Stochastic processes inference theory

CERN Document Server

Rao, Malempati M

2014-01-01

This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.

Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

2016-07-01

The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

Stochastic heating in the cyclotron resonance of electrons

International Nuclear Information System (INIS)

Gutierrez T, C.; Hernandez A, O.

1999-01-01

The study of the different schemes of plasma heating by radiofrequency waves is a very actual problem related with the plasma heating in different machines and the particle acceleration mechanisms. In this work, it is obtained the expression for the temporal evolution of the energy absorbed in the cyclotron resonance of electrons where it is showed the stochastic character of the energy absorption. It is obtained the stochastic criteria in a magnetic configuration of an Ecr type plasma source. (Author)

Stochastic Analysis : A Series of Lectures

CERN Document Server

Dozzi, Marco; Flandoli, Franco; Russo, Francesco

2015-01-01

This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields o...

Stochastic volatility and stochastic leverage

DEFF Research Database (Denmark)

Veraart, Almut; Veraart, Luitgard A. M.

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...

Stochastic reaction-diffusion algorithms for macromolecular crowding

Science.gov (United States)

Sturrock, Marc

2016-06-01

Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.

Multivariate moment closure techniques for stochastic kinetic models

International Nuclear Information System (INIS)

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

2015-01-01

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs

Multivariate moment closure techniques for stochastic kinetic models

Energy Technology Data Exchange (ETDEWEB)

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.

Modeling animal movements using stochastic differential equations

Science.gov (United States)

Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie

2004-01-01

We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...

Adaptive stochastic Galerkin FEM with hierarchical tensor representations

KAUST Repository

Eigel, Martin

2016-01-01

PDE with stochastic data usually lead to very high-dimensional algebraic problems which easily become unfeasible for numerical computations because of the dense coupling structure of the discretised stochastic operator. Recently, an adaptive

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

Science.gov (United States)

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.

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

Science.gov (United States)

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

2012-01-21

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

Monitor-Based Statistical Model Checking for Weighted Metric Temporal Logic

DEFF Research Database (Denmark)

Bulychev, Petr; David, Alexandre; Larsen, Kim Guldstrand

2012-01-01

We present a novel approach and implementation for ana- lysing weighted timed automata (WTA) with respect to the weighted metric temporal logic (WMTL≤ ). Based on a stochastic semantics of WTAs, we apply statistical model checking (SMC) to estimate and test probabilities of satisfaction with desi......We present a novel approach and implementation for ana- lysing weighted timed automata (WTA) with respect to the weighted metric temporal logic (WMTL≤ ). Based on a stochastic semantics of WTAs, we apply statistical model checking (SMC) to estimate and test probabilities of satisfaction...

Linear stochastic neutron transport theory

International Nuclear Information System (INIS)

Lewins, J.

1978-01-01

A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)

The two-regime method for optimizing stochastic reaction-diffusion simulations

KAUST Repository

Flegg, M. B.; Chapman, S. J.; Erban, R.

2011-01-01

Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches

Stochastic quantum gravity

International Nuclear Information System (INIS)

Rumpf, H.

1987-01-01

We begin with a naive application of the Parisi-Wu scheme to linearized gravity. This will lead into trouble as one peculiarity of the full theory, the indefiniteness of the Euclidean action, shows up already at this level. After discussing some proposals to overcome this problem, Minkowski space stochastic quantization will be introduced. This will still not result in an acceptable quantum theory of linearized gravity, as the Feynman propagator turns out to be non-causal. This defect will be remedied only after a careful analysis of general covariance in stochastic quantization has been performed. The analysis requires the notion of a metric on the manifold of metrics, and a natural candidate for this is singled out. With this a consistent stochastic quantization of Einstein gravity becomes possible. It is even possible, at least perturbatively, to return to the Euclidean regime. 25 refs. (Author)

Stochastic ice stream dynamics.

Science.gov (United States)

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

2016-08-09

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

Stochastic dynamics of resistive switching: fluctuations lead to optimal particle number

International Nuclear Information System (INIS)

Radtke, Paul K; Schimansky-Geier, Lutz; Hazel, Andrew L; Straube, Arthur V

2017-01-01

Resistive switching (RS) is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start playing a role that cannot be neglected. A detailed understanding of switching mechanisms and reliability is essential. For this reason, we formulate a particle model based on the stochastic motion of oxygen vacancies. It allows us to investigate fluctuations in the resistance states of a switch with two active zones. The vacancies’ dynamics are governed by a master equation. Upon the application of a voltage pulse, the vacancies travel collectively through the switch. By deriving a generalized Burgers equation we can interpret this collective motion as nonlinear traveling waves, and numerically verify this result. Further, we define binary logical states by means of the underlying vacancy distributions, and establish a framework of writing and reading such memory element with voltage pulses. Considerations about the discriminability of these operations under fluctuations together with the markedness of the RS effect itself lead to the conclusion, that an intermediate vacancy number is optimal for performance. (paper)

Stochastic dynamics of resistive switching: fluctuations lead to optimal particle number

Science.gov (United States)

Radtke, Paul K.; Hazel, Andrew L.; Straube, Arthur V.; Schimansky-Geier, Lutz

2017-09-01

Resistive switching (RS) is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start playing a role that cannot be neglected. A detailed understanding of switching mechanisms and reliability is essential. For this reason, we formulate a particle model based on the stochastic motion of oxygen vacancies. It allows us to investigate fluctuations in the resistance states of a switch with two active zones. The vacancies’ dynamics are governed by a master equation. Upon the application of a voltage pulse, the vacancies travel collectively through the switch. By deriving a generalized Burgers equation we can interpret this collective motion as nonlinear traveling waves, and numerically verify this result. Further, we define binary logical states by means of the underlying vacancy distributions, and establish a framework of writing and reading such memory element with voltage pulses. Considerations about the discriminability of these operations under fluctuations together with the markedness of the RS effect itself lead to the conclusion, that an intermediate vacancy number is optimal for performance.

Breaking the theoretical scaling limit for predicting quasiparticle energies: the stochastic GW approach.

Science.gov (United States)

Neuhauser, Daniel; Gao, Yi; Arntsen, Christopher; Karshenas, Cyrus; Rabani, Eran; Baer, Roi

2014-08-15

We develop a formalism to calculate the quasiparticle energy within the GW many-body perturbation correction to the density functional theory. The occupied and virtual orbitals of the Kohn-Sham Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function G, the polarization potential W, and, thereby, the GW self-energy. The stochastic GW (sGW) formalism relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression, and spatial or temporal stochastic decoupling techniques. Beyond the theoretical interest, the formalism enables linear scaling GW calculations breaking the theoretical scaling limit for GW as well as circumventing the need for energy cutoff approximations. We illustrate the method for silicon nanocrystals of varying sizes with N_{e}>3000 electrons.

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

KAUST Repository

Jaleel, Hassan

2018-04-08

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

Time-translation noninvariance of temporal gauge propagator

International Nuclear Information System (INIS)

Lim, S.C.

1992-07-01

We show that within the framework of stochastic mechanics, the quantization of a free electromagnetic or Yang-Mills field in the temporal gauge can be consistently carried out. The resulting longitudinal component of the photon or gluon propagator is time-translation noninvariant. The exact form of the propagator depends on the additional boundary condition which fully fixes the temporal gauge. (author). 11 refs

Stochastic quantization and topological theories

International Nuclear Information System (INIS)

Fainberg, V.Y.; Subbotin, A.V.; Kuznetsov, A.N.

