilisation network. Bistability of the network provided the cells two discrete phenotypes: the induced and suppressed level of trpC. The two phenotypes permitted the cells to grow or not, respectively, under conditions of tryptophan depletion. We found that stochastic switching between the two states allowed the initially suppressed cells to form a new population with induced trpC in response to tryptophan starvation. However, the frequency of the transition from suppressed to induced state dropped off dramatically in the starved population, in comparison to that in the nourished population. This reduced switching rate was compensated by increasing the initial population size, which probably provided the cell population more chances to wait for the rarely appearing fit cells from the unfit cells. Taken together, adaptation of a starved bacterial population because of stochasticity in the gene rewired from the ancient regulon was experimentally confirmed, and the nutritional status and the population size played a great role in stochastic adaptation. PMID:21931628

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

PubMed Central

Neftci, Emre O.; Pedroni, Bruno U.; Joshi, Siddharth; Al-Shedivat, Maruan; Cauwenberghs, Gert

2016-01-01

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware. PMID:27445650

Stochastic reduced order models for inverse problems under uncertainty

PubMed Central

Warner, James E.; Aquino, Wilkins; Grigoriu, Mircea D.

2014-01-01

This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well. PMID:25558115

Distributed Secure Coordinated Control for Multiagent Systems Under Strategic Attacks.

PubMed

Feng, Zhi; Wen, Guanghui; Hu, Guoqiang

2017-05-01

This paper studies a distributed secure consensus tracking control problem for multiagent systems subject to strategic cyber attacks modeled by a random Markov process. A hybrid stochastic secure control framework is established for designing a distributed secure control law such that mean-square exponential consensus tracking is achieved. A connectivity restoration mechanism is considered and the properties on attack frequency and attack length rate are investigated, respectively. Based on the solutions of an algebraic Riccati equation and an algebraic Riccati inequality, a procedure to select the control gains is provided and stability analysis is studied by using Lyapunov's method.. The effect of strategic attacks on discrete-time systems is also investigated. Finally, numerical examples are provided to illustrate the effectiveness of theoretical analysis.

Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions

NASA Astrophysics Data System (ADS)

Jin, Wang; Penington, Catherine J.; McCue, Scott W.; Simpson, Matthew J.

2016-10-01

Two-dimensional collective cell migration assays are used to study cancer and tissue repair. These assays involve combined cell migration and cell proliferation processes, both of which are modulated by cell-to-cell crowding. Previous discrete models of collective cell migration assays involve a nearest-neighbour proliferation mechanism where crowding effects are incorporated by aborting potential proliferation events if the randomly chosen target site is occupied. There are two limitations of this traditional approach: (i) it seems unreasonable to abort a potential proliferation event based on the occupancy of a single, randomly chosen target site; and, (ii) the continuum limit description of this mechanism leads to the standard logistic growth function, but some experimental evidence suggests that cells do not always proliferate logistically. Motivated by these observations, we introduce a generalised proliferation mechanism which allows non-nearest neighbour proliferation events to take place over a template of r≥slant 1 concentric rings of lattice sites. Further, the decision to abort potential proliferation events is made using a crowding function, f(C), which accounts for the density of agents within a group of sites rather than dealing with the occupancy of a single randomly chosen site. Analysing the continuum limit description of the stochastic model shows that the standard logistic source term, λ C(1-C), where λ is the proliferation rate, is generalised to a universal growth function, λ C f(C). Comparing the solution of the continuum description with averaged simulation data indicates that the continuum model performs well for many choices of f(C) and r. For nonlinear f(C), the quality of the continuum-discrete match increases with r.

Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions.

PubMed

Jin, Wang; Penington, Catherine J; McCue, Scott W; Simpson, Matthew J

2016-10-07

Two-dimensional collective cell migration assays are used to study cancer and tissue repair. These assays involve combined cell migration and cell proliferation processes, both of which are modulated by cell-to-cell crowding. Previous discrete models of collective cell migration assays involve a nearest-neighbour proliferation mechanism where crowding effects are incorporated by aborting potential proliferation events if the randomly chosen target site is occupied. There are two limitations of this traditional approach: (i) it seems unreasonable to abort a potential proliferation event based on the occupancy of a single, randomly chosen target site; and, (ii) the continuum limit description of this mechanism leads to the standard logistic growth function, but some experimental evidence suggests that cells do not always proliferate logistically. Motivated by these observations, we introduce a generalised proliferation mechanism which allows non-nearest neighbour proliferation events to take place over a template of [Formula: see text] concentric rings of lattice sites. Further, the decision to abort potential proliferation events is made using a crowding function, f(C), which accounts for the density of agents within a group of sites rather than dealing with the occupancy of a single randomly chosen site. Analysing the continuum limit description of the stochastic model shows that the standard logistic source term, [Formula: see text], where λ is the proliferation rate, is generalised to a universal growth function, [Formula: see text]. Comparing the solution of the continuum description with averaged simulation data indicates that the continuum model performs well for many choices of f(C) and r. For nonlinear f(C), the quality of the continuum-discrete match increases with r.

An Estimation Procedure for the Structural Parameters of the Unified Cognitive/IRT Model.

ERIC Educational Resources Information Center

Jiang, Hai; And Others

L. V. DiBello, W. F. Stout, and L. A. Roussos (1993) have developed a new item response model, the Unified Model, which brings together the discrete, deterministic aspects of cognition favored by cognitive scientists, and the continuous, stochastic aspects of test response behavior that underlie item response theory (IRT). The Unified Model blends…

Framework based on stochastic L-Systems for modeling IP traffic with multifractal behavior

NASA Astrophysics Data System (ADS)

Salvador, Paulo S.; Nogueira, Antonio; Valadas, Rui

2003-08-01

In a previous work we have introduced a multifractal traffic model based on so-called stochastic L-Systems, which were introduced by biologist A. Lindenmayer as a method to model plant growth. L-Systems are string rewriting techniques, characterized by an alphabet, an axiom (initial string) and a set of production rules. In this paper, we propose a novel traffic model, and an associated parameter fitting procedure, which describes jointly the packet arrival and the packet size processes. The packet arrival process is modeled through a L-System, where the alphabet elements are packet arrival rates. The packet size process is modeled through a set of discrete distributions (of packet sizes), one for each arrival rate. In this way the model is able to capture correlations between arrivals and sizes. We applied the model to measured traffic data: the well-known pOct Bellcore, a trace of aggregate WAN traffic and two traces of specific applications (Kazaa and Operation Flashing Point). We assess the multifractality of these traces using Linear Multiscale Diagrams. The suitability of the traffic model is evaluated by comparing the empirical and fitted probability mass and autocovariance functions; we also compare the packet loss ratio and average packet delay obtained with the measured traces and with traces generated from the fitted model. Our results show that our L-System based traffic model can achieve very good fitting performance in terms of first and second order statistics and queuing behavior.

Quantum stochastic calculus associated with quadratic quantum noises

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in

2016-02-15

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculusmore » extends the Hudson-Parthasarathy quantum stochastic calculus.« less

Reliable gain-scheduled control of discrete-time systems and its application to CSTR model

NASA Astrophysics Data System (ADS)

Sakthivel, R.; Selvi, S.; Mathiyalagan, K.; Shi, Y.

2016-10-01

This paper is focused on reliable gain-scheduled controller design for a class of discrete-time systems with randomly occurring nonlinearities and actuator fault. Further, the nonlinearity in the system model is assumed to occur randomly according to a Bernoulli distribution with measurable time-varying probability in real time. The main purpose of this paper is to design a gain-scheduled controller by implementing a probability-dependent Lyapunov function and linear matrix inequality (LMI) approach such that the closed-loop discrete-time system is stochastically stable for all admissible randomly occurring nonlinearities. The existence conditions for the reliable controller is formulated in terms of LMI constraints. Finally, the proposed reliable gain-scheduled control scheme is applied on continuously stirred tank reactor model to demonstrate the effectiveness and applicability of the proposed design technique.

Stochastic aspects of one-dimensional discrete dynamical systems: Benford's law.

PubMed

Snyder, M A; Curry, J H; Dougherty, A M

2001-08-01

Benford's law owes its discovery to the "Grubby Pages Hypothesis," a 19th century observation made by Simon Newcomb that the beginning pages of logarithm books were grubbier than the last few pages, implying that scientists referenced the values toward the front of the books more frequently. If a data set satisfies Benford's law, then it's significant digits will have a logarithmic distribution, which favors smaller significant digits. In this article we demonstrate two ways of creating discrete one-dimensional dynamical systems that satisfy Benford's law. We also develop a numerical simulation methodology that we use to study dynamical systems when analytical results are not readily available.

Stochastic information transfer from cochlear implant electrodes to auditory nerve fibers

NASA Astrophysics Data System (ADS)

Gao, Xiao; Grayden, David B.; McDonnell, Mark D.

2014-08-01

Cochlear implants, also called bionic ears, are implanted neural prostheses that can restore lost human hearing function by direct electrical stimulation of auditory nerve fibers. Previously, an information-theoretic framework for numerically estimating the optimal number of electrodes in cochlear implants has been devised. This approach relies on a model of stochastic action potential generation and a discrete memoryless channel model of the interface between the array of electrodes and the auditory nerve fibers. Using these models, the stochastic information transfer from cochlear implant electrodes to auditory nerve fibers is estimated from the mutual information between channel inputs (the locations of electrodes) and channel outputs (the set of electrode-activated nerve fibers). Here we describe a revised model of the channel output in the framework that avoids the side effects caused by an "ambiguity state" in the original model and also makes fewer assumptions about perceptual processing in the brain. A detailed comparison of how different assumptions on fibers and current spread modes impact on the information transfer in the original model and in the revised model is presented. We also mathematically derive an upper bound on the mutual information in the revised model, which becomes tighter as the number of electrodes increases. We found that the revised model leads to a significantly larger maximum mutual information and corresponding number of electrodes compared with the original model and conclude that the assumptions made in this part of the modeling framework are crucial to the model's overall utility.

Variance-reduced simulation of lattice discrete-time Markov chains with applications in reaction networks

NASA Astrophysics Data System (ADS)

Maginnis, P. A.; West, M.; Dullerud, G. E.

2016-10-01

We propose an algorithm to accelerate Monte Carlo simulation for a broad class of stochastic processes. Specifically, the class of countable-state, discrete-time Markov chains driven by additive Poisson noise, or lattice discrete-time Markov chains. In particular, this class includes simulation of reaction networks via the tau-leaping algorithm. To produce the speedup, we simulate pairs of fair-draw trajectories that are negatively correlated. Thus, when averaged, these paths produce an unbiased Monte Carlo estimator that has reduced variance and, therefore, reduced error. Numerical results for three example systems included in this work demonstrate two to four orders of magnitude reduction of mean-square error. The numerical examples were chosen to illustrate different application areas and levels of system complexity. The areas are: gene expression (affine state-dependent rates), aerosol particle coagulation with emission and human immunodeficiency virus infection (both with nonlinear state-dependent rates). Our algorithm views the system dynamics as a ;black-box;, i.e., we only require control of pseudorandom number generator inputs. As a result, typical codes can be retrofitted with our algorithm using only minor changes. We prove several analytical results. Among these, we characterize the relationship of covariances between paths in the general nonlinear state-dependent intensity rates case, and we prove variance reduction of mean estimators in the special case of affine intensity rates.

Copula-based analysis of rhythm

NASA Astrophysics Data System (ADS)

García, J. E.; González-López, V. A.; Viola, M. L. Lanfredi

2016-06-01

In this paper we establish stochastic profiles of the rhythm for three languages: English, Japanese and Spanish. We model the increase or decrease of the acoustical energy, collected into three bands coming from the acoustic signal. The number of parameters needed to specify a discrete multivariate Markov chain grows exponentially with the order and dimension of the chain. In this case the size of the database is not large enough for a consistent estimation of the model. We apply a strategy to estimate a multivariate process with an order greater than the order achieved using standard procedures. The new strategy consist on obtaining a partition of the state space which is constructed from a combination of the partitions corresponding to the three marginal processes, one for each band of energy, and the partition coming from to the multivariate Markov chain. Then, all the partitions are linked using a copula, in order to estimate the transition probabilities.

From empirical data to time-inhomogeneous continuous Markov processes.

PubMed

Lencastre, Pedro; Raischel, Frank; Rogers, Tim; Lind, Pedro G

2016-03-01

We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, existing methods to ascertain the existence of continuous Markov processes are based on the assumption that only time-homogeneous generators exist. Here a systematic extension to time inhomogeneity is presented, based on new mathematical propositions incorporating necessary and sufficient conditions, which are then implemented computationally and applied to numerical data. A discussion concerning the bridging between rigorous mathematical results on the existence of generators to its computational implementation is presented. Our detection algorithm shows to be effective in more than 60% of tested matrices, typically 80% to 90%, and for those an estimate of the (nonhomogeneous) generator matrix follows. We also solve the embedding problem analytically for the particular case of three-dimensional circulant matrices. Finally, a discussion of possible applications of our framework to problems in different fields is briefly addressed.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

NASA Astrophysics Data System (ADS)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Algorithms for adaptive stochastic control for a class of linear systems

NASA Technical Reports Server (NTRS)

Toda, M.; Patel, R. V.

1977-01-01

Control of linear, discrete time, stochastic systems with unknown control gain parameters is discussed. Two suboptimal adaptive control schemes are derived: one is based on underestimating future control and the other is based on overestimating future control. Both schemes require little on-line computation and incorporate in their control laws some information on estimation errors. The performance of these laws is studied by Monte Carlo simulations on a computer. Two single input, third order systems are considered, one stable and the other unstable, and the performance of the two adaptive control schemes is compared with that of the scheme based on enforced certainty equivalence and the scheme where the control gain parameters are known.

A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotalczyk, G., E-mail: Gregor.Kotalczyk@uni-due.de; Kruis, F.E.

Monte Carlo simulations based on weighted simulation particles can solve a variety of population balance problems and allow thus to formulate a solution-framework for many chemical engineering processes. This study presents a novel concept for the calculation of coagulation rates of weighted Monte Carlo particles by introducing a family of transformations to non-weighted Monte Carlo particles. The tuning of the accuracy (named ‘stochastic resolution’ in this paper) of those transformations allows the construction of a constant-number coagulation scheme. Furthermore, a parallel algorithm for the inclusion of newly formed Monte Carlo particles due to nucleation is presented in the scope ofmore » a constant-number scheme: the low-weight merging. This technique is found to create significantly less statistical simulation noise than the conventional technique (named ‘random removal’ in this paper). Both concepts are combined into a single GPU-based simulation method which is validated by comparison with the discrete-sectional simulation technique. Two test models describing a constant-rate nucleation coupled to a simultaneous coagulation in 1) the free-molecular regime or 2) the continuum regime are simulated for this purpose.« less

Regenerating time series from ordinal networks.