1992-01-01

In the last two years topological quantum field theories (TQFT) have attached much attention. This paper reports that from the very beginning it was realized that due to a peculiar BRST-like symmetry these models admitted so-called Nicolai mapping: the Nicolai variables, in terms of which actions of the theories become gaussian, are nothing but (anti-) selfduality conditions or their generalizations. This fact became a starting point in the quest of possible stochastic interpretation to topological field theories. The reasons behind were quite simple and included, in particular, the well-known relations between stochastic processes and supersymmetry. The main goal would have been achieved, if it were possible to construct stochastic processes governed by Langevin or Fokker-Planck equations in a real Euclidean time leading to TQFT's path integrals (equivalently: to reformulate TQFTs as non-equilibrium phase dynamics of stochastic processes). Further on, if it would appear that these processes correspond to the stochastic quantization of theories of some definite kind, one could expect (d + 1)-dimensional TQFTs to share some common properties with d-dimensional ones

A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall

Science.gov (United States)

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.

Composite stochastic processes

NARCIS (Netherlands)

Kampen, N.G. van

Certain problems in physics and chemistry lead to the definition of a class of stochastic processes. Although they are not Markovian they can be treated explicitly to some extent. In particular, the probability distribution for large times can be found. It is shown to obey a master equation. This

Stochastic population oscillations in spatial predator-prey models

International Nuclear Information System (INIS)

Taeuber, Uwe C

2011-01-01

It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield long-lived, but ultimately decaying erratic population oscillations, which can be understood through a resonant amplification mechanism for density fluctuations. In Monte Carlo simulations of spatial stochastic predator-prey systems, one observes striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey. In the presence of local particle density restrictions (finite prey carrying capacity), there exists an extinction threshold for the predator population. The accompanying continuous non-equilibrium phase transition is governed by the directed-percolation universality class. We employ field-theoretic methods based on the Doi-Peliti representation of the master equation for stochastic particle interaction models to (i) map the ensuing action in the vicinity of the absorbing state phase transition to Reggeon field theory, and (ii) to quantitatively address fluctuation-induced renormalizations of the population oscillation frequency, damping, and diffusion coefficients in the species coexistence phase.

Stochastic approach to microphysics

Energy Technology Data Exchange (ETDEWEB)

Aron, J.C.

1987-01-01

The presently widespread idea of ''vacuum population'', together with the quantum concept of vacuum fluctuations leads to assume a random level below that of matter. This stochastic approach starts by a reminder of the author's previous work, first on the relation of diffusion laws with the foundations of microphysics, and then on hadron spectrum. Following the latter, a random quark model is advanced; it gives to quark pairs properties similar to those of a harmonic oscillator or an elastic string, imagined as an explanation to their asymptotic freedom and their confinement. The stochastic study of such interactions as electron-nucleon, jets in e/sup +/e/sup -/ collisions, or pp -> ..pi../sup 0/ + X, gives form factors closely consistent with experiment. The conclusion is an epistemological comment (complementarity between stochastic and quantum domains, E.P.R. paradox, etc...).

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

Science.gov (United States)

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

Quantum Ito's formula and stochastic evolutions

International Nuclear Information System (INIS)

Hudson, R.L.; Parthasarathy, K.R.

1984-01-01

Using only the Boson canonical commutation relations and the Riemann-Lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes. This leads to a noncommutative Ito product formula, a realisation of the classical Poisson process in Fock space which gives a noncommutative central limit theorem, the construction of solutions of certain noncommutative stochastic differential equations, and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps. The classical Ito product formula for stochastic differentials with respect to Brownian motion and the Poisson process is a special case. (orig.)

PC analysis of stochastic differential equations driven by Wiener noise

KAUST Repository

Le Maitre, Olivier; Knio, Omar

2015-01-01

A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads

Temporal-varying failures of nodes in networks

Science.gov (United States)

Knight, Georgie; Cristadoro, Giampaolo; Altmann, Eduardo G.

2015-08-01

We consider networks in which random walkers are removed because of the failure of specific nodes. We interpret the rate of loss as a measure of the importance of nodes, a notion we denote as failure centrality. We show that the degree of the node is not sufficient to determine this measure and that, in a first approximation, the shortest loops through the node have to be taken into account. We propose approximations of the failure centrality which are valid for temporal-varying failures, and we dwell on the possibility of externally changing the relative importance of nodes in a given network by exploiting the interference between the loops of a node and the cycles of the temporal pattern of failures. In the limit of long failure cycles we show analytically that the escape in a node is larger than the one estimated from a stochastic failure with the same failure probability. We test our general formalism in two real-world networks (air-transportation and e-mail users) and show how communities lead to deviations from predictions for failures in hubs.

Stochasticity in the yeast mating pathway

International Nuclear Information System (INIS)

Hong-Li, Wang; Zheng-Ping, Fu; Xin-Hang, Xu; Qi, Ouyang

2009-01-01

We report stochastic simulations of the yeast mating signal transduction pathway. The effects of intrinsic and external noise, the influence of cell-to-cell difference in the pathway capacity, and noise propagation in the pathway have been examined. The stochastic temporal behaviour of the pathway is found to be robust to the influence of inherent fluctuations, and intrinsic noise propagates in the pathway in a uniform pattern when the yeasts are treated with pheromones of different stimulus strengths and of varied fluctuations. In agreement with recent experimental findings, extrinsic noise is found to play a more prominent role than intrinsic noise in the variability of proteins. The occurrence frequency for the reactions in the pathway are also examined and a more compact network is obtained by dropping most of the reactions of least occurrence

Stochastic Averaging and Stochastic Extremum Seeking

CERN Document Server

Liu, Shu-Jun

2012-01-01

Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering  and analysis of bacterial  convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...

Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition

KAUST Repository

Bessaih, Hakima

2015-11-02

The two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.

A stochastic model of enzyme kinetics

Science.gov (United States)

Stefanini, Marianne; Newman, Timothy; McKane, Alan

2003-10-01

Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.

Modeling noninvasive neurostimulation in epilepsy as stochastic interference in brain networks.

Science.gov (United States)

Stamoulis, Catherine; Chang, Bernard S

2013-05-01

Noninvasive brain stimulation is one of very few potential therapies for medically refractory epilepsy. However, its efficacy remains suboptimal and its therapeutic value has not been consistently assessed. This is in part due to the nonoptimized spatio-temporal application of stimulation protocols for seizure prevention or arrest, and incomplete knowledge of the neurodynamics of seizure evolution. Through simulations, this study investigated electroencephalography (EEG)-guided, stochastic interference with aberrantly coordinated neuronal networks, to prevent seizure onset or interrupt a propagating partial seizure, and prevent it from spreading to large areas of the brain. Brain stimulation was modeled as additive white or band-limited noise, and simulations using real EEGs and data generated from a network of integrate-and-fire neuronal ensembles were used to quantify spatio-temporal noise effects. It was shown that additive stochastic signals (noise) may destructively interfere with network dynamics and decrease or abolish synchronization associated with progressively coupled networks. Furthermore, stimulation parameters, particularly amplitude and spatio-temporal application, may be optimized based on patient-specific neurodynamics estimated directly from noninvasive EEGs.

Using stochastic models to incorporate spatial and temporal variability [Exercise 14

Science.gov (United States)

Carolyn Hull Sieg; Rudy M. King; Fred Van Dyke

2003-01-01

To this point, our analysis of population processes and viability in the western prairie fringed orchid has used only deterministic models. In this exercise, we conduct a similar analysis, using a stochastic model instead. This distinction is of great importance to population biology in general and to conservation biology in particular. In deterministic models,...

Stochasticity and the m = 1 mode in tokamaks

International Nuclear Information System (INIS)

Izzo, R.; Monticello, D.A.; Stodiek, W.; Park, W.

1986-05-01

It has recently been proposed that stochasticity resulting from toroidal coupling could lead to a saturation of the m = 1 internal mode in tokamaks. We present results from the nonlinear evolution of the m = 1 mode with toroidal coupling that show that stochasticity is not enough to cause saturation of the m = 1 mode

Stochastic models of cell motility

DEFF Research Database (Denmark)

Gradinaru, Cristian

2012-01-01

Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new...... interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic...... models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental...

Libor at crossroads: Stochastic switching detection using information theory quantifiers

International Nuclear Information System (INIS)

Bariviera, Aurelio F.; Guercio, M. Belén; Martinez, Lisana B.; Rosso, Osvaldo A.

2016-01-01

Highlights: • 28 time series of Libor rates, classified in seven maturities and four currencies, during the last 14 years, were considered. • The analysis was performed using a novel technique in financial economics: the Complexity–Entropy Causality Plane. • Our analysis unveils an abnormal movement of Libor time series around the period of the 2007 financial crisis. • This alteration in the stochastic dynamics of Libor is contemporary of what press called “Libor scandal”. - Abstract: This paper studies the 28 time series of Libor rates, classified in seven maturities and four currencies, during the last 14 years. The analysis was performed using a novel technique in financial economics: the Complexity–Entropy Causality Plane. This planar representation allows the discrimination of different stochastic and chaotic regimes. Using a temporal analysis based on moving windows, this paper unveils an abnormal movement of Libor time series around the period of the 2007 financial crisis. This alteration in the stochastic dynamics of Libor is contemporary of what press called “Libor scandal”, i.e. the manipulation of interest rates carried out by several prime banks. We argue that our methodology is suitable as a market watch mechanism, as it makes visible the temporal redution in informational efficiency of the market.

Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks.

Science.gov (United States)

Vestergaard, Christian L; Génois, Mathieu

2015-10-01

Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling.

TIME-DEPENDENT STOCHASTIC ACCELERATION MODEL FOR FERMI BUBBLES

Energy Technology Data Exchange (ETDEWEB)

Sasaki, Kento; Asano, Katsuaki; Terasawa, Toshio, E-mail: kentos@icrr.u-tokyo.ac.jp, E-mail: asanok@icrr.u-tokyo.ac.jp, E-mail: terasawa@icrr.u-tokyo.ac.jp [Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582 (Japan)

2015-12-01

We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin–Helmholtz, Rayleigh–Taylor, or Richtmyer–Meshkov instabilities, and plasma particles are continuously accelerated by the interaction with the turbulence. The turbulence gradually decays as it goes away from the shock fronts. Adopting a phenomenological model for the stochastic acceleration, we explicitly solve the temporal evolution of the particle energy distribution in the turbulence. Our results show that the spatial distribution of high-energy particles is different from those for a steady solution. We also show that the contribution of electrons that escaped from the acceleration regions significantly softens the photon spectrum. The photon spectrum and surface brightness profile are reproduced by our models. If the escape efficiency is very high, the radio flux from the escaped low-energy electrons can be comparable to that of the WMAP haze. We also demonstrate hadronic models with the stochastic acceleration, but they are unlikely in the viewpoint of the energy budget.

Problems of Mathematical Finance by Stochastic Control Methods

Science.gov (United States)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

Noise-induced temporal dynamics in Turing systems

KAUST Repository

Schumacher, Linus J.

2013-04-25

We examine the ability of intrinsic noise to produce complex temporal dynamics in Turing pattern formation systems, with particular emphasis on the Schnakenberg kinetics. Using power spectral methods, we characterize the behavior of the system using stochastic simulations at a wide range of points in parameter space and compare with analytical approximations. Specifically, we investigate whether polarity switching of stochastic patterns occurs at a defined frequency. We find that it can do so in individual realizations of a stochastic simulation, but that the frequency is not defined consistently across realizations in our samples of parameter space. Further, we examine the effect of noise on deterministically predicted traveling waves and find them increased in amplitude and decreased in speed. © 2013 American Physical Society.

Simulation and inference for stochastic processes with YUIMA a comprehensive R framework for SDEs and other stochastic processes

CERN Document Server

Iacus, Stefano M

2018-01-01

The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes or fractional Brownian motion, as well as CARMA processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these ...

Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

KAUST Repository

Richtarik, Peter; Taká č, Martin

2017-01-01

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

KAUST Repository

Richtarik, Peter

2017-06-04

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

Robustness of Populations in Stochastic Environments

DEFF Research Database (Denmark)

Gießen, Christian; Kötzing, Timo

2016-01-01

We consider stochastic versions of OneMax and LeadingOnes and analyze the performance of evolutionary algorithms with and without populations on these problems. It is known that the (1+1) EA on OneMax performs well in the presence of very small noise, but poorly for higher noise levels. We extend...... the abilities of the (1+1) EA. Larger population sizes are even more beneficial; we consider both parent and offspring populations. In this sense, populations are robust in these stochastic settings....

Binocular rivalry produced by temporal frequency differences

Directory of Open Access Journals (Sweden)

David eAlais

2012-07-01

Full Text Available Binocular rivalry occurs when each eye views images that are markedly different. Rather than seeing a binocular fusion of the two, each image is seen exclusively in a stochastic alternation of the monocular images. Here we examine whether temporal frequency differences will trigger binocular rivalry by presenting two random dot arrays that are spatially matched but which modulate temporally at two different rates and contained no net translation. We found that a perceptual alternation between the two temporal frequencies did indeed occur, provided the frequencies were sufficiently different, indicating that temporal information can produce binocular rivalry in the absence of spatial conflict. This finding is discussed with regard to the dependence of rivalry on conflict between spatial and temporal channels.

Doubly stochastic Poisson process models for precipitation at fine time-scales

Science.gov (United States)

Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao

2012-09-01

This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.

Temporal correlation between two channels EEG of bipolar lead in the head midline is associated with sleep-wake stages.

Science.gov (United States)

Li, Yanjun; Tang, Xiaoying; Xu, Zhi; Liu, Weifeng; Li, Jing

2016-03-01

Whether the temporal correlation between inter-leads Electroencephalogram (EEG) that located on the boundary between left and right brain hemispheres is associated with sleep stages or not is still unknown. The purpose of this paper is to evaluate the role of correlation coefficients between EEG leads Fpz-Cz and Pz-Oz for automatic classification of sleep stages. A total number of 39 EEG recordings (about 20 h each) were selected from the expanded sleep database in European data format for temporal correlation analysis. Original waveform of EEG was decomposed into sub-bands δ (1-4 Hz), θ (4-8 Hz), α (8-13 Hz) and β (13-30 Hz). The correlation coefficient between original EEG leads Fpz-Cz and Pz-Oz within frequency band 0.5-30 Hz was defined as r(EEG) and was calculated every 30 s, while that between the two leads EEG in sub-bands δ, θ, α and β were defined as r(δ), r(θ), r(α) and r(β), respectively. Classification of wakefulness and sleep was processed by fixed threshold that derived from the probability density function of correlation coefficients. There was no correlation between EEG leads Fpz-Cz and Pz-Oz during wakefulness (|r| r > 0.1 for r(EEG) and r(δ)), while low correlation existed during sleep (r ≈ -0.4 for r(EEG), r(δ), r(θ), r(α) and r(β)). There were significant differences (analysis of variance, P correlation index between EEG leads Fpz-Cz and Pz-Oz could distinguish all five types of wakefulness, rapid eye movement (REM) sleep, N1 sleep, N2 sleep and N3 sleep. In conclusion, the temporal correlation between EEG bipolar leads Fpz-Cz and Pz-Oz are highly associated with sleep-wake stages. Moreover, high accuracy of sleep-wake classification could be achieved by the temporal correlation within frequency band 0.5-30 Hz between EEG leads Fpz-Cz and Pz-Oz.