PubMed

McCullough, Michael; Sakellariou, Konstantinos; Stemler, Thomas; Small, Michael

2017-03-01

Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations of the deterministic flow time series from which the network models are constructed. In this paper, we construct ordinal networks from discrete sampled continuous chaotic time series and then regenerate new time series by taking random walks on the ordinal network. We then investigate the extent to which the dynamics of the original time series are encoded in the ordinal networks and retained through the process of regenerating new time series by using several distinct quantitative approaches. First, we use recurrence quantification analysis on traditional recurrence plots and order recurrence plots to compare the temporal structure of the original time series with random walk surrogate time series. Second, we estimate the largest Lyapunov exponent from the original time series and investigate the extent to which this invariant measure can be estimated from the surrogate time series. Finally, estimates of correlation dimension are computed to compare the topological properties of the original and surrogate time series dynamics. Our findings show that ordinal networks constructed from univariate time series data constitute stochastic models which approximate important dynamical properties of the original systems.

Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches

PubMed Central

Taylor, P. R.; Baker, R. E.; Simpson, M. J.; Yates, C. A.

2016-01-01

Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic models to accurately capture the behaviour of a system, especially when the number of diffusing particles is low. The stochastic models we consider in this paper are ‘compartment-based’: the domain is discretized into compartments, and particles can jump between these compartments. Volume-excluding effects (crowding) can be incorporated by blocking movement with some probability. Recent work has established the connection between fine- and coarse-grained models incorporating volume exclusion, but only for uniform lattices. In this paper, we consider non-uniform, hybrid lattices that incorporate both fine- and coarse-grained regions, and present two different approaches to describe the interface of the regions. We test both techniques in a range of scenarios to establish their accuracy, benchmarking against fine-grained models, and show that the hybrid models developed in this paper can be significantly faster to simulate than the fine-grained models in certain situations and are at least as fast otherwise. PMID:27383421

Regenerating time series from ordinal networks

NASA Astrophysics Data System (ADS)

McCullough, Michael; Sakellariou, Konstantinos; Stemler, Thomas; Small, Michael

2017-03-01

Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations of the deterministic flow time series from which the network models are constructed. In this paper, we construct ordinal networks from discrete sampled continuous chaotic time series and then regenerate new time series by taking random walks on the ordinal network. We then investigate the extent to which the dynamics of the original time series are encoded in the ordinal networks and retained through the process of regenerating new time series by using several distinct quantitative approaches. First, we use recurrence quantification analysis on traditional recurrence plots and order recurrence plots to compare the temporal structure of the original time series with random walk surrogate time series. Second, we estimate the largest Lyapunov exponent from the original time series and investigate the extent to which this invariant measure can be estimated from the surrogate time series. Finally, estimates of correlation dimension are computed to compare the topological properties of the original and surrogate time series dynamics. Our findings show that ordinal networks constructed from univariate time series data constitute stochastic models which approximate important dynamical properties of the original systems.

Study of selected phenotype switching strategies in time varying environment

NASA Astrophysics Data System (ADS)

Horvath, Denis; Brutovsky, Branislav

2016-03-01

Population heterogeneity plays an important role across many research, as well as the real-world, problems. The population heterogeneity relates to the ability of a population to cope with an environment change (or uncertainty) preventing its extinction. However, this ability is not always desirable as can be exemplified by an intratumor heterogeneity which positively correlates with the development of resistance to therapy. Causation of population heterogeneity is therefore in biology and medicine an intensively studied topic. In this paper the evolution of a specific strategy of population diversification, the phenotype switching, is studied at a conceptual level. The presented simulation model studies evolution of a large population of asexual organisms in a time-varying environment represented by a stochastic Markov process. Each organism disposes with a stochastic or nonlinear deterministic switching strategy realized by discrete-time models with evolvable parameters. We demonstrate that under rapidly varying exogenous conditions organisms operate in the vicinity of the bet-hedging strategy, while the deterministic patterns become relevant as the environmental variations are less frequent. Statistical characterization of the steady state regimes of the populations is done using the Hellinger and Kullback-Leibler functional distances and the Hamming distance.

Relaxation and coarsening of weakly-interacting breathers in a simplified DNLS chain

NASA Astrophysics Data System (ADS)

Iubini, Stefano; Politi, Antonio; Politi, Paolo

2017-07-01

The discrete nonlinear Schrödinger (DNLS) equation displays a parameter region characterized by the presence of localized excitations (breathers). While their formation is well understood and it is expected that the asymptotic configuration comprises a single breather on top of a background, it is not clear why the dynamics of a multi-breather configuration is essentially frozen. In order to investigate this question, we introduce simple stochastic models, characterized by suitable conservation laws. We focus on the role of the coupling strength between localized excitations and background. In the DNLS model, higher breathers interact more weakly, as a result of their faster rotation. In our stochastic models, the strength of the coupling is controlled directly by an amplitude-dependent parameter. In the case of a power-law decrease, the associated coarsening process undergoes a slowing down if the decay rate is larger than a critical value. In the case of an exponential decrease, a freezing effect is observed that is reminiscent of the scenario observed in the DNLS. This last regime arises spontaneously when direct energy diffusion between breathers and background is blocked below a certain threshold.

On the Mathematical Consequences of Binning Spike Trains.

PubMed

Cessac, Bruno; Le Ny, Arnaud; Löcherbach, Eva

2017-01-01

We initiate a mathematical analysis of hidden effects induced by binning spike trains of neurons. Assuming that the original spike train has been generated by a discrete Markov process, we show that binning generates a stochastic process that is no longer Markov but is instead a variable-length Markov chain (VLMC) with unbounded memory. We also show that the law of the binned raster is a Gibbs measure in the DLR (Dobrushin-Lanford-Ruelle) sense coined in mathematical statistical mechanics. This allows the derivation of several important consequences on statistical properties of binned spike trains. In particular, we introduce the DLR framework as a natural setting to mathematically formalize anticipation, that is, to tell "how good" our nervous system is at making predictions. In a probabilistic sense, this corresponds to condition a process by its future, and we discuss how binning may affect our conclusions on this ability. We finally comment on the possible consequences of binning in the detection of spurious phase transitions or in the detection of incorrect evidence of criticality.

Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance

NASA Astrophysics Data System (ADS)

Chen, Yen-Luan; Chang, Chin-Chih; Sheu, Dwan-Fang

2016-04-01

This paper proposes the generalised random and age replacement policies for a multi-state system composed of multi-state elements. The degradation of the multi-state element is assumed to follow the non-homogeneous continuous time Markov process which is a continuous time and discrete state process. A recursive approach is presented to efficiently compute the time-dependent state probability distribution of the multi-state element. The state and performance distribution of the entire multi-state system is evaluated via the combination of the stochastic process and the Lz-transform method. The concept of customer-centred reliability measure is developed based on the system performance and the customer demand. We develop the random and age replacement policies for an aging multi-state system subject to imperfect maintenance in a failure (or unacceptable) state. For each policy, the optimum replacement schedule which minimises the mean cost rate is derived analytically and discussed numerically.

Optimization of Shipboard Manning Levels Using Imprint Pro Forces Module

DTIC Science & Technology

2015-09-01

NPS-OR-15-008 NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA OPTIMIZATION OF SHIPBOARD MANNING LEVELS USING IMPRINT PRO...Optimization of Shipboard Manning Levels Using IMPRINT Pro Forces Module 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...ABSTRACT The Improved Performance Research Integration Tool ( IMPRINT ) is a dynamic, stochastic, discrete-event modeling tool used to develop a model

Mimicking Nonequilibrium Steady States with Time-Periodic Driving

NASA Astrophysics Data System (ADS)

Raz, Oren; Subasi, Yigit; Jarzynski, Christopher

Under static conditions, a system satisfying detailed balance generically relaxes to an equilibrium state in which there are no currents: to generate persistent currents, either detailed balance must be broken or the system must be driven in a time-dependent manner. A stationary system that violates detailed balance evolves to a nonequilibrium steady state (NESS) characterized by fixed currents. Conversely, a system that satisfies instantaneous detailed balance but is driven by the time-periodic variation of external parameters - also known as a stochastic pump (SP) - reaches a periodic state with non-vanishing currents. In both cases, these currents are maintained at the cost of entropy production. Are these two paradigmatic scenarios effectively equivalent? For discrete-state systems we establish a mapping between NESS and SP. Given a NESS characterized by a particular set of stationary probabilities, currents and entropy production rates, we show how to construct a SP with exactly the same (time-averaged) values. The mapping works in the opposite direction as well. These results establish a proof of principle: they show that SP are able to mimic the behavior of NESS, and vice-versa, within the theoretical framework of discrete-state stochastic thermodynamics.

Mum, why do you keep on growing? Impacts of environmental variability on optimal growth and reproduction allocation strategies of annual plants.

PubMed

De Lara, Michel

2006-05-01

In their 1990 paper Optimal reproductive efforts and the timing of reproduction of annual plants in randomly varying environments, Amir and Cohen considered stochastic environments consisting of i.i.d. sequences in an optimal allocation discrete-time model. We suppose here that the sequence of environmental factors is more generally described by a Markov chain. Moreover, we discuss the connection between the time interval of the discrete-time dynamic model and the ability of the plant to rebuild completely its vegetative body (from reserves). We formulate a stochastic optimization problem covering the so-called linear and logarithmic fitness (corresponding to variation within and between years), which yields optimal strategies. For "linear maximizers'', we analyse how optimal strategies depend upon the environmental variability type: constant, random stationary, random i.i.d., random monotonous. We provide general patterns in terms of targets and thresholds, including both determinate and indeterminate growth. We also provide a partial result on the comparison between ;"linear maximizers'' and "log maximizers''. Numerical simulations are provided, allowing to give a hint at the effect of different mathematical assumptions.

Risk management for sulfur dioxide abatement under multiple uncertainties

NASA Astrophysics Data System (ADS)

Dai, C.; Sun, W.; Tan, Q.; Liu, Y.; Lu, W. T.; Guo, H. C.

2016-03-01

In this study, interval-parameter programming, two-stage stochastic programming (TSP), and conditional value-at-risk (CVaR) were incorporated into a general optimization framework, leading to an interval-parameter CVaR-based two-stage programming (ICTP) method. The ICTP method had several advantages: (i) its objective function simultaneously took expected cost and risk cost into consideration, and also used discrete random variables and discrete intervals to reflect uncertain properties; (ii) it quantitatively evaluated the right tail of distributions of random variables which could better calculate the risk of violated environmental standards; (iii) it was useful for helping decision makers to analyze the trade-offs between cost and risk; and (iv) it was effective to penalize the second-stage costs, as well as to capture the notion of risk in stochastic programming. The developed model was applied to sulfur dioxide abatement in an air quality management system. The results indicated that the ICTP method could be used for generating a series of air quality management schemes under different risk-aversion levels, for identifying desired air quality management strategies for decision makers, and for considering a proper balance between system economy and environmental quality.

Stochastic simulations on a model of circadian rhythm generation.

PubMed

Miura, Shigehiro; Shimokawa, Tetsuya; Nomura, Taishin

2008-01-01

Biological phenomena are often modeled by differential equations, where states of a model system are described by continuous real values. When we consider concentrations of molecules as dynamical variables for a set of biochemical reactions, we implicitly assume that numbers of the molecules are large enough so that their changes can be regarded as continuous and they are described deterministically. However, for a system with small numbers of molecules, changes in their numbers are apparently discrete and molecular noises become significant. In such cases, models with deterministic differential equations may be inappropriate, and the reactions must be described by stochastic equations. In this study, we focus a clock gene expression for a circadian rhythm generation, which is known as a system involving small numbers of molecules. Thus it is appropriate for the system to be modeled by stochastic equations and analyzed by methodologies of stochastic simulations. The interlocked feedback model proposed by Ueda et al. as a set of deterministic ordinary differential equations provides a basis of our analyses. We apply two stochastic simulation methods, namely Gillespie's direct method and the stochastic differential equation method also by Gillespie, to the interlocked feedback model. To this end, we first reformulated the original differential equations back to elementary chemical reactions. With those reactions, we simulate and analyze the dynamics of the model using two methods in order to compare them with the dynamics obtained from the original deterministic model and to characterize dynamics how they depend on the simulation methodologies.

Stochastic-Strength-Based Damage Simulation of Ceramic Matrix Composite Laminates

NASA Technical Reports Server (NTRS)

Nemeth, Noel N.; Mital, Subodh K.; Murthy, Pappu L. N.; Bednarcyk, Brett A.; Pineda, Evan J.; Bhatt, Ramakrishna T.; Arnold, Steven M.

2016-01-01

The Finite Element Analysis-Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to characterize and predict the progressive damage response of silicon-carbide-fiber-reinforced reaction-bonded silicon nitride matrix (SiC/RBSN) composite laminate tensile specimens. Studied were unidirectional laminates [0] (sub 8), [10] (sub 8), [45] (sub 8), and [90] (sub 8); cross-ply laminates [0 (sub 2) divided by 90 (sub 2),]s; angled-ply laminates [plus 45 (sub 2) divided by -45 (sub 2), ]s; doubled-edge-notched [0] (sub 8), laminates; and central-hole laminates. Results correlated well with the experimental data. This work was performed as a validation and benchmarking exercise of the FEAMAC/CARES program. FEAMAC/CARES simulates stochastic-based discrete-event progressive damage of ceramic matrix composite and polymer matrix composite material structures. It couples three software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/Life), and (3) the Abaqus finite element analysis program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating-unit-cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC, and Abaqus is used to model the overall composite structure. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events that incrementally progress until ultimate structural failure.

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jakeman, J.D., E-mail: jdjakem@sandia.gov; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchicalmore » surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

Stochastic models for inferring genetic regulation from microarray gene expression data.

PubMed

Tian, Tianhai

2010-03-01

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information. 2009 Elsevier Ireland Ltd. All rights reserved.

A Discrete Fracture Network Model with Stress-Driven Nucleation and Growth

NASA Astrophysics Data System (ADS)

Lavoine, E.; Darcel, C.; Munier, R.; Davy, P.