Network interdiction and stochastic integer programming

CERN Document Server

2003-01-01

On March 15, 2002 we held a workshop on network interdiction and the more general problem of stochastic mixed integer programming at the University of California, Davis. Jesús De Loera and I co-chaired the event, which included presentations of on-going research and discussion. At the workshop, we decided to produce a volume of timely work on the topics. This volume is the result. Each chapter represents state-of-the-art research and all of them were refereed by leading investigators in the respective fields. Problems - sociated with protecting and attacking computer, transportation, and social networks gain importance as the world becomes more dep- dent on interconnected systems. Optimization models that address the stochastic nature of these problems are an important part of the research agenda. This work relies on recent efforts to provide methods for - dressing stochastic mixed integer programs. The book is organized with interdiction papers first and the stochastic programming papers in the second part....

Stochastic Effects; Application in Nuclear Physics

International Nuclear Information System (INIS)

Mazonka, O.

2000-04-01

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

Fornix and medial temporal lobe lesions lead to comparable deficits in complex visual perception.

Science.gov (United States)

Lech, Robert K; Koch, Benno; Schwarz, Michael; Suchan, Boris

2016-05-04

Recent research dealing with the structures of the medial temporal lobe (MTL) has shifted away from exclusively investigating memory-related processes and has repeatedly incorporated the investigation of complex visual perception. Several studies have demonstrated that higher level visual tasks can recruit structures like the hippocampus and perirhinal cortex in order to successfully perform complex visual discriminations, leading to a perceptual-mnemonic or representational view of the medial temporal lobe. The current study employed a complex visual discrimination paradigm in two patients suffering from brain lesions with differing locations and origin. Both patients, one with extensive medial temporal lobe lesions (VG) and one with a small lesion of the anterior fornix (HJK), were impaired in complex discriminations while showing otherwise mostly intact cognitive functions. The current data confirmed previous results while also extending the perceptual-mnemonic theory of the MTL to the main output structure of the hippocampus, the fornix. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Spatial and temporal variation in lead and cadmium in the Laughing Gull, Larus atricilla

Energy Technology Data Exchange (ETDEWEB)

Reid, M; Hacker, C S

1982-11-01

Lead and cadmium concentrations were measured in eggs and in bone, kidney, liver and stomach contents of downy young, prefledgling, and adult Laughing Gulls collected from Matagorda Bay and Galveston Bay, Texas. Matagorda Bay drains a rural, moderately industrialized region while the Galveston Bay area is heavily urbanized and industrialized. Lead levels were lower in birds from Matagorda Bay and decreased in birds from Galveston Bay between 1977 and 1980. Cadmium levels were also lower in birds from Matagorda Bay but increased over the three-year period in those from Galveston Bay. The temporal decrease in lead may be associated with such environmental control efforts as reduced point source emissions and substitution of unleaded gasoline.

The role of stochasticity in sawtooth oscillation

International Nuclear Information System (INIS)

Lichtenberg, A.J.; Itoh, Kimitaka; Itoh, Sanae; Fukuyama, Atsushi.

1991-08-01

In this paper we have demonstrated that stochastization of field lines, resulting from the interaction of the fundamental m/n=1/1 helical mode with other periodicities, plays an important role in sawtooth oscillations. The time scale for the stochastic temperature diffusion has been determined. It was shown to be sufficiently fast to account for the fast sawtooth crash, and is generally shorter than the time scales for the redistribution of current. The enhancement of the electron and ion viscosity, arising from the stochastic field lines, has been calculated. The enhanced electron viscosity always leads to an initial increase in the growth rate of the mode; the enhanced ion viscosity can ultimately lead to mode stabilization before a complete temperature redistribution or flux reconnection has occurred. A dynamical model has been introduced to calculate the path of the sawtooth oscillation through a parameter space of shear and amplitude of the helical perturbation. The stochastic trigger to the enhanced growth rate and the stabilization by the ion viscosity are also included in the mode. A reasonable prescription for the flux reconnection at the end of the growth phase allows us to determine the initial q-value for the successive sawtooth ramps. (J.P.N.)

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

Science.gov (United States)

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

2010-09-21

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

Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations

Science.gov (United States)

Christensen, H. M.; Dawson, A.; Palmer, T.

2017-12-01

Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.

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

OpenAIRE

A. N. Gelfan; V. M. Moreido

2014-01-01

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

Spatio-temporal dynamics of security investments in an interdependent risk environment

Science.gov (United States)

Shafi, Kamran; Bender, Axel; Zhong, Weicai; Abbass, Hussein A.

2012-10-01

In a globalised world where risks spread through contagion, the decision of an entity to invest in securing its premises from stochastic risks no longer depends solely on its own actions but also on the actions of other interacting entities in the system. This phenomenon is commonly seen in many domains including airline, logistics and computer security and is referred to as Interdependent Security (IDS). An IDS game models this decision problem from a game-theoretic perspective and deals with the behavioural dynamics of risk-reduction investments in such settings. This paper enhances this model and investigates the spatio-temporal aspects of the IDS games. The spatio-temporal dynamics are studied using simple replicator dynamics on a variety of network structures and for various security cost tradeoffs that lead to different Nash equilibria in an IDS game. The simulation results show that the neighbourhood configuration has a greater effect on the IDS game dynamics than network structure. An in-depth empirical analysis of game dynamics is carried out on regular graphs, which leads to the articulation of necessary and sufficient conditions for dominance in IDS games under spatial constraints.

Large scale stochastic spatio-temporal modelling with PCRaster

NARCIS (Netherlands)

Karssenberg, D.J.; Drost, N.; Schmitz, O.; Jong, K. de; Bierkens, M.F.P.

2013-01-01

PCRaster is a software framework for building spatio-temporal models of land surface processes (http://www.pcraster.eu). Building blocks of models are spatial operations on raster maps, including a large suite of operations for water and sediment routing. These operations are available to model

Stochastic thermodynamics

Science.gov (United States)

Eichhorn, Ralf; Aurell, Erik

2014-04-01

many leading experts in the field. During the program, the most recent developments, open questions and new ideas in stochastic thermodynamics were presented and discussed. From the talks and debates, the notion of information in stochastic thermodynamics, the fundamental properties of entropy production (rate) in non-equilibrium, the efficiency of small thermodynamic machines and the characteristics of optimal protocols for the applied (cyclic) forces were crystallizing as main themes. Surprisingly, the long-studied adiabatic piston, its peculiarities and its relation to stochastic thermodynamics were also the subject of intense discussions. The comment on the Nordita program Stochastic Thermodynamics published in this issue of Physica Scripta exploits the Jarzynski relation for determining free energy differences in the adiabatic piston. This scientific program and the contribution presented here were made possible by the financial and administrative support of The Nordic Institute for Theoretical Physics.

Hourly temporal distribution of wind

Science.gov (United States)

Deligiannis, Ilias; Dimitriadis, Panayiotis; Koutsoyiannis, Demetris

2016-04-01

The wind process is essential for hydrometeorology and additionally, is one of the basic renewable energy resources. Most stochastic forecast models are limited up to daily scales disregarding the hourly scale which is significant for renewable energy management. Here, we analyze hourly wind timeseries giving emphasis on the temporal distribution of wind within the day. We finally present a periodic model based on statistical as well as hydrometeorological reasoning that shows good agreement with data. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

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

Directory of Open Access Journals (Sweden)

Wenlei Bai

2017-12-01

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

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

Science.gov (United States)

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

2014-10-01

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

Stochastic inflation in phase space: is slow roll a stochastic attractor?

Energy Technology Data Exchange (ETDEWEB)

Grain, Julien [Institut d' Astrophysique Spatiale, UMR8617, CNRS, Univ. Paris Sud, Université Paris-Saclay, Bt. 121, Orsay, F-91405 (France); Vennin, Vincent, E-mail: julien.grain@ias.u-psud.fr, E-mail: vincent.vennin@port.ac.uk [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO13FX (United Kingdom)

2017-05-01

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

A possible dynamical process leading to fractal structures

Indian Academy of Sciences (India)

In this paper, we propose a stochastic evolution of the early Universe which can lead to a fractal correlation in galactic distribution in the Universe. The stochastic equation of state, due to fluctuating creation rates of various components in a many-component fluid, leads to a fluctuating expansion rate for the Universe in the ...