2017-12-01

The realism of Discrete Fracture Network (DFN) models, beyond the bulk statistical properties, relies on the spatial organization of fractures, which is not issued by purely stochastic DFN models. The realism can be improved by injecting prior information in DFN from a better knowledge of the geological fracturing processes. We first develop a model using simple kinematic rules for mimicking the growth of fractures from nucleation to arrest, in order to evaluate the consequences of the DFN structure on the network connectivity and flow properties. The model generates fracture networks with power-law scaling distributions and a percentage of T-intersections that are consistent with field observations. Nevertheless, a larger complexity relying on the spatial variability of natural fractures positions cannot be explained by the random nucleation process. We propose to introduce a stress-driven nucleation in the timewise process of this kinematic model to study the correlations between nucleation, growth and existing fracture patterns. The method uses the stress field generated by existing fractures and remote stress as an input for a Monte-Carlo sampling of nuclei centers at each time step. Networks so generated are found to have correlations over a large range of scales, with a correlation dimension that varies with time and with the function that relates the nucleation probability to stress. A sensibility analysis of input parameters has been performed in 3D to quantify the influence of fractures and remote stress field orientations.

A comparison of LOD and UT1-UTC forecasts by different combined prediction techniques

NASA Astrophysics Data System (ADS)

Kosek, W.; Kalarus, M.; Johnson, T. J.; Wooden, W. H.; McCarthy, D. D.; Popiński, W.

Stochastic prediction techniques including autocovariance, autoregressive, autoregressive moving average, and neural networks were applied to the UT1-UTC and Length of Day (LOD) International Earth Rotation and Reference Systems Servive (IERS) EOPC04 time series to evaluate the capabilities of each method. All known effects such as leap seconds and solid Earth zonal tides were first removed from the observed values of UT1-UTC and LOD. Two combination procedures were applied to predict the resulting LODR time series: 1) the combination of the least-squares (LS) extrapolation with a stochastic predition method, and 2) the combination of the discrete wavelet transform (DWT) filtering and a stochastic prediction method. The results of the combination of the LS extrapolation with different stochastic prediction techniques were compared with the results of the UT1-UTC prediction method currently used by the IERS Rapid Service/Prediction Centre (RS/PC). It was found that the prediction accuracy depends on the starting prediction epochs, and for the combined forecast methods, the mean prediction errors for 1 to about 70 days in the future are of the same order as those of the method used by the IERS RS/PC.

Cox process representation and inference for stochastic reaction-diffusion processes

NASA Astrophysics Data System (ADS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2016-05-01

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

NASA Technical Reports Server (NTRS)

Williams Colin P.

1999-01-01

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Ronco, Michele

2017-10-01

We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

Event-Based $H_\\infty $ State Estimation for Time-Varying Stochastic Dynamical Networks With State- and Disturbance-Dependent Noises.

PubMed

Sheng, Li; Wang, Zidong; Zou, Lei; Alsaadi, Fuad E

2017-10-01

In this paper, the event-based finite-horizon H ∞ state estimation problem is investigated for a class of discrete time-varying stochastic dynamical networks with state- and disturbance-dependent noises [also called (x,v) -dependent noises]. An event-triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator, where the signal is transmitted only when certain conditions are satisfied. The purpose of the problem addressed is to design a time-varying state estimator in order to estimate the network states through available output measurements. By employing the completing-the-square technique and the stochastic analysis approach, sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed H ∞ performance constraint over a finite horizon. The desired estimator parameters can be designed via solving coupled backward recursive Riccati difference equations. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme.

Bayesian inference for dynamic transcriptional regulation; the Hes1 system as a case study.

PubMed

Heron, Elizabeth A; Finkenstädt, Bärbel; Rand, David A

2007-10-01

In this study, we address the problem of estimating the parameters of regulatory networks and provide the first application of Markov chain Monte Carlo (MCMC) methods to experimental data. As a case study, we consider a stochastic model of the Hes1 system expressed in terms of stochastic differential equations (SDEs) to which rigorous likelihood methods of inference can be applied. When fitting continuous-time stochastic models to discretely observed time series the lengths of the sampling intervals are important, and much of our study addresses the problem when the data are sparse. We estimate the parameters of an autoregulatory network providing results both for simulated and real experimental data from the Hes1 system. We develop an estimation algorithm using MCMC techniques which are flexible enough to allow for the imputation of latent data on a finer time scale and the presence of prior information about parameters which may be informed from other experiments as well as additional measurement error.

Stochastic optimization model for order acceptance with multiple demand classes and uncertain demand/supply

NASA Astrophysics Data System (ADS)

Yang, Wen; Fung, Richard Y. K.

2014-06-01

This article considers an order acceptance problem in a make-to-stock manufacturing system with multiple demand classes in a finite time horizon. Demands in different periods are random variables and are independent of one another, and replenishments of inventory deviate from the scheduled quantities. The objective of this work is to maximize the expected net profit over the planning horizon by deciding the fraction of the demand that is going to be fulfilled. This article presents a stochastic order acceptance optimization model and analyses the existence of the optimal promising policies. An example of a discrete problem is used to illustrate the policies by applying the dynamic programming method. In order to solve the continuous problems, a heuristic algorithm based on stochastic approximation (HASA) is developed. Finally, the computational results of a case example illustrate the effectiveness and efficiency of the HASA approach, and make the application of the proposed model readily acceptable.

Evolving cell models for systems and synthetic biology.

PubMed

Cao, Hongqing; Romero-Campero, Francisco J; Heeb, Stephan; Cámara, Miguel; Krasnogor, Natalio

2010-03-01

This paper proposes a new methodology for the automated design of cell models for systems and synthetic biology. Our modelling framework is based on P systems, a discrete, stochastic and modular formal modelling language. The automated design of biological models comprising the optimization of the model structure and its stochastic kinetic constants is performed using an evolutionary algorithm. The evolutionary algorithm evolves model structures by combining different modules taken from a predefined module library and then it fine-tunes the associated stochastic kinetic constants. We investigate four alternative objective functions for the fitness calculation within the evolutionary algorithm: (1) equally weighted sum method, (2) normalization method, (3) randomly weighted sum method, and (4) equally weighted product method. The effectiveness of the methodology is tested on four case studies of increasing complexity including negative and positive autoregulation as well as two gene networks implementing a pulse generator and a bandwidth detector. We provide a systematic analysis of the evolutionary algorithm's results as well as of the resulting evolved cell models.

A stochastic hybrid model for pricing forward-start variance swaps

NASA Astrophysics Data System (ADS)

Roslan, Teh Raihana Nazirah

2017-11-01

Recently, market players have been exposed to the astounding increase in the trading volume of variance swaps. In this paper, the forward-start nature of a variance swap is being inspected, where hybridizations of equity and interest rate models are used to evaluate the price of discretely-sampled forward-start variance swaps. The Heston stochastic volatility model is being extended to incorporate the dynamics of the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. This is essential since previous studies on variance swaps were mainly focusing on instantaneous-start variance swaps without considering the interest rate effects. This hybrid model produces an efficient semi-closed form pricing formula through the development of forward characteristic functions. The performance of this formula is investigated via simulations to demonstrate how the formula performs for different sampling times and against the real market scenario. Comparison done with the Monte Carlo simulation which was set as our main reference point reveals that our pricing formula gains almost the same precision in a shorter execution time.

Finite state projection based bounds to compare chemical master equation models using single-cell data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fox, Zachary; Neuert, Gregor; Department of Pharmacology, School of Medicine, Vanderbilt University, Nashville, Tennessee 37232

2016-08-21

Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort.more » In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast.« less

Stochastic cellular automata model for stock market dynamics

NASA Astrophysics Data System (ADS)

Bartolozzi, M.; Thomas, A. W.

2004-04-01

In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two-dimensional grid. Active traders are characterized by the decision to buy, σi (t)=+1 , or sell, σi (t)=-1 , a stock at a certain discrete time step. The remaining cells are inactive, σi (t)=0 . The trading dynamics is then determined by the stochastic interaction between traders belonging to the same cluster. Extreme, intermittent events, such as crashes or bubbles, are triggered by a phase transition in the state of the bigger clusters present on the grid, where almost all the active traders come to share the same spin orientation. Most of the stylized aspects of the financial market time series, including multifractal proprieties, are reproduced by the model. A direct comparison is made with the daily closures of the S&P500 index.

Navier-Stokes Dynamics by a Discrete Boltzmann Model

NASA Technical Reports Server (NTRS)

Rubinstein, Robet

2010-01-01

This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

Solving complex maintenance planning optimization problems using stochastic simulation and multi-criteria fuzzy decision making

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tahvili, Sahar; Österberg, Jonas; Silvestrov, Sergei

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 ofmore » a suggested framework model based on discrete event simulation.« less

MOSES: A Matlab-based open-source stochastic epidemic simulator.

PubMed

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.

Stable schemes for dissipative particle dynamics with conserved energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoltz, Gabriel, E-mail: stoltz@cermics.enpc.fr

2017-07-01

This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal conduction) to effective single-variable dynamics, and to approximate the solution of these dynamics with one step of a Metropolis–Hastings algorithm. This ensures by construction that no negative internal energies are encountered during the simulation, and hence allows to increase the admissible timesteps to integrate the dynamics, even for systems with small heat capacities. Stability is only limited by the Hamiltonian part of the dynamics, which suggests resorting to multiplemore » timestep strategies where the stochastic part is integrated less frequently than the Hamiltonian one.« less

Nonparametric weighted stochastic block models

NASA Astrophysics Data System (ADS)

Peixoto, Tiago P.

2018-01-01

We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the model, which are instead inferred from data. We give a comprehensive treatment of different kinds of edge weights (i.e., continuous or discrete, signed or unsigned, bounded or unbounded), as well as arbitrary weight transformations, and describe an unsupervised model selection approach to choose the best network description. We illustrate the application of our method to a variety of empirical weighted networks, such as global migrations, voting patterns in congress, and neural connections in the human brain.

Combinatoric analysis of heterogeneous stochastic self-assembly.

PubMed

D'Orsogna, Maria R; Zhao, Bingyu; Berenji, Bijan; Chou, Tom

2013-09-28

We analyze a fully stochastic model of heterogeneous nucleation and self-assembly in a closed system with a fixed total particle number M, and a fixed number of seeds Ns. Each seed can bind a maximum of N particles. A discrete master equation for the probability distribution of the cluster sizes is derived and the corresponding cluster concentrations are found using kinetic Monte-Carlo simulations in terms of the density of seeds, the total mass, and the maximum cluster size. In the limit of slow detachment, we also find new analytic expressions and recursion relations for the cluster densities at intermediate times and at equilibrium. Our analytic and numerical findings are compared with those obtained from classical mass-action equations and the discrepancies between the two approaches analyzed.

Generic emergence of power law distributions and Lévy-Stable intermittent fluctuations in discrete logistic systems

NASA Astrophysics Data System (ADS)

Biham, Ofer; Malcai, Ofer; Levy, Moshe; Solomon, Sorin

1998-08-01

The dynamics of generic stochastic Lotka-Volterra (discrete logistic) systems of the form wi(t+1)=λ(t)wi(t)+aw¯(t)-bwi(t)w¯(t) is studied by computer simulations. The variables wi, i=1,...,N, are the individual system components and w¯(t)=(1/N)∑iwi(t) is their average. The parameters a and b are constants, while λ(t) is randomly chosen at each time step from a given distribution. Models of this type describe the temporal evolution of a large variety of systems such as stock markets and city populations. These systems are characterized by a large number of interacting objects and the dynamics is dominated by multiplicative processes. The instantaneous probability distribution P(w,t) of the system components wi turns out to fulfill a Pareto power law P(w,t)~w-1-α. The time evolution of w¯(t) presents intermittent fluctuations parametrized by a Lévy-stable distribution with the same index α, showing an intricate relation between the distribution of the wi's at a given time and the temporal fluctuations of their average.

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

PubMed

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

A manifold independent approach to understanding transport in stochastic dynamical systems

NASA Astrophysics Data System (ADS)

Bollt, Erik M.; Billings, Lora; Schwartz, Ira B.

2002-12-01

We develop a new collection of tools aimed at studying stochastically perturbed dynamical systems. Specifically, in the setting of bi-stability, that is a two-attractor system, it has previously been numerically observed that a small noise volume is sufficient to destroy would be zero-noise case barriers in the phase space (pseudo-barriers), thus creating a pre-heteroclinic tangency chaos-like behavior. The stochastic dynamical system has a corresponding Frobenius-Perron operator with a stochastic kernel, which describes how densities of initial conditions move under the noisy map. Thus in studying the action of the Frobenius-Perron operator, we learn about the transport of the map; we have employed a Galerkin-Ulam-like method to project the Frobenius-Perron operator onto a discrete basis set of characteristic functions to highlight this action localized in specified regions of the phase space. Graph theoretic methods allow us to re-order the resulting finite dimensional Markov operator approximation so as to highlight the regions of the original phase space which are particularly active pseudo-barriers of the stochastic dynamics. Our toolbox allows us to find: (1) regions of high activity of transport, (2) flux across pseudo-barriers, and also (3) expected time of escape from pseudo-basins. Some of these quantities are also possible via the manifold dependent stochastic Melnikov method, but Melnikov only applies to a very special class of models for which the unperturbed homoclinic orbit is available. Our methods are unique in that they can essentially be considered as a “black-box” of tools which can be applied to a wide range of stochastic dynamical systems in the absence of a priori knowledge of manifold structures. We use here a model of childhood diseases to showcase our methods. Our tools will allow us to make specific observations of: (1) loss of reducibility between basins with increasing noise, (2) identification in the phase space of active regions of stochastic transport, (3) stochastic flux which essentially completes the heteroclinic tangle.

Stochastic Forcing for Ocean Uncertainty Prediction

DTIC Science & Technology

2013-09-30

using the desired dynamics and the fitting of that velocity field to the bathymetry, coasts and discretization for the desired simulation. New algorithms...numerical bias is removed. Pdfs of the forecast errors are shown to capture and evolve non- Gaussian statistics. Comparing the Kullback - Leibler ...advances in collaborative sea exercises of opportunity vi) Strengthen existing and initiate new collaborations with NRL, using and leveraging the MIT

Combinational Optimal Stopping Problems

DTIC Science & Technology

2016-04-01

such as final, technical, interim, memorandum, master’s thesis, progress, quarterly, research , special, group study, etc. 3. DATES COVERED...Vinel, A. and P. Krokhmal (2015) Certainty equivalent measures of risk, Annals of Operations Research , DOI:10.1007/s10479-015-1801-0. [3] Chernikov...Operations Research , 50(3):415–423, 2002. [16] I. Ljubi, P. Mutzel, and B. Zey. Stochastic survivable network design problems. Electronic Notes in Discrete

Stochastic Community Assembly: Does It Matter in Microbial Ecology?