Stochastic spatio-temporal model of coral cover as a function of herbivorous grazers, water quality, and coral demographics

Science.gov (United States)

Neuhausler, R.; Robinson, M.; Bruna, M.

2017-12-01

Over the last 60 years we have seen an increased amount of ecological regime shifts in tropical coastal zones, from coral reefs to macroalgae dominated states, as a result of natural and anthropogenic stresses. However, these shifts are not always immediate- macroalgae are generally present in coral reefs, with their distribution regulated by herbivorous fish. This is especially true in Moorea, French Polynesia, where macroalgae are shown to flourish in spaces that provide refuge from roaming herbivores. While there are currently modeling efforts in projecting ecological regime shifts in Moorea, temporal deterministic models have been utilized, which fail to capture metastability between multiple steady states and can have issues when dealing with very small populations. To address these concerns, we build on these models to account for spatial variations and individual organisms, as well as stochasticity. Our model can project the percent cover of coral, macroalgae, and algae turf as a function of herbivorous grazers, water quality, and coral demographics. Grazers, included as individual fish (particles), evolve according to a kinetic model and interact with neighbouring benthic assemblages, represented as nodes. Water quality and coral demographics are input parameters that can vary over time, allowing our model to be run for temporally changing scenarios and to be adjusted for different reefs. We plan to engage with previous Moorea Reef Resilience Models through a comparative analysis of our models' outcomes and existing Moorea data. Coupling projective models with available data is useful for informing environmental policy and advancing the modeling field.

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

Energy Technology Data Exchange (ETDEWEB)

Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Zhou, Weien, E-mail: weienzhou@nudt.edu.cn [College of Science, National University of Defense Technology, Changsha 410073 (China)

2017-08-01

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.

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

International Nuclear Information System (INIS)

Cui, Jianbo; Hong, Jialin; Liu, Zhihui; Zhou, Weien

2017-01-01

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.

PC analysis of stochastic differential equations driven by Wiener noise

KAUST Repository

Le Maitre, Olivier

2015-03-01

A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads to the definition of a hierarchy of stochastic differential equations governing the evolution of the PC modes. Under the mild assumption that the Wiener and uncertain parameters can be treated as independent random variables, it is also shown that the Galerkin formalism naturally separates parametric uncertainty and stochastic forcing dependences. This enables us to perform an orthogonal decomposition of the process variance, and consequently identify contributions arising from the uncertainty in parameters, the stochastic forcing, and a coupled term. Insight gained from this decomposition is illustrated in light of implementation to simplified linear and non-linear problems; the case of a stochastic bifurcation is also considered.

Stochastic samples versus vacuum expectation values in cosmology

International Nuclear Information System (INIS)

Tsamis, N.C.; Tzetzias, Aggelos; Woodard, R.P.

2010-01-01

Particle theorists typically use expectation values to study the quantum back-reaction on inflation, whereas many cosmologists stress the stochastic nature of the process. While expectation values certainly give misleading results for some things, such as the stress tensor, we argue that operators exist for which there is no essential problem. We quantify this by examining the stochastic properties of a noninteracting, massless, minimally coupled scalar on a locally de Sitter background. The square of the stochastic realization of this field seems to provide an example of great relevance for which expectation values are not misleading. We also examine the frequently expressed concern that significant back-reaction from expectation values necessarily implies large stochastic fluctuations between nearby spatial points. Rather than viewing the stochastic formalism in opposition to expectation values, we argue that it provides a marvelously simple way of capturing the leading infrared logarithm corrections to the latter, as advocated by Starobinsky

Temporal acceleration of spatially distributed kinetic Monte Carlo simulations

International Nuclear Information System (INIS)

Chatterjee, Abhijit; Vlachos, Dionisios G.

2006-01-01

The computational intensity of kinetic Monte Carlo (KMC) simulation is a major impediment in simulating large length and time scales. In recent work, an approximate method for KMC simulation of spatially uniform systems, termed the binomial τ-leap method, was introduced [A. Chatterjee, D.G. Vlachos, M.A. Katsoulakis, Binomial distribution based τ-leap accelerated stochastic simulation, J. Chem. Phys. 122 (2005) 024112], where molecular bundles instead of individual processes are executed over coarse-grained time increments. This temporal coarse-graining can lead to significant computational savings but its generalization to spatially lattice KMC simulation has not been realized yet. Here we extend the binomial τ-leap method to lattice KMC simulations by combining it with spatially adaptive coarse-graining. Absolute stability and computational speed-up analyses for spatial systems along with simulations provide insights into the conditions where accuracy and substantial acceleration of the new spatio-temporal coarse-graining method are ensured. Model systems demonstrate that the r-time increment criterion of Chatterjee et al. obeys the absolute stability limit for values of r up to near 1

Fractional Stochastic Field Theory

Science.gov (United States)

Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

Stochastic fractional differential equations: Modeling, method and analysis

International Nuclear Information System (INIS)

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

2012-01-01

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

Temporal Vulnerability and the Post-Disaster 'Window of Opportunity to Woo:' a Case Study of an African-American Floodplain Neighborhood after Hurricane Floyd in North Carolina.

Science.gov (United States)

de Vries, Daniel H

2017-01-01

After major flooding associated with Hurricane Floyd (1999) in North Carolina, mitigation managers seized upon the "window of opportunity" to woo residents to accept residential buyout offers despite sizable community resistance. I present a theoretical explanation of how post-crisis periods turn into "opportunities" based on a temporal referential theory that complements alternative explanations based on temporal coincidence, panarchy, and shock-doctrine theories. Results from fieldwork conducted from 2002 to 2004 illustrate how several temporal influences compromised collective calibration of "normalcy" in local cultural models, leading to an especially heightened vulnerability to collective surprise. Four factors particularly influenced this temporal vulnerability: 1) epistemological uncertainty of floodplain dynamics due to colonization; 2) cultural practices that maintained a casual amnesia; 3) meaning attributed to stochastic timing of floods; and 4) competitive impact of referential flood baseline attractors.

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

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen

2008-01-01

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

Stochastic Approaches Within a High Resolution Rapid Refresh Ensemble

Science.gov (United States)

Jankov, I.

2017-12-01

It is well known that global and regional numerical weather prediction (NWP) ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system is the use of stochastic physics. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), and Stochastic Perturbation of Physics Tendencies (SPPT). The focus of this study is to assess model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) using a variety of stochastic approaches. A single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model was utilized and ensemble members produced by employing stochastic methods. Parameter perturbations (using SPP) for select fields were employed in the Rapid Update Cycle (RUC) land surface model (LSM) and Mellor-Yamada-Nakanishi-Niino (MYNN) Planetary Boundary Layer (PBL) schemes. Within MYNN, SPP was applied to sub-grid cloud fraction, mixing length, roughness length, mass fluxes and Prandtl number. In the RUC LSM, SPP was applied to hydraulic conductivity and tested perturbing soil moisture at initial time. First iterative testing was conducted to assess the initial performance of several configuration settings (e.g. variety of spatial and temporal de-correlation lengths). Upon selection of the most promising candidate configurations using SPP, a 10-day time period was run and more robust statistics were gathered. SKEB and SPPT were included in additional retrospective tests to assess the impact of using

BRS invariant stochastic quantization of Einstein gravity

International Nuclear Information System (INIS)

Nakazawa, Naohito.