PubMed

Zhou, Jizhong; Ning, Daliang

2017-12-01

Understanding the mechanisms controlling community diversity, functions, succession, and biogeography is a central, but poorly understood, topic in ecology, particularly in microbial ecology. Although stochastic processes are believed to play nonnegligible roles in shaping community structure, their importance relative to deterministic processes is hotly debated. The importance of ecological stochasticity in shaping microbial community structure is far less appreciated. Some of the main reasons for such heavy debates are the difficulty in defining stochasticity and the diverse methods used for delineating stochasticity. Here, we provide a critical review and synthesis of data from the most recent studies on stochastic community assembly in microbial ecology. We then describe both stochastic and deterministic components embedded in various ecological processes, including selection, dispersal, diversification, and drift. We also describe different approaches for inferring stochasticity from observational diversity patterns and highlight experimental approaches for delineating ecological stochasticity in microbial communities. In addition, we highlight research challenges, gaps, and future directions for microbial community assembly research. Copyright © 2017 American Society for Microbiology.

Light induced kickoff of magnetic domain walls in Ising chains

NASA Astrophysics Data System (ADS)

Bogani, Lapo

2012-02-01

Controlling the speed at which systems evolve is a challenge shared by all disciplines, and otherwise unrelated areas use common theoretical frameworks towards this goal. A particularly widespread model is Glauber dynamics, which describes the time evolution of the Ising model and can be applied to any binary system. Here we show, using molecular nanowires under irradiation, that Glauber dynamics can be controlled by a novel domain-wall kickoff mechanism. Contrary to known processes, the kickoff has unambiguous fingerprints, slowing down the spin-flip attempt rate by several orders of magnitude, and following a scaling law. The required irradiation power is very low, a substantial improvement over present methods of magnetooptical switching: in our experimental demonstration we switched molecular nanowires with light, using powers thousands of times lower than in previous optical switching methods. This manipulation of stochastic dynamic processes is extremely clean, leading to fingerprint signatures and scaling laws. These observations can be used, in material science, to better study domain-wall displacements and solitons in discrete lattices. These results provide a new way to control and study stochastic dynamic processes. Being general for Glauber dynamics, they can be extended to different kinds of magnetic nanowires and to a myriad of fields, ranging from social evolution to neural networks and chemical reactivity. For nanoelectronics and molecular spintronics the kickoff affords external control of molecular spin-valves and a magnetic fingerprint in single molecule measurements. It can also be applied to the dynamics of mechanical switches and the related study of phasons and order-disorder transitions.

Topographic signatures of deep-seated landslides and a general landscape evolution model

NASA Astrophysics Data System (ADS)

Booth, A. M.; Roering, J. J.; Rempel, A. W.

2012-12-01

A fundamental goal of studying earth surface processes is to disentangle the complex web of interactions among baselevel, climate, and rock properties that generate characteristic landforms. Mechanistic geomorphic transport laws can quantitatively address this goal, but no widely accepted law for landslides exists. Here, we propose a transport law for deep-seated landslides and demonstrate its utility using a two-dimensional numerical landscape evolution model informed by study areas in the Waipaoa catchment, New Zealand and the Eel River catchment, California. We define a non-dimensional landslide number, which is the ratio of uplift to landslide flow time scales, that predicts three distinct landscape types. The first is dominated by stochastic landsliding, whereby discrete landslide events episodically erode material at rates far exceeding the long term uplift rate. The second is characterized by steady landsliding, in which the landslide flux at any location remains constant through time and is largest at the steepest locations in the catchment. The third is not significantly affected by landsliding. In both the "stochastic landsliding" and "steady landsliding" regimes, increases in the non-dimensional landslide number systematically reduce catchment relief and widen valley spacing, producing long, quasi-planar, low angle hillslopes despite high uplift rates. The stochastic landsliding regime best captures the frequent observation that deep-seated landslides produce a large sediment flux from a small aerial extent while being active only a fraction of the time. We suggest that this model is adaptable to a wide range of geologic settings and may be useful for interpreting climate-driven changes in landslide behavior.

Topographic signatures and a general transport law for deep-seated landslides in a landscape evolution model

NASA Astrophysics Data System (ADS)

Booth, Adam M.; Roering, Josh J.; Rempel, Alan W.

2013-06-01

A fundamental goal of studying earth surface processes is to disentangle the complex web of interactions among baselevel, tectonics, climate, and rock properties that generate characteristic landforms. Mechanistic geomorphic transport laws can quantitatively address this goal, but no widely accepted law for landslides exists. Here we propose a transport law for deep-seated landslides in weathered bedrock and demonstrate its utility using a two-dimensional numerical landscape evolution model informed by study areas in the Waipaoa catchment, New Zealand, and the Eel River catchment, California. We define a non-dimensional landslide number, which is the ratio of the horizontal landslide flux to the vertical tectonic flux, that characterizes three distinct landscape types. One is dominated by stochastic landsliding, whereby discrete landslide events episodically erode material at rates exceeding the long-term uplift rate. Another is characterized by steady landsliding, in which the landslide flux at any location remains constant through time and is greatest at the steepest locations in the catchment. The third is not significantly affected by landsliding. In both the "stochastic landsliding" and "steady landsliding" regimes, increases in the non-dimensional landslide number systematically reduce catchment relief and widen valley spacing, producing long, low angle hillslopes despite high uplift rates. The stochastic landsliding regime captures the frequent observation that deep-seated landslides produce large sediment fluxes from small areal extents while being active only a fraction of the time. We suggest that this model is adaptable to a wide range of geologic settings and is useful for interpreting climate-driven changes in landslide behavior.

Method and apparatus for manufacturing gas tags

DOEpatents

Gross, K.C.; Laug, M.T.

1996-12-17

For use in the manufacture of gas tags employed in a gas tagging failure detection system for a nuclear reactor, a plurality of commercial feed gases each having a respective noble gas isotopic composition are blended under computer control to provide various tag gas mixtures having selected isotopic ratios which are optimized for specified defined conditions such as cost. Using a new approach employing a discrete variable structure rather than the known continuous-variable optimization problem, the computer controlled gas tag manufacturing process employs an analytical formalism from condensed matter physics known as stochastic relaxation, which is a special case of simulated annealing, for input feed gas selection. For a tag blending process involving M tag isotopes with N distinct feed gas mixtures commercially available from an enriched gas supplier, the manufacturing process calculates the cost difference between multiple combinations and specifies gas mixtures which approach the optimum defined conditions. The manufacturing process is then used to control tag blending apparatus incorporating tag gas canisters connected by stainless-steel tubing with computer controlled valves, with the canisters automatically filled with metered quantities of the required feed gases. 4 figs.

Method and apparatus for manufacturing gas tags

DOEpatents

Gross, Kenny C.; Laug, Matthew T.

1996-01-01

For use in the manufacture of gas tags employed in a gas tagging failure detection system for a nuclear reactor, a plurality of commercial feed gases each having a respective noble gas isotopic composition are blended under computer control to provide various tag gas mixtures having selected isotopic ratios which are optimized for specified defined conditions such as cost. Using a new approach employing a discrete variable structure rather than the known continuous-variable optimization problem, the computer controlled gas tag manufacturing process employs an analytical formalism from condensed matter physics known as stochastic relaxation, which is a special case of simulated annealing, for input feed gas selection. For a tag blending process involving M tag isotopes with N distinct feed gas mixtures commercially available from an enriched gas supplier, the manufacturing process calculates the cost difference between multiple combinations and specifies gas mixtures which approach the optimum defined conditions. The manufacturing process is then used to control tag blending apparatus incorporating tag gas canisters connected by stainless-steel tubing with computer controlled valves, with the canisters automatically filled with metered quantities of the required feed gases.

The pdf approach to turbulent polydispersed two-phase flows

NASA Astrophysics Data System (ADS)

Minier, Jean-Pierre; Peirano, Eric

2001-10-01

The purpose of this paper is to develop a probabilistic approach to turbulent polydispersed two-phase flows. The two-phase flows considered are composed of a continuous phase, which is a turbulent fluid, and a dispersed phase, which represents an ensemble of discrete particles (solid particles, droplets or bubbles). Gathering the difficulties of turbulent flows and of particle motion, the challenge is to work out a general modelling approach that meets three requirements: to treat accurately the physically relevant phenomena, to provide enough information to address issues of complex physics (combustion, polydispersed particle flows, …) and to remain tractable for general non-homogeneous flows. The present probabilistic approach models the statistical dynamics of the system and consists in simulating the joint probability density function (pdf) of a number of fluid and discrete particle properties. A new point is that both the fluid and the particles are included in the pdf description. The derivation of the joint pdf model for the fluid and for the discrete particles is worked out in several steps. The mathematical properties of stochastic processes are first recalled. The various hierarchies of pdf descriptions are detailed and the physical principles that are used in the construction of the models are explained. The Lagrangian one-particle probabilistic description is developed first for the fluid alone, then for the discrete particles and finally for the joint fluid and particle turbulent systems. In the case of the probabilistic description for the fluid alone or for the discrete particles alone, numerical computations are presented and discussed to illustrate how the method works in practice and the kind of information that can be extracted from it. Comments on the current modelling state and propositions for future investigations which try to link the present work with other ideas in physics are made at the end of the paper.

SIMULATION FROM ENDPOINT-CONDITIONED, CONTINUOUS-TIME MARKOV CHAINS ON A FINITE STATE SPACE, WITH APPLICATIONS TO MOLECULAR EVOLUTION.

PubMed

Hobolth, Asger; Stone, Eric A

2009-09-01

Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging from computational finance to human genetics and genomics. A common theme among these diverse applications is the need to simulate sample paths of a CTMC conditional on realized data that is discretely observed. Here we present a general solution to this sampling problem when the CTMC is defined on a discrete and finite state space. Specifically, we consider the generation of sample paths, including intermediate states and times of transition, from a CTMC whose beginning and ending states are known across a time interval of length T. We first unify the literature through a discussion of the three predominant approaches: (1) modified rejection sampling, (2) direct sampling, and (3) uniformization. We then give analytical results for the complexity and efficiency of each method in terms of the instantaneous transition rate matrix Q of the CTMC, its beginning and ending states, and the length of sampling time T. In doing so, we show that no method dominates the others across all model specifications, and we give explicit proof of which method prevails for any given Q, T, and endpoints. Finally, we introduce and compare three applications of CTMCs to demonstrate the pitfalls of choosing an inefficient sampler.

Stochastic architecture for Hopfield neural nets

NASA Technical Reports Server (NTRS)

Pavel, Sandy

1992-01-01

An expandable stochastic digital architecture for recurrent (Hopfield like) neural networks is proposed. The main features and basic principles of stochastic processing are presented. The stochastic digital architecture is based on a chip with n full interconnected neurons with a pipeline, bit processing structure. For large applications, a flexible way to interconnect many such chips is provided.

Doubly stochastic Poisson processes in artificial neural learning.

PubMed

Card, H C

1998-01-01

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

Development of the Architectural Simulation Model for Future Launch Systems and its Application to an Existing Launch Fleet

NASA Technical Reports Server (NTRS)

Rabadi, Ghaith

2005-01-01

A significant portion of lifecycle costs for launch vehicles are generated during the operations phase. Research indicates that operations costs can account for a large percentage of the total life-cycle costs of reusable space transportation systems. These costs are largely determined by decisions made early during conceptual design. Therefore, operational considerations are an important part of vehicle design and concept analysis process that needs to be modeled and studied early in the design phase. However, this is a difficult and challenging task due to uncertainties of operations definitions, the dynamic and combinatorial nature of the processes, and lack of analytical models and the scarcity of historical data during the conceptual design phase. Ultimately, NASA would like to know the best mix of launch vehicle concepts that would meet the missions launch dates at the minimum cost. To answer this question, we first need to develop a model to estimate the total cost, including the operational cost, to accomplish this set of missions. In this project, we have developed and implemented a discrete-event simulation model using ARENA (a simulation modeling environment) to determine this cost assessment. Discrete-event simulation is widely used in modeling complex systems, including transportation systems, due to its flexibility, and ability to capture the dynamics of the system. The simulation model accepts manifest inputs including the set of missions that need to be accomplished over a period of time, the clients (e.g., NASA or DoD) who wish to transport the payload to space, the payload weights, and their destinations (e.g., International Space Station, LEO, or GEO). A user of the simulation model can define an architecture of reusable or expendable launch vehicles to achieve these missions. Launch vehicles may belong to different families where each family may have it own set of resources, processing times, and cost factors. The goal is to capture the required resource levels of the major launch elements and their required facilities. The model s output can show whether or not a certain architecture of vehicles can meet the launch dates, and if not, how much the delay cost would be. It will also produce aggregate figures of missions cost based on element procurement cost, processing cost, cargo integration cost, delay cost, and mission support cost. One of the most useful features of this model is that it is stochastic where it accepts statistical distributions to represent the processing times mimicking the stochastic nature of real systems.

Numerical modeling for dilute and dense sprays

NASA Technical Reports Server (NTRS)

Chen, C. P.; Kim, Y. M.; Shang, H. M.; Ziebarth, J. P.; Wang, T. S.

1992-01-01

We have successfully implemented a numerical model for spray-combustion calculations. In this model, the governing gas-phase equations in Eulerian coordinate are solved by a time-marching multiple pressure correction procedure based on the operator-splitting technique. The droplet-phase equations in Lagrangian coordinate are solved by a stochastic discrete particle technique. In order to simplify the calculation procedure for the circulating droplets, the effective conductivity model is utilized. The k-epsilon models are utilized to characterize the time and length scales of the gas phase in conjunction with turbulent modulation by droplets and droplet dispersion by turbulence. This method entails random sampling of instantaneous gas flow properties and the stochastic process requires a large number of computational parcels to produce the satisfactory dispersion distributions even for rather dilute sprays. Two major improvements in spray combustion modelings were made. Firstly, we have developed a probability density function approach in multidimensional space to represent a specific computational particle. Secondly, we incorporate the Taylor Analogy Breakup (TAB) model for handling the dense spray effects. This breakup model is based on the reasonable assumption that atomization and drop breakup are indistinguishable processes within a dense spray near the nozzle exit. Accordingly, atomization is prescribed by injecting drops which have a characteristic size equal to the nozzle exit diameter. Example problems include the nearly homogeneous and inhomogeneous turbulent particle dispersion, and the non-evaporating, evaporating, and burning dense sprays. Comparison with experimental data will be discussed in detail.

Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks.

PubMed

Bressloff, Paul C

2015-01-01

We consider applications of path-integral methods to the analysis of a stochastic hybrid model representing a network of synaptically coupled spiking neuronal populations. The state of each local population is described in terms of two stochastic variables, a continuous synaptic variable and a discrete activity variable. The synaptic variables evolve according to piecewise-deterministic dynamics describing, at the population level, synapses driven by spiking activity. The dynamical equations for the synaptic currents are only valid between jumps in spiking activity, and the latter are described by a jump Markov process whose transition rates depend on the synaptic variables. We assume a separation of time scales between fast spiking dynamics with time constant [Formula: see text] and slower synaptic dynamics with time constant τ. This naturally introduces a small positive parameter [Formula: see text], which can be used to develop various asymptotic expansions of the corresponding path-integral representation of the stochastic dynamics. First, we derive a variational principle for maximum-likelihood paths of escape from a metastable state (large deviations in the small noise limit [Formula: see text]). We then show how the path integral provides an efficient method for obtaining a diffusion approximation of the hybrid system for small ϵ. The resulting Langevin equation can be used to analyze the effects of fluctuations within the basin of attraction of a metastable state, that is, ignoring the effects of large deviations. We illustrate this by using the Langevin approximation to analyze the effects of intrinsic noise on pattern formation in a spatially structured hybrid network. In particular, we show how noise enlarges the parameter regime over which patterns occur, in an analogous fashion to PDEs. Finally, we carry out a [Formula: see text]-loop expansion of the path integral, and use this to derive corrections to voltage-based mean-field equations, analogous to the modified activity-based equations generated from a neural master equation.

Kinetic Network Study of the Diversity and Temperature Dependence of Trp-Cage Folding Pathways: Combining Transition Path Theory with Stochastic Simulations

PubMed Central

Zheng, Weihua; Gallicchio, Emilio; Deng, Nanjie; Andrec, Michael; Levy, Ronald M.

2011-01-01

We present a new approach to study a multitude of folding pathways and different folding mechanisms for the 20-residue mini-protein Trp-Cage using the combined power of replica exchange molecular dynamics (REMD) simulations for conformational sampling, Transition Path Theory (TPT) for constructing folding pathways and stochastic simulations for sampling the pathways in a high dimensional structure space. REMD simulations of Trp-Cage with 16 replicas at temperatures between 270K and 566K are carried out with an all-atom force field (OPLSAA) and an implicit solvent model (AGBNP). The conformations sampled from all temperatures are collected. They form a discretized state space that can be used to model the folding process. The equilibrium population for each state at a target temperature can be calculated using the Weighted-Histogram-Analysis Method (WHAM). By connecting states with similar structures and creating edges satisfying detailed balance conditions, we construct a kinetic network that preserves the equilibrium population distribution of the state space. After defining the folded and unfolded macrostates, committor probabilities (Pfold) are calculated by solving a set of linear equations for each node in the network and pathways are extracted together with their fluxes using the TPT algorithm. By clustering the pathways into folding “tubes”, a more physically meaningful picture of the diversity of folding routes emerges. Stochastic simulations are carried out on the network and a procedure is developed to project sampled trajectories onto the folding tubes. The fluxes through the folding tubes calculated from the stochastic trajectories are in good agreement with the corresponding values obtained from the TPT analysis. The temperature dependence of the ensemble of Trp-Cage folding pathways is investigated. Above the folding temperature, a large number of diverse folding pathways with comparable fluxes flood the energy landscape. At low temperature, however, the folding transition is dominated by only a few localized pathways. PMID:21254767

Kinetic network study of the diversity and temperature dependence of Trp-Cage folding pathways: combining transition path theory with stochastic simulations.

PubMed

Zheng, Weihua; Gallicchio, Emilio; Deng, Nanjie; Andrec, Michael; Levy, Ronald M

2011-02-17

We present a new approach to study a multitude of folding pathways and different folding mechanisms for the 20-residue mini-protein Trp-Cage using the combined power of replica exchange molecular dynamics (REMD) simulations for conformational sampling, transition path theory (TPT) for constructing folding pathways, and stochastic simulations for sampling the pathways in a high dimensional structure space. REMD simulations of Trp-Cage with 16 replicas at temperatures between 270 and 566 K are carried out with an all-atom force field (OPLSAA) and an implicit solvent model (AGBNP). The conformations sampled from all temperatures are collected. They form a discretized state space that can be used to model the folding process. The equilibrium population for each state at a target temperature can be calculated using the weighted-histogram-analysis method (WHAM). By connecting states with similar structures and creating edges satisfying detailed balance conditions, we construct a kinetic network that preserves the equilibrium population distribution of the state space. After defining the folded and unfolded macrostates, committor probabilities (P(fold)) are calculated by solving a set of linear equations for each node in the network and pathways are extracted together with their fluxes using the TPT algorithm. By clustering the pathways into folding "tubes", a more physically meaningful picture of the diversity of folding routes emerges. Stochastic simulations are carried out on the network, and a procedure is developed to project sampled trajectories onto the folding tubes. The fluxes through the folding tubes calculated from the stochastic trajectories are in good agreement with the corresponding values obtained from the TPT analysis. The temperature dependence of the ensemble of Trp-Cage folding pathways is investigated. Above the folding temperature, a large number of diverse folding pathways with comparable fluxes flood the energy landscape. At low temperature, however, the folding transition is dominated by only a few localized pathways.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems.

PubMed

Winkelmann, Stefanie; Schütte, Christof

2017-09-21

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

A new multiscale noise tuning stochastic resonance for enhanced fault diagnosis in wind turbine drivetrains

NASA Astrophysics Data System (ADS)

Hu, Bingbing; Li, Bing

2016-02-01

It is very difficult to detect weak fault signatures due to the large amount of noise in a wind turbine system. Multiscale noise tuning stochastic resonance (MSTSR) has proved to be an effective way to extract weak signals buried in strong noise. However, the MSTSR method originally based on discrete wavelet transform (DWT) has disadvantages such as shift variance and the aliasing effects in engineering application. In this paper, the dual-tree complex wavelet transform (DTCWT) is introduced into the MSTSR method, which makes it possible to further improve the system output signal-to-noise ratio and the accuracy of fault diagnosis by the merits of DTCWT (nearly shift invariant and reduced aliasing effects). Moreover, this method utilizes the relationship between the two dual-tree wavelet basis functions, instead of matching the single wavelet basis function to the signal being analyzed, which may speed up the signal processing and be employed in on-line engineering monitoring. The proposed method is applied to the analysis of bearing outer ring and shaft coupling vibration signals carrying fault information. The results confirm that the method performs better in extracting the fault features than the original DWT-based MSTSR, the wavelet transform with post spectral analysis, and EMD-based spectral analysis methods.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems

NASA Astrophysics Data System (ADS)

Winkelmann, Stefanie; Schütte, Christof

2017-09-01

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

A continuous stochastic model for non-equilibrium dense gases

NASA Astrophysics Data System (ADS)

Sadr, M.; Gorji, M. H.

2017-12-01

While accurate simulations of dense gas flows far from the equilibrium can be achieved by direct simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order to cope with that, an efficient yet accurate solution algorithm based on the Fokker-Planck approximation of the Enskog equation is devised in this paper; the approximation is very much associated with the Fokker-Planck model derived from the Boltzmann equation by Jenny et al. ["A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion," J. Comput. Phys. 229, 1077-1098 (2010)] and Gorji et al. ["Fokker-Planck model for computational studies of monatomic rarefied gas flows," J. Fluid Mech. 680, 574-601 (2011)]. The idea behind these Fokker-Planck descriptions is to project the dynamics of discrete collisions implied by the molecular encounters into a set of continuous Markovian processes subject to the drift and diffusion. Thereby, the evolution of particles representing the governing stochastic process becomes independent from each other and thus very efficient numerical schemes can be constructed. By close inspection of the Enskog operator, it is observed that the dense gas effects contribute further to the advection of molecular quantities. That motivates a modelling approach where the dense gas corrections can be cast in the extra advection of particles. Therefore, the corresponding Fokker-Planck approximation is derived such that the evolution in the physical space accounts for the dense effects present in the pressure, stress tensor, and heat fluxes. Hence the consistency between the devised Fokker-Planck approximation and the Enskog operator is shown for the velocity moments up to the heat fluxes. For validation studies, a homogeneous gas inside a box besides Fourier, Couette, and lid-driven cavity flow setups is considered. The results based on the Fokker-Planck model are compared with respect to benchmark simulations, where good agreement is found for the flow field along with the transport properties.

Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium.

PubMed

Ceccato, Alessandro; Frezzato, Diego

2018-02-14

The chemical Langevin equation and the associated chemical Fokker-Planck equation are well-known continuous approximations of the discrete stochastic evolution of reaction networks. In this work, we show that these approximations suffer from a physical inconsistency, namely, the presence of nonphysical probability currents at the thermal equilibrium even for closed and fully detailed-balanced kinetic schemes. An illustration is given for a model case.

A stochastic approach to uncertainty in the equations of MHD kinematics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phillips, Edward G., E-mail: egphillips@math.umd.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2015-03-01

The magnetohydrodynamic (MHD) kinematics model describes the electromagnetic behavior of an electrically conducting fluid when its hydrodynamic properties are assumed to be known. In particular, the MHD kinematics equations can be used to simulate the magnetic field induced by a given velocity field. While prescribing the velocity field leads to a simpler model than the fully coupled MHD system, this may introduce some epistemic uncertainty into the model. If the velocity of a physical system is not known with certainty, the magnetic field obtained from the model may not be reflective of the magnetic field seen in experiments. Additionally, uncertaintymore » in physical parameters such as the magnetic resistivity may affect the reliability of predictions obtained from this model. By modeling the velocity and the resistivity as random variables in the MHD kinematics model, we seek to quantify the effects of uncertainty in these fields on the induced magnetic field. We develop stochastic expressions for these quantities and investigate their impact within a finite element discretization of the kinematics equations. We obtain mean and variance data through Monte Carlo simulation for several test problems. Toward this end, we develop and test an efficient block preconditioner for the linear systems arising from the discretized equations.« less

Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions.

PubMed

Lei, Youming; Zheng, Fan

2016-12-01

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

Autogenic geomorphic processes determine the resolution and fidelity of terrestrial paleoclimate records.

PubMed

Foreman, Brady Z; Straub, Kyle M

2017-09-01

Terrestrial paleoclimate records rely on proxies hosted in alluvial strata whose beds are deposited by unsteady and nonlinear geomorphic processes. It is broadly assumed that this renders the resultant time series of terrestrial paleoclimatic variability noisy and incomplete. We evaluate this assumption using a model of oscillating climate and the precise topographic evolution of an experimental alluvial system. We find that geomorphic stochasticity can create aliasing in the time series and spurious climate signals, but these issues are eliminated when the period of climate oscillation is longer than a key time scale of internal dynamics in the geomorphic system. This emergent autogenic geomorphic behavior imparts regularity to deposition and represents a natural discretization interval of the continuous climate signal. We propose that this time scale in nature could be in excess of 10 4 years but would still allow assessments of the rates of climate change at resolutions finer than the existing age model techniques in isolation.

Killing (absorption) versus survival in random motion

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr

2017-09-01

We address diffusion processes in a bounded domain, while focusing on somewhat unexplored affinities between the presence of absorbing and/or inaccessible boundaries. For the Brownian motion (Lévy-stable cases are briefly mentioned) model-independent features are established of the dynamical law that underlies the short-time behavior of these random paths, whose overall lifetime is predefined to be long. As a by-product, the limiting regime of a permanent trapping in a domain is obtained. We demonstrate that the adopted conditioning method, involving the so-called Bernstein transition function, works properly also in an unbounded domain, for stochastic processes with killing (Feynman-Kac kernels play the role of transition densities), provided the spectrum of the related semigroup operator is discrete. The method is shown to be useful in the case, when the spectrum of the generator goes down to zero and no isolated minimal (ground state) eigenvalue is in existence, like in the problem of the long-term survival on a half-line with a sink at origin.

Autogenic geomorphic processes determine the resolution and fidelity of terrestrial paleoclimate records

PubMed Central

Foreman, Brady Z.; Straub, Kyle M.

2017-01-01

Terrestrial paleoclimate records rely on proxies hosted in alluvial strata whose beds are deposited by unsteady and nonlinear geomorphic processes. It is broadly assumed that this renders the resultant time series of terrestrial paleoclimatic variability noisy and incomplete. We evaluate this assumption using a model of oscillating climate and the precise topographic evolution of an experimental alluvial system. We find that geomorphic stochasticity can create aliasing in the time series and spurious climate signals, but these issues are eliminated when the period of climate oscillation is longer than a key time scale of internal dynamics in the geomorphic system. This emergent autogenic geomorphic behavior imparts regularity to deposition and represents a natural discretization interval of the continuous climate signal. We propose that this time scale in nature could be in excess of 104 years but would still allow assessments of the rates of climate change at resolutions finer than the existing age model techniques in isolation. PMID:28924607

Event-Based Variance-Constrained ${\\mathcal {H}}_{\\infty }$ Filtering for Stochastic Parameter Systems Over Sensor Networks With Successive Missing Measurements.

PubMed

Wang, Licheng; Wang, Zidong; Han, Qing-Long; Wei, Guoliang

2018-03-01

This paper is concerned with the distributed filtering problem for a class of discrete time-varying stochastic parameter systems with error variance constraints over a sensor network where the sensor outputs are subject to successive missing measurements. The phenomenon of the successive missing measurements for each sensor is modeled via a sequence of mutually independent random variables obeying the Bernoulli binary distribution law. To reduce the frequency of unnecessary data transmission and alleviate the communication burden, an event-triggered mechanism is introduced for the sensor node such that only some vitally important data is transmitted to its neighboring sensors when specific events occur. The objective of the problem addressed is to design a time-varying filter such that both the requirements and the variance constraints are guaranteed over a given finite-horizon against the random parameter matrices, successive missing measurements, and stochastic noises. By recurring to stochastic analysis techniques, sufficient conditions are established to ensure the existence of the time-varying filters whose gain matrices are then explicitly characterized in term of the solutions to a series of recursive matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of the developed event-triggered distributed filter design strategy.

Mixing Single Scattering Properties in Vector Radiative Transfer for Deterministic and Stochastic Solutions

NASA Astrophysics Data System (ADS)

Mukherjee, L.; Zhai, P.; Hu, Y.; Winker, D. M.

2016-12-01

Among the primary factors, which determine the polarized radiation, field of a turbid medium are the single scattering properties of the medium. When multiple types of scatterers are present, the single scattering properties of the scatterers need to be properly mixed in order to find the solutions to the vector radiative transfer theory (VRT). The VRT solvers can be divided into two types: deterministic and stochastic. The deterministic solver can only accept one set of single scattering property in its smallest discretized spatial volume. When the medium contains more than one kind of scatterer, their single scattering properties are averaged, and then used as input for the deterministic solver. The stochastic solver, can work with different kinds of scatterers explicitly. In this work, two different mixing schemes are studied using the Successive Order of Scattering (SOS) method and Monte Carlo (MC) methods. One scheme is used for deterministic and the other is used for the stochastic Monte Carlo method. It is found that the solutions from the two VRT solvers using two different mixing schemes agree with each other extremely well. This confirms the equivalence to the two mixing schemes and also provides a benchmark for the VRT solution for the medium studied.

Minimum uncertainty and squeezing in diffusion processes and stochastic quantization

NASA Technical Reports Server (NTRS)

Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe

1994-01-01

We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.

Stochasticity and organization of tropical convection: Role of stratiform heating in the simulation of MJO in an aquaplanet coarse resolution GCM using a stochastic multicloud parameterization

NASA Astrophysics Data System (ADS)

Khouider, B.; Majda, A.; Deng, Q.; Ravindran, A. M.

2015-12-01

Global climate models (GCMs) are large computer codes based on the discretization of the equations of atmospheric and oceanic motions coupled to various processes of transfer of heat, moisture and other constituents between land, atmosphere, and oceans. Because of computing power limitations, typical GCM grid resolution is on the order of 100 km and the effects of many physical processes, occurring on smaller scales, on the climate system are represented through various closure recipes known as parameterizations. The parameterization of convective motions and many processes associated with cumulus clouds such as the exchange of latent heat and cloud radiative forcing are believed to be behind much of uncertainty in GCMs. Based on a lattice particle interacting system, the stochastic multicloud model (SMCM) provide a novel and efficient representation of the unresolved variability in GCMs due to organized tropical convection and the cloud cover. It is widely recognized that stratiform heating contributes significantly to tropical rainfall and to the dynamics of tropical convective systems by inducing a front-to-rear tilt in the heating profile. Stratiform anvils forming in the wake of deep convection play a central role in the dynamics of tropical mesoscale convective systems. Here, aquaplanet simulations with a warm pool like surface forcing, based on a coarse-resolution GCM , of ˜170 km grid mesh, coupled with SMCM, are used to demonstrate the importance of stratiform heating for the organization of convection on planetary and intraseasonal scales. When some key model parameters are set to produce higher stratiform heating fractions, the model produces low-frequency and planetary-scale Madden Julian oscillation (MJO)-like wave disturbances while lower to moderate stratiform heating fractions yield mainly synoptic-scale convectively coupled Kelvin-like waves. Rooted from the stratiform instability, it is conjectured here that the strength and extent of stratiform downdrafts are key contributors to the scale selection of convective organizations perhaps with mechanisms that are in essence similar to those of mesoscale convective systems.

Implementation Strategies for Large-Scale Transport Simulations Using Time Domain Particle Tracking

NASA Astrophysics Data System (ADS)

Painter, S.; Cvetkovic, V.; Mancillas, J.; Selroos, J.

2008-12-01

Time domain particle tracking is an emerging alternative to the conventional random walk particle tracking algorithm. With time domain particle tracking, particles are moved from node to node on one-dimensional pathways defined by streamlines of the groundwater flow field or by discrete subsurface features. The time to complete each deterministic segment is sampled from residence time distributions that include the effects of advection, longitudinal dispersion, a variety of kinetically controlled retention (sorption) processes, linear transformation, and temporal changes in groundwater velocities and sorption parameters. The simulation results in a set of arrival times at a monitoring location that can be post-processed with a kernel method to construct mass discharge (breakthrough) versus time. Implementation strategies differ for discrete flow (fractured media) systems and continuous porous media systems. The implementation strategy also depends on the scale at which hydraulic property heterogeneity is represented in the supporting flow model. For flow models that explicitly represent discrete features (e.g., discrete fracture networks), the sampling of residence times along segments is conceptually straightforward. For continuous porous media, such sampling needs to be related to the Lagrangian velocity field. Analytical or semi-analytical methods may be used to approximate the Lagrangian segment velocity distributions in aquifers with low-to-moderate variability, thereby capturing transport effects of subgrid velocity variability. If variability in hydraulic properties is large, however, Lagrangian velocity distributions are difficult to characterize and numerical simulations are required; in particular, numerical simulations are likely to be required for estimating the velocity integral scale as a basis for advective segment distributions. Aquifers with evolving heterogeneity scales present additional challenges. Large-scale simulations of radionuclide transport at two potential repository sites for high-level radioactive waste will be used to demonstrate the potential of the method. The simulations considered approximately 1000 source locations, multiple radionuclides with contrasting sorption properties, and abrupt changes in groundwater velocity associated with future glacial scenarios. Transport pathways linking the source locations to the accessible environment were extracted from discrete feature flow models that include detailed representations of the repository construction (tunnels, shafts, and emplacement boreholes) embedded in stochastically generated fracture networks. Acknowledgment The authors are grateful to SwRI Advisory Committee for Research, the Swedish Nuclear Fuel and Waste Management Company, and Posiva Oy for financial support.

Bidirectional Classical Stochastic Processes with Measurements and Feedback

NASA Technical Reports Server (NTRS)

Hahne, G. E.

2005-01-01

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

On the predictivity of pore-scale simulations: Estimating uncertainties with multilevel Monte Carlo

NASA Astrophysics Data System (ADS)

Icardi, Matteo; Boccardo, Gianluca; Tempone, Raúl

2016-09-01

A fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another ;equivalent; sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [1], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics.

Comparing root architectural models

NASA Astrophysics Data System (ADS)

Schnepf, Andrea; Javaux, Mathieu; Vanderborght, Jan

2017-04-01

Plant roots play an important role in several soil processes (Gregory 2006). Root architecture development determines the sites in soil where roots provide input of carbon and energy and take up water and solutes. However, root architecture is difficult to determine experimentally when grown in opaque soil. Thus, root architectural models have been widely used and been further developed into functional-structural models that are able to simulate the fate of water and solutes in the soil-root system (Dunbabin et al. 2013). Still, a systematic comparison of the different root architectural models is missing. In this work, we focus on discrete root architecture models where roots are described by connected line segments. These models differ (a) in their model concepts, such as the description of distance between branches based on a prescribed distance (inter-nodal distance) or based on a prescribed time interval. Furthermore, these models differ (b) in the implementation of the same concept, such as the time step size, the spatial discretization along the root axes or the way stochasticity of parameters such as root growth direction, growth rate, branch spacing, branching angles are treated. Based on the example of two such different root models, the root growth module of R-SWMS and RootBox, we show the impact of these differences on simulated root architecture and aggregated information computed from this detailed simulation results, taking into account the stochastic nature of those models. References Dunbabin, V.M., Postma, J.A., Schnepf, A., Pagès, L., Javaux, M., Wu, L., Leitner, D., Chen, Y.L., Rengel, Z., Diggle, A.J. Modelling root-soil interactions using three-dimensional models of root growth, architecture and function (2013) Plant and Soil, 372 (1-2), pp. 93 - 124. Gregory (2006) Roots, rhizosphere and soil: the route to a better understanding of soil science? European Journal of Soil Science 57: 2-12.

Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited.

PubMed

Vellela, Melissa; Qian, Hong

2009-10-06

Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.

System design and improvement of an emergency department using Simulation-Based Multi-Objective Optimization

NASA Astrophysics Data System (ADS)

Goienetxea Uriarte, A.; Ruiz Zúñiga, E.; Urenda Moris, M.; Ng, A. H. C.

2015-05-01

Discrete Event Simulation (DES) is nowadays widely used to support decision makers in system analysis and improvement. However, the use of simulation for improving stochastic logistic processes is not common among healthcare providers. The process of improving healthcare systems involves the necessity to deal with trade-off optimal solutions that take into consideration a multiple number of variables and objectives. Complementing DES with Multi-Objective Optimization (SMO) creates a superior base for finding these solutions and in consequence, facilitates the decision-making process. This paper presents how SMO has been applied for system improvement analysis in a Swedish Emergency Department (ED). A significant number of input variables, constraints and objectives were considered when defining the optimization problem. As a result of the project, the decision makers were provided with a range of optimal solutions which reduces considerably the length of stay and waiting times for the ED patients. SMO has proved to be an appropriate technique to support healthcare system design and improvement processes. A key factor for the success of this project has been the involvement and engagement of the stakeholders during the whole process.

Exact event-driven implementation for recurrent networks of stochastic perfect integrate-and-fire neurons.

PubMed

Taillefumier, Thibaud; Touboul, Jonathan; Magnasco, Marcelo

2012-12-01

In vivo cortical recording reveals that indirectly driven neural assemblies can produce reliable and temporally precise spiking patterns in response to stereotyped stimulation. This suggests that despite being fundamentally noisy, the collective activity of neurons conveys information through temporal coding. Stochastic integrate-and-fire models delineate a natural theoretical framework to study the interplay of intrinsic neural noise and spike timing precision. However, there are inherent difficulties in simulating their networks' dynamics in silico with standard numerical discretization schemes. Indeed, the well-posedness of the evolution of such networks requires temporally ordering every neuronal interaction, whereas the order of interactions is highly sensitive to the random variability of spiking times. Here, we answer these issues for perfect stochastic integrate-and-fire neurons by designing an exact event-driven algorithm for the simulation of recurrent networks, with delayed Dirac-like interactions. In addition to being exact from the mathematical standpoint, our proposed method is highly efficient numerically. We envision that our algorithm is especially indicated for studying the emergence of polychronized motifs in networks evolving under spike-timing-dependent plasticity with intrinsic noise.

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Granita, E-mail: granitafc@gmail.com; Bahar, A.

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

Interrupted monitoring of a stochastic process

NASA Technical Reports Server (NTRS)

Palmer, E.

1977-01-01

Normative strategies are developed for tasks where the pilot must interrupt his monitoring of a stochastic process in order to attend to other duties. Results are given as to how characteristics of the stochastic process and the other tasks affect the optimal strategies. The optimum strategy is also compared to the strategies used by subjects in a pilot experiment.

An estimator for the relative entropy rate of path measures for stochastic differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Opper, Manfred, E-mail: manfred.opper@tu-berlin.de

2017-02-01

We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.

Estimation of Parameters from Discrete Random Nonstationary Time Series

NASA Astrophysics Data System (ADS)

Takayasu, H.; Nakamura, T.

For the analysis of nonstationary stochastic time series we introduce a formulation to estimate the underlying time-dependent parameters. This method is designed for random events with small numbers that are out of the applicability range of the normal distribution. The method is demonstrated for numerical data generated by a known system, and applied to time series of traffic accidents, batting average of a baseball player and sales volume of home electronics.

Spectral analysis of a two-species competition model: Determining the effects of extreme conditions on the color of noise generated from simulated time series

NASA Astrophysics Data System (ADS)

Golinski, M. R.

2006-07-01

Ecologists have observed that environmental noise affects population variance in the logistic equation for one-species growth. Interactions between deterministic and stochastic dynamics in a one-dimensional system result in increased variance in species population density over time. Since natural populations do not live in isolation, the present paper simulates a discrete-time two-species competition model with environmental noise to determine the type of colored population noise generated by extreme conditions in the long-term population dynamics of competing populations. Discrete Fourier analysis is applied to the simulation results and the calculated Hurst exponent ( H) is used to determine how the color of population noise for the two species corresponds to extreme conditions in population dynamics. To interpret the biological meaning of the color of noise generated by the two-species model, the paper determines the color of noise generated by three reference models: (1) A two-dimensional discrete-time white noise model (0⩽ H<1/2); (2) A two-dimensional fractional Brownian motion model (H=1/2); and (3) A two-dimensional discrete-time model with noise for unbounded growth of two uncoupled species (1/2< H⩽1).

Discretely Integrated Condition Event (DICE) Simulation for Pharmacoeconomics.

PubMed

Caro, J Jaime

2016-07-01

Several decision-analytic modeling techniques are in use for pharmacoeconomic analyses. Discretely integrated condition event (DICE) simulation is proposed as a unifying approach that has been deliberately designed to meet the modeling requirements in a straightforward transparent way, without forcing assumptions (e.g., only one transition per cycle) or unnecessary complexity. At the core of DICE are conditions that represent aspects that persist over time. They have levels that can change and many may coexist. Events reflect instantaneous occurrences that may modify some conditions or the timing of other events. The conditions are discretely integrated with events by updating their levels at those times. Profiles of determinant values allow for differences among patients in the predictors of the disease course. Any number of valuations (e.g., utility, cost, willingness-to-pay) of conditions and events can be applied concurrently in a single run. A DICE model is conveniently specified in a series of tables that follow a consistent format and the simulation can be implemented fully in MS Excel, facilitating review and validation. DICE incorporates both state-transition (Markov) models and non-resource-constrained discrete event simulation in a single formulation; it can be executed as a cohort or a microsimulation; and deterministically or stochastically.

A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes.

PubMed

Hahl, Sayuri K; Kremling, Andreas

2016-01-01

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still expected to provide relevant indications on the underlying dynamics.

Stochastic Nature in Cellular Processes

NASA Astrophysics Data System (ADS)

Liu, Bo; Liu, Sheng-Jun; Wang, Qi; Yan, Shi-Wei; Geng, Yi-Zhao; Sakata, Fumihiko; Gao, Xing-Fa

2011-11-01

The importance of stochasticity in cellular processes is increasingly recognized in both theoretical and experimental studies. General features of stochasticity in gene regulation and expression are briefly reviewed in this article, which include the main experimental phenomena, classification, quantization and regulation of noises. The correlation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methods that can capture effects of intrinsic and extrinsic noise are described.