1989-11-01

We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in the sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space of the first-class constrained systems. The phase space is spanned by the dynamical variables, their canonical conjugate momentum variables, Faddeev-Popov ghost and anti-ghost. We apply the general BRS invariant formulation to stochastic quantization of gravity which is described as a second-class constrained system in terms of a pair of Langevin equations coupled with white noises. It is shown that the stochastic action of gravity includes explicitly the De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)

Age distribution dynamics with stochastic jumps in mortality.

Science.gov (United States)

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

2017-11-01

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

Behavioural evidence for separate mechanisms of audiovisual temporal binding as a function of leading sensory modality.

Science.gov (United States)

Cecere, Roberto; Gross, Joachim; Thut, Gregor

2016-06-01

The ability to integrate auditory and visual information is critical for effective perception and interaction with the environment, and is thought to be abnormal in some clinical populations. Several studies have investigated the time window over which audiovisual events are integrated, also called the temporal binding window, and revealed asymmetries depending on the order of audiovisual input (i.e. the leading sense). When judging audiovisual simultaneity, the binding window appears narrower and non-malleable for auditory-leading stimulus pairs and wider and trainable for visual-leading pairs. Here we specifically examined the level of independence of binding mechanisms when auditory-before-visual vs. visual-before-auditory input is bound. Three groups of healthy participants practiced audiovisual simultaneity detection with feedback, selectively training on auditory-leading stimulus pairs (group 1), visual-leading stimulus pairs (group 2) or both (group 3). Subsequently, we tested for learning transfer (crossover) from trained stimulus pairs to non-trained pairs with opposite audiovisual input. Our data confirmed the known asymmetry in size and trainability for auditory-visual vs. visual-auditory binding windows. More importantly, practicing one type of audiovisual integration (e.g. auditory-visual) did not affect the other type (e.g. visual-auditory), even if trainable by within-condition practice. Together, these results provide crucial evidence that audiovisual temporal binding for auditory-leading vs. visual-leading stimulus pairs are independent, possibly tapping into different circuits for audiovisual integration due to engagement of different multisensory sampling mechanisms depending on leading sense. Our results have implications for informing the study of multisensory interactions in healthy participants and clinical populations with dysfunctional multisensory integration. © 2016 The Authors. European Journal of Neuroscience published by Federation

Stochastic acceleration by a single wave in a magnetized plasma

International Nuclear Information System (INIS)

Smith, R.

1977-01-01

A particularly simple problem exhibiting stochasticity is the motion of a charged particle in a uniform magnetic field and a single wave. Detailed studies of this wave-particle interaction show the following features. An electrostatic wave propagating obliquely to the magnetic field causes stochastic motion if the wave amplitude exceeds a certain threshold. The overlap of cyclotron resonances then destroys a constant of the motion, allowing strong particle acceleration. A wave of large enough amplitude would thus suffer severe damping and lead to rapid heating of a particle distribution. The stochastic motion resembles a diffusion process even though the wave spectrum contains only a single wave. The motion of ions in a nonuniform magnetic field and a single electrostatic wave is treated in our study of a possible saturation mechanism of the dissipative trapped-ion instability in a tokamak. A theory involving the overlap of bounce resonances predicts the main features found in the numerical integration of the equations of motion. Ions in a layer near the trapped-circulating boundary move stochastically. This motion leads to nonlinear stabilization mechanisms which are described qualitatively

Dynamic stochastic optimization

CERN Document Server

Ermoliev, Yuri; Pflug, Georg

2004-01-01

Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic­ itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec­ tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci­ sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu­ tions. Objective an...

On the Langevin equation for stochastic quantization of gravity

International Nuclear Information System (INIS)

Nakazawa, Naohito.

1989-10-01

We study the Langevin equation for stochastic quantization of gravity. By introducing two independent variables with a second-class constraint for the gravitational field, we formulate a pair of the Langevin equations for gravity which couples with white noises. After eliminating the multiplier field for the second-class constraint, we show that the equations leads to stochastic quantization of gravity including an unique superspace metric. (author)

Stochastic Analysis 2010

CERN Document Server

Crisan, Dan

2011-01-01

"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa

System Entropy Measurement of Stochastic Partial Differential Systems

Directory of Open Access Journals (Sweden)

Bor-Sen Chen

2016-03-01

Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.

Time series analysis of temporal networks

Science.gov (United States)

Sikdar, Sandipan; Ganguly, Niloy; Mukherjee, Animesh

2016-01-01

A common but an important feature of all real-world networks is that they are temporal in nature, i.e., the network structure changes over time. Due to this dynamic nature, it becomes difficult to propose suitable growth models that can explain the various important characteristic properties of these networks. In fact, in many application oriented studies only knowing these properties is sufficient. For instance, if one wishes to launch a targeted attack on a network, this can be done even without the knowledge of the full network structure; rather an estimate of some of the properties is sufficient enough to launch the attack. We, in this paper show that even if the network structure at a future time point is not available one can still manage to estimate its properties. We propose a novel method to map a temporal network to a set of time series instances, analyze them and using a standard forecast model of time series, try to predict the properties of a temporal network at a later time instance. To our aim, we consider eight properties such as number of active nodes, average degree, clustering coefficient etc. and apply our prediction framework on them. We mainly focus on the temporal network of human face-to-face contacts and observe that it represents a stochastic process with memory that can be modeled as Auto-Regressive-Integrated-Moving-Average (ARIMA). We use cross validation techniques to find the percentage accuracy of our predictions. An important observation is that the frequency domain properties of the time series obtained from spectrogram analysis could be used to refine the prediction framework by identifying beforehand the cases where the error in prediction is likely to be high. This leads to an improvement of 7.96% (for error level ≤20%) in prediction accuracy on an average across all datasets. As an application we show how such prediction scheme can be used to launch targeted attacks on temporal networks. Contribution to the Topical Issue

Expansions of general stationary stochastic optical fields: general formalism

International Nuclear Information System (INIS)

Martinez-Herrero, R.; Mejias, P.M.

1985-01-01

A new expansion of a general stationary stochastic optical field is derived. Each term of the series is seen to represent a recently defined new class of optical fields, the so-called spectrally quasi-factorizable fields. Alternative expansion in terms of nonstationary fields that obey the wave equation is also shown. A relationship between temporal and spatial features of stationary free optical fields is discussed

Light Optics for Optical Stochastic Cooling

Energy Technology Data Exchange (ETDEWEB)

Andorf, Matthew [NICADD, DeKalb; Lebedev, Valeri [Fermilab; Piot, Philippe [NICADD, DeKalb; Ruan, Jinhao [Fermilab

2016-06-01

In Optical Stochastic Cooling (OSC) radiation generated by a particle in a "pickup" undulator is amplified and transported to a downstream "kicker" undulator where it interacts with the same particle which radiated it. Fermilab plans to carry out both passive (no optical amplifier) and active (optical amplifier) tests of OSC at the Integrable Optics Test Accelerator (IOTA) currently in construction*. The performace of the optical system is analyzed with simulations in Synchrotron Radiation Workshop (SRW) accounting for the specific temporal and spectral properties of undulator radiation and being augmented to include dispersion of lens material.

Advances in stochastic and deterministic global optimization

CERN Document Server

Zhigljavsky, Anatoly; Žilinskas, Julius

2016-01-01

Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to multidimensional data visualization, regression, survey calibration, inventory management, timetabling, chemical engineering, energy systems, and competitive facility location. Graduate students, researchers, and scientists in computer science, numerical analysis, optimization, and applied mathematics will be fascinated by the theoretical, computational, and application-oriented aspects of stochastic and deterministic global optimization explored in this book. This volume is dedicated to the 70th birthday of Antanas Žilinskas who is a leading world expert in global optimization. Professor Žilinskas's research has concentrated on studying models for the objective function, the development and implementation of efficient algorithms for global optimization with single and mu...