The open quantum Brownian motions

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2014-09-01

Using quantum parallelism on random walks as the original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers—with internal degrees of freedom which serve as random gyroscopes—interacting with a series of probes which serve as quantum coins. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: the quantum trajectory, the quantum dynamical map and the quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as an internal gyroscope, illustrating the interplay between the ballistic and diffusive behaviors at work in these processes. Notation H_z : orbital (walker) Hilbert space, {C}^{{Z}} in the discrete, L^2({R}) in the continuum H_c : internal spin (or gyroscope) Hilbert space H_sys=H_z\\otimesH_c : system Hilbert space H_p : probe (or quantum coin) Hilbert space, H_p={C}^2 \\rho^tot_t : density matrix for the total system (walker + internal spin + quantum coins) \\bar \\rho_t : reduced density matrix on H_sys : \\bar\\rho_t=\\int dxdy\\, \\bar\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | \\hat \\rho_t : system density matrix in a quantum trajectory: \\hat\\rho_t=\\int dxdy\\, \\hat\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | . If diagonal and localized in position: \\hat \\rho_t=\\rho_t\\otimes| X_t \\rangle _z\\langle X_t | ρt: internal density matrix in a simple quantum trajectory Xt: walker position in a simple quantum trajectory Bt: normalized Brownian motion ξt, \\xi_t^\\dagger : quantum noises

Discrete-time Quantum Walks via Interchange Framework and Memory in Quantum Evolution

NASA Astrophysics Data System (ADS)

Dimcovic, Zlatko

One of the newer and rapidly developing approaches in quantum computing is based on "quantum walks," which are quantum processes on discrete space that evolve in either discrete or continuous time and are characterized by mixing of components at each step. The idea emerged in analogy with the classical random walks and stochastic techniques, but these unitary processes are very different even as they have intriguing similarities. This thesis is concerned with study of discrete-time quantum walks. The original motivation from classical Markov chains required for discrete-time quantum walks that one adds an auxiliary Hilbert space, unrelated to the one in which the system evolves, in order to be able to mix components in that space and then take the evolution steps accordingly (based on the state in that space). This additional, "coin," space is very often an internal degree of freedom like spin. We have introduced a general framework for construction of discrete-time quantum walks in a close analogy with the classical random walks with memory that is rather different from the standard "coin" approach. In this method there is no need to bring in a different degree of freedom, while the full state of the system is still described in the direct product of spaces (of states). The state can be thought of as an arrow pointing from the previous to the current site in the evolution, representing the one-step memory. The next step is then controlled by a single local operator assigned to each site in the space, acting quite like a scattering operator. This allows us to probe and solve some problems of interest that have not had successful approaches with "coined" walks. We construct and solve a walk on the binary tree, a structure of great interest but until our result without an explicit discrete time quantum walk, due to difficulties in managing coin spaces necessary in the standard approach. Beyond algorithmic interests, the model based on memory allows one to explore effects of history on the quantum evolution and the subtle emergence of classical features as "memory" is explicitly kept for additional steps. We construct and solve a walk with an additional correlation step, finding interesting new features. On the other hand, the fact that the evolution is driven entirely by a local operator, not involving additional spaces, enables us to choose the Fourier transform as an operator completely controlling the evolution. This in turn allows us to combine the quantum walk approach with Fourier transform based techniques, something decidedly not possible in classical computational physics. We are developing a formalism for building networks manageable by walks constructed with this framework, based on the surprising efficiency of our framework in discovering internals of a simple network that we so far solved. Finally, in line with our expectation that the field of quantum walks can take cues from the rich history of development of the classical stochastic techniques, we establish starting points for the work on non-Abelian quantum walks, with a particular quantum-walk analog of the classical "card shuffling," the walk on the permutation group. In summary, this thesis presents a new framework for construction of discrete time quantum walks, employing and exploring memoried nature of unitary evolution. It is applied to fully solving the problems of: A walk on the binary tree and exploration of the quantum-to-classical transition with increased correlation length (history). It is then used for simple network discovery, and to lay the groundwork for analysis of complex networks, based on combined power of efficient exploration of the Hilbert space (as a walk mixing components) and Fourier transformation (since we can choose this for the evolution operator). We hope to establish this as a general technique as its power would be unmatched by any approaches available in the classical computing. We also looked at the promising and challenging prospect of walks on non-Abelian structures by setting up the problem of "quantum card shuffling," a quantum walk on the permutation group. Relation to other work is thoroughly discussed throughout, along with examination of the context of our work and overviews of our current and future work.

Distributed parallel computing in stochastic modeling of groundwater systems.

PubMed

Dong, Yanhui; Li, Guomin; Xu, Haizhen

2013-03-01

Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.

Mode identification using stochastic hybrid models with applications to conflict detection and resolution

NASA Astrophysics Data System (ADS)

Naseri Kouzehgarani, Asal

2009-12-01

Most models of aircraft trajectories are non-linear and stochastic in nature; and their internal parameters are often poorly defined. The ability to model, simulate and analyze realistic air traffic management conflict detection scenarios in a scalable, composable, multi-aircraft fashion is an extremely difficult endeavor. Accurate techniques for aircraft mode detection are critical in order to enable the precise projection of aircraft conflicts, and for the enactment of altitude separation resolution strategies. Conflict detection is an inherently probabilistic endeavor; our ability to detect conflicts in a timely and accurate manner over a fixed time horizon is traded off against the increased human workload created by false alarms---that is, situations that would not develop into an actual conflict, or would resolve naturally in the appropriate time horizon-thereby introducing a measure of probabilistic uncertainty in any decision aid fashioned to assist air traffic controllers. The interaction of the continuous dynamics of the aircraft, used for prediction purposes, with the discrete conflict detection logic gives rise to the hybrid nature of the overall system. The introduction of the probabilistic element, common to decision alerting and aiding devices, places the conflict detection and resolution problem in the domain of probabilistic hybrid phenomena. A hidden Markov model (HMM) has two stochastic components: a finite-state Markov chain and a finite set of output probability distributions. In other words an unobservable stochastic process (hidden) that can only be observed through another set of stochastic processes that generate the sequence of observations. The problem of self separation in distributed air traffic management reduces to the ability of aircraft to communicate state information to neighboring aircraft, as well as model the evolution of aircraft trajectories between communications, in the presence of probabilistic uncertain dynamics as well as partially observable and uncertain data. We introduce the Hybrid Hidden Markov Modeling (HHMM) formalism to enable the prediction of the stochastic aircraft states (and thus, potential conflicts), by combining elements of the probabilistic timed input output automaton and the partially observable Markov decision process frameworks, along with the novel addition of a Markovian scheduler to remove the non-deterministic elements arising from the enabling of several actions simultaneously. Comparisons of aircraft in level, climbing/descending and turning flight are performed, and unknown flight track data is evaluated probabilistically against the tuned model in order to assess the effectiveness of the model in detecting the switch between multiple flight modes for a given aircraft. This also allows for the generation of probabilistic distribution over the execution traces of the hybrid hidden Markov model, which then enables the prediction of the states of aircraft based on partially observable and uncertain data. Based on the composition properties of the HHMM, we study a decentralized air traffic system where aircraft are moving along streams and can perform cruise, accelerate, climb and turn maneuvers. We develop a common decentralized policy for conflict avoidance with spatially distributed agents (aircraft in the sky) and assure its safety properties via correctness proofs.

Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description

NASA Astrophysics Data System (ADS)

Alber, Mark; Chen, Nan; Glimm, Tilmann; Lushnikov, Pavel M.

2006-05-01

The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.

On the use of reverse Brownian motion to accelerate hybrid simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bakarji, Joseph; Tartakovsky, Daniel M., E-mail: tartakovsky@stanford.edu

Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategiesmore » for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.« less

Effect of Stochastic Charge Fluctuations on Dust Dynamics

NASA Astrophysics Data System (ADS)

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.

Application of stochastic discrete event system framework for detection of induced low rate TCP attack.

PubMed

Barbhuiya, F A; Agarwal, Mayank; Purwar, Sanketh; Biswas, Santosh; Nandi, Sukumar

2015-09-01

TCP is the most widely accepted transport layer protocol. The major emphasis during the development of TCP was its functionality and efficiency. However, not much consideration was given on studying the possibility of attackers exploiting the protocol, which has lead to several attacks on TCP. This paper deals with the induced low rate TCP attack. Since the attack is relatively new, only a few schemes have been proposed to mitigate it. However, the main issues with these schemes are scalability, change in TCP header, lack of formal frameworks, etc. In this paper, we have adapted the stochastic DES framework for detecting the attack, which addresses most of these issues. We have successfully deployed and tested the proposed DES based IDS on a test bed. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

PubMed Central

Zhang, Zhihua

2014-01-01

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842

Stochastic Processes in Physics: Deterministic Origins and Control

NASA Astrophysics Data System (ADS)

Demers, Jeffery

Stochastic processes are ubiquitous in the physical sciences and engineering. While often used to model imperfections and experimental uncertainties in the macroscopic world, stochastic processes can attain deeper physical significance when used to model the seemingly random and chaotic nature of the underlying microscopic world. Nowhere more prevalent is this notion than in the field of stochastic thermodynamics - a modern systematic framework used describe mesoscale systems in strongly fluctuating thermal environments which has revolutionized our understanding of, for example, molecular motors, DNA replication, far-from equilibrium systems, and the laws of macroscopic thermodynamics as they apply to the mesoscopic world. With progress, however, come further challenges and deeper questions, most notably in the thermodynamics of information processing and feedback control. Here it is becoming increasingly apparent that, due to divergences and subtleties of interpretation, the deterministic foundations of the stochastic processes themselves must be explored and understood. This thesis presents a survey of stochastic processes in physical systems, the deterministic origins of their emergence, and the subtleties associated with controlling them. First, we study time-dependent billiards in the quivering limit - a limit where a billiard system is indistinguishable from a stochastic system, and where the simplified stochastic system allows us to view issues associated with deterministic time-dependent billiards in a new light and address some long-standing problems. Then, we embark on an exploration of the deterministic microscopic Hamiltonian foundations of non-equilibrium thermodynamics, and we find that important results from mesoscopic stochastic thermodynamics have simple microscopic origins which would not be apparent without the benefit of both the micro and meso perspectives. Finally, we study the problem of stabilizing a stochastic Brownian particle with feedback control, and we find that in order to avoid paradoxes involving the first law of thermodynamics, we need a model for the fine details of the thermal driving noise. The underlying theme of this thesis is the argument that the deterministic microscopic perspective and stochastic mesoscopic perspective are both important and useful, and when used together, we can more deeply and satisfyingly understand the physics occurring over either scale.

Stochasticity in materials structure, properties, and processing—A review

NASA Astrophysics Data System (ADS)

Hull, Robert; Keblinski, Pawel; Lewis, Dan; Maniatty, Antoinette; Meunier, Vincent; Oberai, Assad A.; Picu, Catalin R.; Samuel, Johnson; Shephard, Mark S.; Tomozawa, Minoru; Vashishth, Deepak; Zhang, Shengbai

2018-03-01

We review the concept of stochasticity—i.e., unpredictable or uncontrolled fluctuations in structure, chemistry, or kinetic processes—in materials. We first define six broad classes of stochasticity: equilibrium (thermodynamic) fluctuations; structural/compositional fluctuations; kinetic fluctuations; frustration and degeneracy; imprecision in measurements; and stochasticity in modeling and simulation. In this review, we focus on the first four classes that are inherent to materials phenomena. We next develop a mathematical framework for describing materials stochasticity and then show how it can be broadly applied to these four materials-related stochastic classes. In subsequent sections, we describe structural and compositional fluctuations at small length scales that modify material properties and behavior at larger length scales; systems with engineered fluctuations, concentrating primarily on composite materials; systems in which stochasticity is developed through nucleation and kinetic phenomena; and configurations in which constraints in a given system prevent it from attaining its ground state and cause it to attain several, equally likely (degenerate) states. We next describe how stochasticity in these processes results in variations in physical properties and how these variations are then accentuated by—or amplify—stochasticity in processing and manufacturing procedures. In summary, the origins of materials stochasticity, the degree to which it can be predicted and/or controlled, and the possibility of using stochastic descriptions of materials structure, properties, and processing as a new degree of freedom in materials design are described.

Stochastic modelling of microstructure formation in solidification processes

NASA Astrophysics Data System (ADS)

Nastac, Laurentiu; Stefanescu, Doru M.

1997-07-01

To relax many of the assumptions used in continuum approaches, a general stochastic model has been developed. The stochastic model can be used not only for an accurate description of the fraction of solid evolution, and therefore accurate cooling curves, but also for simulation of microstructure formation in castings. The advantage of using the stochastic approach is to give a time- and space-dependent description of solidification processes. Time- and space-dependent processes can also be described by partial differential equations. Unlike a differential formulation which, in most cases, has to be transformed into a difference equation and solved numerically, the stochastic approach is essentially a direct numerical algorithm. The stochastic model is comprehensive, since the competition between various phases is considered. Furthermore, grain impingement is directly included through the structure of the model. In the present research, all grain morphologies are simulated with this procedure. The relevance of the stochastic approach is that the simulated microstructures can be directly compared with microstructures obtained from experiments. The computer becomes a `dynamic metallographic microscope'. A comparison between deterministic and stochastic approaches has been performed. An important objective of this research was to answer the following general questions: (1) `Would fully deterministic approaches continue to be useful in solidification modelling?' and (2) `Would stochastic algorithms be capable of entirely replacing purely deterministic models?'

Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture

NASA Astrophysics Data System (ADS)

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 transmission process: A combinatorial stochastic process for the evolution of transmission trees over networks.

PubMed

Sainudiin, Raazesh; Welch, David

2016-12-07

We derive a combinatorial stochastic process for the evolution of the transmission tree over the infected vertices of a host contact network in a susceptible-infected (SI) model of an epidemic. Models of transmission trees are crucial to understanding the evolution of pathogen populations. We provide an explicit description of the transmission process on the product state space of (rooted planar ranked labelled) binary transmission trees and labelled host contact networks with SI-tags as a discrete-state continuous-time Markov chain. We give the exact probability of any transmission tree when the host contact network is a complete, star or path network - three illustrative examples. We then develop a biparametric Beta-splitting model that directly generates transmission trees with exact probabilities as a function of the model parameters, but without explicitly modelling the underlying contact network, and show that for specific values of the parameters we can recover the exact probabilities for our three example networks through the Markov chain construction that explicitly models the underlying contact network. We use the maximum likelihood estimator (MLE) to consistently infer the two parameters driving the transmission process based on observations of the transmission trees and use the exact MLE to characterize equivalence classes over the space of contact networks with a single initial infection. An exploratory simulation study of the MLEs from transmission trees sampled from three other deterministic and four random families of classical contact networks is conducted to shed light on the relation between the MLEs of these families with some implications for statistical inference along with pointers to further extensions of our models. The insights developed here are also applicable to the simplest models of "meme" evolution in online social media networks through transmission events that can be distilled from observable actions such as "likes", "mentions", "retweets" and "+1s" along with any concomitant comments. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Energy consumption and entropy production in a stochastic formulation of BCM learning

NASA Astrophysics Data System (ADS)

de Oliveira, L. R.; Castellani, G.; Turchetti, G.

2013-12-01

Biochemical processes in living cells are open systems, therefore they exchange materials with their environment and they consume chemical energy. These processes are molecular-based and for that reason the role of fluctuations can not be ignored and the stochastic description is the most appropriate one. The chemical master equation describes in exact way the probabilistic dynamics of a given discrete set of states and helps us to understand and clarify the differences between closed and open systems. A closed system is related to a condition of detailed balance (DB), i.e. an equilibrium state. After a sufficiently long period, an open system will reach a non-equilibrium steady state (NESS) that is sustained by a flux of external energy. We demonstrate that two implementations of the BCM learning rule (BCM82) and (BCM92) are, respectively, always in DB, and never in DB. We define a one parameter parametrization of the BCM learning rule that interpolates between these two extremes. We compute thermodynamical quantities such as internal energy, free energy (both Helmholtz and Gibbs) and entropy. The entropy variation in the case of open systems (i.e. when DB does not hold) can be divided into internal entropy production and entropy exchanged with surroundings. We show how the entropy variation can be used to find the optimal value (corresponding to increased robustness and stability) for the parameter used in the BCM parametrization. Finally, we use the calculation of the work to drive the system from an initial state to the steady state as the parameter of the plasticity of the system.

Beyond the spectral theorem: Spectrally decomposing arbitrary functions of nondiagonalizable operators

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-06-01

Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, the familiar linear operator techniques that one would then hope to use often fail since the operators cannot be diagonalized. The curse of nondiagonalizability also plays an important role even in finite-dimensional linear operators, leading to analytical impediments that occur across many scientific domains. We show how to circumvent it via two tracks. First, using the well-known holomorphic functional calculus, we develop new practical results about spectral projection operators and the relationship between left and right generalized eigenvectors. Second, we generalize the holomorphic calculus to a meromorphic functional calculus that can decompose arbitrary functions of nondiagonalizable linear operators in terms of their eigenvalues and projection operators. This simultaneously simplifies and generalizes functional calculus so that it is readily applicable to analyzing complex physical systems. Together, these results extend the spectral theorem of normal operators to a much wider class, including circumstances in which poles and zeros of the function coincide with the operator spectrum. By allowing the direct manipulation of individual eigenspaces of nonnormal and nondiagonalizable operators, the new theory avoids spurious divergences. As such, it yields novel insights and closed-form expressions across several areas of physics in which nondiagonalizable dynamics arise, including memoryful stochastic processes, open nonunitary quantum systems, and far-from-equilibrium thermodynamics. The technical contributions include the first full treatment of arbitrary powers of an operator, highlighting the special role of the zero eigenvalue. Furthermore, we show that the Drazin inverse, previously only defined axiomatically, can be derived as the negative-one power of singular operators within the meromorphic functional calculus and we give a new general method to construct it. We provide new formulae for constructing spectral projection operators and delineate the relations among projection operators, eigenvectors, and left and right generalized eigenvectors. By way of illustrating its application, we explore several, rather distinct examples. First, we analyze stochastic transition operators in discrete and continuous time. Second, we show that nondiagonalizability can be a robust feature of a stochastic process, induced even by simple counting. As a result, we directly derive distributions of the time-dependent Poisson process and point out that nondiagonalizability is intrinsic to it and the broad class of hidden semi-Markov processes. Third, we show that the Drazin inverse arises naturally in stochastic thermodynamics and that applying the meromorphic functional calculus provides closed-form solutions for the dynamics of key thermodynamic observables. Finally, we draw connections to the Ruelle-Frobenius-Perron and Koopman operators for chaotic dynamical systems and propose how to extract eigenvalues from a time-series.

Dynamic stability of spinning pretwisted beams subjected to axial random forces

NASA Astrophysics Data System (ADS)

Young, T. H.; Gau, C. Y.

2003-11-01

This paper studies the dynamic stability of a pretwisted cantilever beam spinning along its longitudinal axis and subjected to an axial random force at the free end. The axial force is assumed as the sum of a constant force and a random process with a zero mean. Due to this axial force, the beam may experience parametric random instability. In this work, the finite element method is first applied to yield discretized system equations. The stochastic averaging method is then adopted to obtain Ito's equations for the response amplitudes of the system. Finally the mean-square stability criterion is utilized to determine the stability condition of the system. Numerical results show that the stability boundary of the system converges as the first three modes are taken into calculation. Before the convergence is reached, the stability condition predicted is not conservative enough.

Multiscale Modeling of Virus Entry via Receptor-Mediated Endocytosis

NASA Astrophysics Data System (ADS)

Liu, Jin

2012-11-01

Virus infections are ubiquitous and remain major threats to human health worldwide. Viruses are intracellular parasites and must enter host cells to initiate infection. Receptor-mediated endocytosis is the most common entry pathway taken by viruses, the whole process is highly complex and dictated by various events, such as virus motions, membrane deformations, receptor diffusion and ligand-receptor reactions, occurring at multiple length and time scales. We develop a multiscale model for virus entry through receptor-mediated endocytosis. The binding of virus to cell surface is based on a mesoscale three dimensional stochastic adhesion model, the internalization (endocytosis) of virus and cellular membrane deformation is based on the discretization of Helfrich Hamiltonian in a curvilinear space using Monte Carlo method. The multiscale model is based on the combination of these two models. We will implement this model to study the herpes simplex virus entry into B78 cells and compare the model predictions with experimental measurements.

Characterization of the Distance Relationship Between Localized Serotonin Receptors and Glia Cells on Fluorescence Microscopy Images of Brain Tissue.

PubMed

Jacak, Jaroslaw; Schaller, Susanne; Borgmann, Daniela; Winkler, Stephan M

2015-08-01

We here present two new methods for the characterization of fluorescent localization microscopy images obtained from immunostained brain tissue sections. Direct stochastic optical reconstruction microscopy images of 5-HT1A serotonin receptors and glial fibrillary acidic proteins in healthy cryopreserved brain tissues are analyzed. In detail, we here present two image processing methods for characterizing differences in receptor distribution on glial cells and their distribution on neural cells: One variant relies on skeleton extraction and adaptive thresholding, the other on k-means based discrete layer segmentation. Experimental results show that both methods can be applied for distinguishing classes of images with respect to serotonin receptor distribution. Quantification of nanoscopic changes in relative protein expression on particular cell types can be used to analyze degeneration in tissues caused by diseases or medical treatment.

Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification

NASA Astrophysics Data System (ADS)

Arnst, M.; Abello Álvarez, B.; Ponthot, J.-P.; Boman, R.

2017-11-01

This paper is concerned with the characterization and the propagation of errors associated with data limitations in polynomial-chaos-based stochastic methods for uncertainty quantification. Such an issue can arise in uncertainty quantification when only a limited amount of data is available. When the available information does not suffice to accurately determine the probability distributions that must be assigned to the uncertain variables, the Bayesian method for assigning these probability distributions becomes attractive because it allows the stochastic model to account explicitly for insufficiency of the available information. In previous work, such applications of the Bayesian method had already been implemented by using the Metropolis-Hastings and Gibbs Markov Chain Monte Carlo (MCMC) methods. In this paper, we present an alternative implementation, which uses an alternative MCMC method built around an Itô stochastic differential equation (SDE) that is ergodic for the Bayesian posterior. We draw together from the mathematics literature a number of formal properties of this Itô SDE that lend support to its use in the implementation of the Bayesian method, and we describe its discretization, including the choice of the free parameters, by using the implicit Euler method. We demonstrate the proposed methodology on a problem of uncertainty quantification in a complex nonlinear engineering application relevant to metal forming.

Finite-Horizon H∞ Consensus Control of Time-Varying Multiagent Systems With Stochastic Communication Protocol.

PubMed

Zou, Lei; Wang, Zidong; Gao, Huijun; Alsaadi, Fuad E

2017-03-31

This paper is concerned with the distributed H∞ consensus control problem for a discrete time-varying multiagent system with the stochastic communication protocol (SCP). A directed graph is used to characterize the communication topology of the multiagent network. The data transmission between each agent and the neighboring ones is implemented via a constrained communication channel where only one neighboring agent is allowed to transmit data at each time instant. The SCP is applied to schedule the signal transmission of the multiagent system. A sequence of random variables is utilized to capture the scheduling behavior of the SCP. By using the mapping technology combined with the Hadamard product, the closed-loop multiagent system is modeled as a time-varying system with a stochastic parameter matrix. The purpose of the addressed problem is to design a cooperative controller for each agent such that, for all probabilistic scheduling behaviors, the H∞ consensus performance is achieved over a given finite horizon for the closed-loop multiagent system. A necessary and sufficient condition is derived to ensure the H∞ consensus performance based on the completing squares approach and the stochastic analysis technique. Then, the controller parameters are obtained by solving two coupled backward recursive Riccati difference equations. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design scheme.

A stochastic-field description of finite-size spiking neural networks

PubMed Central

Longtin, André

2017-01-01

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics. PMID:28787447

Solving multistage stochastic programming models of portfolio selection with outstanding liabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Edirisinghe, C.

1994-12-31

Models for portfolio selection in the presence of an outstanding liability have received significant attention, for example, models for pricing options. The problem may be described briefly as follows: given a set of risky securities (and a riskless security such as a bond), and given a set of cash flows, i.e., outstanding liability, to be met at some future date, determine an initial portfolio and a dynamic trading strategy for the underlying securities such that the initial cost of the portfolio is within a prescribed wealth level and the expected cash surpluses arising from trading is maximized. While the tradingmore » strategy should be self-financing, there may also be other restrictions such as leverage and short-sale constraints. Usually the treatment is limited to binomial evolution of uncertainty (of stock price), with possible extensions for developing computational bounds for multinomial generalizations. Posing as stochastic programming models of decision making, we investigate alternative efficient solution procedures under continuous evolution of uncertainty, for discrete time economies. We point out an important moment problem arising in the portfolio selection problem, the solution (or bounds) on which provides the basis for developing efficient computational algorithms. While the underlying stochastic program may be computationally tedious even for a modest number of trading opportunities (i.e., time periods), the derived algorithms may used to solve problems whose sizes are beyond those considered within stochastic optimization.« less

Introduction to Stochastic Simulations for Chemical and Physical Processes: Principles and Applications

ERIC Educational Resources Information Center

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…

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

PubMed

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.

BACKWARD ESTIMATION OF STOCHASTIC PROCESSES WITH FAILURE EVENTS AS TIME ORIGINS1

PubMed Central

Gary Chan, Kwun Chuen; Wang, Mei-Cheng

2011-01-01

Stochastic processes often exhibit sudden systematic changes in pattern a short time before certain failure events. Examples include increase in medical costs before death and decrease in CD4 counts before AIDS diagnosis. To study such terminal behavior of stochastic processes, a natural and direct way is to align the processes using failure events as time origins. This paper studies backward stochastic processes counting time backward from failure events, and proposes one-sample nonparametric estimation of the mean of backward processes when follow-up is subject to left truncation and right censoring. We will discuss benefits of including prevalent cohort data to enlarge the identifiable region and large sample properties of the proposed estimator with related extensions. A SEER–Medicare linked data set is used to illustrate the proposed methodologies. PMID:21359167

Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case

NASA Astrophysics Data System (ADS)

Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L.

2010-06-01

Continuous-time random walks, or compound renewal processes, are pure-jump stochastic processes with several applications in insurance, finance, economics and physics. Based on heuristic considerations, a definition is given for stochastic integrals driven by continuous-time random walks, which includes the Itô and Stratonovich cases. It is then shown how the definition can be used to compute these two stochastic integrals by means of Monte Carlo simulations. Our example is based on the normal compound Poisson process, which in the diffusive limit converges to the Wiener process.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

PROPAGATOR: a synchronous stochastic wildfire propagation model with distributed computation engine

NASA Astrophysics Data System (ADS)

D´Andrea, M.; Fiorucci, P.; Biondi, G.; Negro, D.

2012-04-01

PROPAGATOR is a stochastic model of forest fire spread, useful as a rapid method for fire risk assessment. The model is based on a 2D stochastic cellular automaton. The domain of simulation is discretized using a square regular grid with cell size of 20x20 meters. The model uses high-resolution information such as elevation and type of vegetation on the ground. Input parameters are wind direction, speed and the ignition point of fire. The simulation of fire propagation is done via a stochastic mechanism of propagation between a burning cell and a non-burning cell belonging to its neighbourhood, i.e. the 8 adjacent cells in the rectangular grid. The fire spreads from one cell to its neighbours with a certain base probability, defined using vegetation types of two adjacent cells, and modified by taking into account the slope between them, wind direction and speed. The simulation is synchronous, and takes into account the time needed by the burning fire to cross each cell. Vegetation cover, slope, wind speed and direction affect the fire-propagation speed from cell to cell. The model simulates several mutually independent realizations of the same stochastic fire propagation process. Each of them provides a map of the area burned at each simulation time step. Propagator simulates self-extinction of the fire, and the propagation process continues until at least one cell of the domain is burning in each realization. The output of the model is a series of maps representing the probability of each cell of the domain to be affected by the fire at each time-step: these probabilities are obtained by evaluating the relative frequency of ignition of each cell with respect to the complete set of simulations. Propagator is available as a module in the OWIS (Opera Web Interfaces) system. The model simulation runs on a dedicated server and it is remote controlled from the client program, NAZCA. Ignition points of the simulation can be selected directly in a high-resolution, three-dimensional graphical representation of the Italian territory within NAZCA. The other simulation parameters, namely wind speed and direction, number of simulations, computing grid size and temporal resolution, can be selected from within the program interface. The output of the simulation is showed in real-time during the simulation, and are also available off-line and on the DEWETRA system, a Web GIS-based system for environmental risk assessment, developed according to OGC-INSPIRE standards. The model execution is very fast, providing a full prevision for the scenario in few minutes, and can be useful for real-time active fire management and suppression.