Alfven-wave current drive and magnetic field stochasticity

International Nuclear Information System (INIS)

Litwin, C.; Hegna, C.C.

1993-01-01

Propagating Alfven waves can generate parallel current through an alpha effect. In resistive MHD however, the dynamo field is proportional to resistivity and as such cannot drive significant currents for realistic parameters. In the search for an enhancement of this effect the authors investigate the role of magnetic field stochasticity. They show that the presence of a stochastic magnetic field, either spontaneously generated by instabilities or induced externally, can enhance the alpha effect of the wave. This enhancement is caused by an increased wave dissipation due to both current diffusion and filamentation. For the range of parameters of current drive experiments at Phaedrus-T tokamak, a moderate field stochasticity leads to significant modifications in the loop voltage

Computational stochastic model of ions implantation

Energy Technology Data Exchange (ETDEWEB)

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

2015-03-10

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

Adaptive stochastic Galerkin FEM with hierarchical tensor representations

KAUST Repository

Eigel, Martin

2016-01-08

PDE with stochastic data usually lead to very high-dimensional algebraic problems which easily become unfeasible for numerical computations because of the dense coupling structure of the discretised stochastic operator. Recently, an adaptive stochastic Galerkin FEM based on a residual a posteriori error estimator was presented and the convergence of the adaptive algorithm was shown. While this approach leads to a drastic reduction of the complexity of the problem due to the iterative discovery of the sparsity of the solution, the problem size and structure is still rather limited. To allow for larger and more general problems, we exploit the tensor structure of the parametric problem by representing operator and solution iterates in the tensor train (TT) format. The (successive) compression carried out with these representations can be seen as a generalisation of some other model reduction techniques, e.g. the reduced basis method. We show that this approach facilitates the efficient computation of different error indicators related to the computational mesh, the active polynomial chaos index set, and the TT rank. In particular, the curse of dimension is avoided.

Analysis of Stochastic Radio Channels with Temporal Birth-Death Dynamics

DEFF Research Database (Denmark)

Jakobsen, Morten Lomholt; Pedersen, Troels; Fleury, Bernard Henri

2014-01-01

). The proof of this result is a consequence of the point process perspective, in particular by circumventing enumeration issues arising from the use of integer-indexed path components in traditional channel modeling approaches. The practical importance of being able to analytically characterize the birth......, with the underlying stochastic birth-death mechanism governed by two facilitating assumptions. Well-known analytical properties of this class of channel models are reestablished by simple arguments and several new results are derived. The primary tool used to obtain these results is Campbell's Theorem which enables......-death channel models is clearly evidenced, e.g., by the fact that key parameters enter explicitly in measurable quantities such as the power-delay profile....

Balancing Two-Player Stochastic Games with Soft Q-Learning

OpenAIRE

Grau-Moya, Jordi; Leibfried, Felix; Bou-Ammar, Haitham

2018-01-01

Within the context of video games the notion of perfectly rational agents can be undesirable as it leads to uninteresting situations, where humans face tough adversarial decision makers. Current frameworks for stochastic games and reinforcement learning prohibit tuneable strategies as they seek optimal performance. In this paper, we enable such tuneable behaviour by generalising soft Q-learning to stochastic games, where more than one agent interact strategically. We contribute both theoretic...

The role of temporal structure in human vision.

Science.gov (United States)

Blake, Randolph; Lee, Sang-Hun

2005-03-01

Gestalt psychologists identified several stimulus properties thought to underlie visual grouping and figure/ground segmentation, and among those properties was common fate: the tendency to group together individual objects that move together in the same direction at the same speed. Recent years have witnessed an upsurge of interest in visual grouping based on other time-dependent sources of visual information, including synchronized changes in luminance, in motion direction, and in figure/ ground relations. These various sources of temporal grouping information can be subsumed under the rubric temporal structure. In this article, the authors review evidence bearing on the effectiveness of temporal structure in visual grouping. They start with an overview of evidence bearing on temporal acuity of human vision, covering studies dealing with temporal integration and temporal differentiation. They then summarize psychophysical studies dealing with figure/ground segregation based on temporal phase differences in deterministic and stochastic events. The authors conclude with a brief discussion of neurophysiological implications of these results.

A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs

Science.gov (United States)

Khoshnevisan, Davar; Kim, Kunwoo; Xiao, Yimin

2018-05-01

It is generally argued that the solution to a stochastic PDE with multiplicative noise—such as \\dot{u}= 1/2 u''+uξ, where {ξ} denotes space-time white noise—routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (Arch Ration Mech Anal 177:115-150, 2005), Gibbon and Titi (Proc R Soc A 461:3089-3097, 2005), and Zimmermann et al. (Phys Rev Lett 85(17):3612-3615, 2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (J Phys A 22(13):2621-2626, 1989; Proc Lond Math Soc (3) 64:125-152, 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.

A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs

Science.gov (United States)

Khoshnevisan, Davar; Kim, Kunwoo; Xiao, Yimin

2018-04-01

It is generally argued that the solution to a stochastic PDE with multiplicative noise—such as \\dot{u}= 1/2 u''+uξ, where {ξ} denotes space-time white noise—routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (Arch Ration Mech Anal 177:115-150, 2005), Gibbon and Titi (Proc R Soc A 461:3089-3097, 2005), and Zimmermann et al. (Phys Rev Lett 85(17):3612-3615, 2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (J Phys A 22(13):2621-2626, 1989; Proc Lond Math Soc (3) 64:125-152, 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.

Modeling stochasticity and robustness in gene regulatory networks.

Science.gov (United States)

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

2009-06-15

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

BRS symmetry in stochastic quantization of the gravitational field

International Nuclear Information System (INIS)

Nakazawa, Naohito.

1989-12-01

We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in a sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space for gravity (in general, for the first-class constrained systems). The stochastic action of gravity includes explicitly an unique De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)

Cooperativity Leads to Temporally-Correlated Fluctuations in the Bacteriophage Lambda Genetic Switch

Directory of Open Access Journals (Sweden)

Jacob Quinn Shenker

2015-04-01

Full Text Available Cooperative interactions are widespread in biochemical networks, providing the nonlinear response that underlies behavior such as ultrasensitivity and robust switching. We introduce a temporal correlation function—the conditional activity—to study the behavior of these phenomena. Applying it to the bistable genetic switch in bacteriophage lambda, we find that cooperative binding between binding sites on the prophage DNA lead to non-Markovian behavior, as quantified by the conditional activity. Previously, the conditional activity has been used to predict allosteric pathways in proteins; here, we show that it identifies the rare unbinding events which underlie induction from lysogeny to lysis.

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

International Nuclear Information System (INIS)

Sabass, Benedikt; Schwarz, Ulrich S

2010-01-01

In migrating cells, retrograde flow of the actin cytoskeleton is related to traction at adhesion sites located at the base of the lamellipodium. The coupling between the moving cytoskeleton and the stationary adhesions is mediated by the continuous association and dissociation of molecular bonds. We introduce a simple model for the competition between the stochastic dynamics of elastic bonds at the moving interface and relaxation within the moving actin cytoskeleton represented by an internal viscous friction coefficient. Using exact stochastic simulations and an analytical mean field theory, we show that the stochastic bond dynamics lead to biphasic friction laws as observed experimentally. At low internal dissipation, stochastic bond dynamics lead to a regime of irregular stick-and-slip motion. High internal dissipation effectively suppresses cooperative effects among bonds and hence stabilizes the adhesion.

Environmental versus demographic variability in stochastic predator–prey models

International Nuclear Information System (INIS)

Dobramysl, U; Täuber, U C

2013-01-01

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

Stochastic and non-stochastic effects - a conceptual analysis

International Nuclear Information System (INIS)

Karhausen, L.R.

1980-01-01

The attempt to divide radiation effects into stochastic and non-stochastic effects is discussed. It is argued that radiation or toxicological effects are contingently related to radiation or chemical exposure. Biological effects in general can be described by general laws but these laws never represent a necessary connection. Actually stochastic effects express contingent, or empirical, connections while non-stochastic effects represent semantic and non-factual connections. These two expressions stem from two different levels of discourse. The consequence of this analysis for radiation biology and radiation protection is discussed. (author)

Stochastic theory for classical and quantum mechanical systems

International Nuclear Information System (INIS)

Pena, L. de la; Cetto, A.M.

1975-01-01

From first principles a theory of stochastic processes in configuration space is formulated. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schroedinger equation, which is derived with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section

Electricity price modeling with stochastic time change

International Nuclear Information System (INIS)

Borovkova, Svetlana; Schmeck, Maren Diane

2017-01-01

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

Temporal dynamics and transcriptional control using single-cell gene expression analysis.

Science.gov (United States)

Kouno, Tsukasa; de Hoon, Michiel; Mar, Jessica C; Tomaru, Yasuhiro; Kawano, Mitsuoki; Carninci, Piero; Suzuki, Harukazu; Hayashizaki, Yoshihide; Shin, Jay W

2013-01-01

Changes in environmental conditions lead to expression variation that manifest at the level of gene regulatory networks. Despite a strong understanding of the role noise plays in synthetic biological systems, it remains unclear how propagation of expression heterogeneity in an endogenous regulatory network is distributed and utilized by cells transitioning through a key developmental event. Here we investigate the temporal dynamics of a single-cell transcriptional network of 45 transcription factors in THP-1 human myeloid monocytic leukemia cells undergoing differentiation to macrophages. We systematically measure temporal regulation of expression and variation by profiling 120 single cells at eight distinct time points, and infer highly controlled regulatory modules through which signaling operates with stochastic effects. This reveals dynamic and specific rewiring as a cellular strategy for differentiation. The integration of both positive and negative co-expression networks further identifies the proto-oncogene MYB as a network hinge to modulate both the pro- and anti-differentiation pathways. Compared to averaged cell populations, temporal single-cell expression profiling provides a much more powerful technique to probe for mechanistic insights underlying cellular differentiation. We believe that our approach will form the basis of novel strategies to study the regulation of transcription at a single-cell level.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

Science.gov (United States)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

Science.gov (United States)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Spatio-temporal regulation of Hsp90-ligand complex leads to immune activation.

Directory of Open Access Journals (Sweden)

Yasuaki eTamura

2016-05-01

Full Text Available Hsp90 is the most abundant cytosolic HSP and is known to act as a molecular chaperone. We found that an Hsp90-cancer antigen peptide complex was efficiently cross-presented by human monocyte-derived dendritic cells and induced peptide-specific cytotoxic T lymphocytes. Furthermore, we observed that the internalized Hsp90-peptide complex was strictly sorted to the Rab5+, EEA1+ static early endosome and the Hsp90-chaperoned peptide was processed and bound to MHC class I molecules through a endosome-recycling pathway. We also found that extracellular Hsp90 complexed with CpG-A or self-DNA stimulates production of a large amount of IFN-α from pDCs via static early endosome targeting. Thus, extracellular Hsp90 can target the antigen or nucleic acid to a static early endosome by spatio-temporal regulation. Moreover, we showed that Hsp90 associates with and delivers TLR7/9 from the ER to early endosomes for ligand recognition. Hsp90 inhibitor, geldanamycin derivative inhibited the Hsp90 association with TLR7/9, resulting in inhibition IFN-α production, leading to improvement of SLE symptoms. Interstingly, we observed that serum Hsp90 is clearly increased in patients with active SLE compared with that in patients with inactive disease. Serum Hsp90 detected in SLE patients binds to self-DNA and/or anti-DNA Ab, thus leading to stimulation of pDCs to produce IFN-α. Thus, Hsp90 plays a crucial role in the pathogenesis of SLE and that an Hsp90 inhibitor will therefore provide a new therapeutic approach to SLE and other nucleic acid-related autoimmune diseases. We will discuss how spatio-temporal regulation of Hsp90-ligand complexes within antigen-presenting cells affects the innate immunity and adaptive immunity.

Spatially explicit and stochastic simulation of forest landscape fire disturbance and succession

Science.gov (United States)

Hong S. He; David J. Mladenoff

1999-01-01

Understanding disturbance and recovery of forest landscapes is a challenge because of complex interactions over a range of temporal and spatial scales. Landscape simulation models offer an approach to studying such systems at broad scales. Fire can be simulated spatially using mechanistic or stochastic approaches. We describe the fire module in a spatially explicit,...

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

Energy Technology Data Exchange (ETDEWEB)

Yu, Haitao; Guo, Xinmeng; Wang, Jiang, E-mail: jiangwang@tju.edu.cn; Deng, Bin; Wei, Xile [School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072 (China)

2014-09-01

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

International Nuclear Information System (INIS)

Yu, Haitao; Guo, Xinmeng; Wang, Jiang; Deng, Bin; Wei, Xile

2014-01-01

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks

Stochastic shock response spectrum decomposition method based on probabilistic definitions of temporal peak acceleration, spectral energy, and phase lag distributions of mechanical impact pyrotechnic shock test data

Science.gov (United States)

Hwang, James Ho-Jin; Duran, Adam

2016-08-01

Most of the times pyrotechnic shock design and test requirements for space systems are provided in Shock Response Spectrum (SRS) without the input time history. Since the SRS does not describe the input or the environment, a decomposition method is used to obtain the source time history. The main objective of this paper is to develop a decomposition method producing input time histories that can satisfy the SRS requirement based on the pyrotechnic shock test data measured from a mechanical impact test apparatus. At the heart of this decomposition method is the statistical representation of the pyrotechnic shock test data measured from the MIT Lincoln Laboratory (LL) designed Universal Pyrotechnic Shock Simulator (UPSS). Each pyrotechnic shock test data measured at the interface of a test unit has been analyzed to produce the temporal peak acceleration, Root Mean Square (RMS) acceleration, and the phase lag at each band center frequency. Maximum SRS of each filtered time history has been calculated to produce a relationship between the input and the response. Two new definitions are proposed as a result. The Peak Ratio (PR) is defined as the ratio between the maximum SRS and the temporal peak acceleration at each band center frequency. The ratio between the maximum SRS and the RMS acceleration is defined as the Energy Ratio (ER) at each band center frequency. Phase lag is estimated based on the time delay between the temporal peak acceleration at each band center frequency and the peak acceleration at the lowest band center frequency. This stochastic process has been applied to more than one hundred pyrotechnic shock test data to produce probabilistic definitions of the PR, ER, and the phase lag. The SRS is decomposed at each band center frequency using damped sinusoids with the PR and the decays obtained by matching the ER of the damped sinusoids to the ER of the test data. The final step in this stochastic SRS decomposition process is the Monte Carlo (MC

From complex to simple: interdisciplinary stochastic models

International Nuclear Information System (INIS)

Mazilu, D A; Zamora, G; Mazilu, I

2012-01-01

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions for certain physical quantities, such as the time dependence of the length of the microtubules, and diffusion coefficients. The second one is a stochastic adsorption model with applications in surface deposition, epidemics and voter systems. We introduce the ‘empty interval method’ and show sample calculations for the time-dependent particle density. These models can serve as an introduction to the field of non-equilibrium statistical physics, and can also be used as a pedagogical tool to exemplify standard statistical physics concepts, such as random walks or the kinetic approach of the master equation. (paper)

3D replicon distributions arise from stochastic initiation and domino-like DNA replication progression.

Science.gov (United States)

Löb, D; Lengert, N; Chagin, V O; Reinhart, M; Casas-Delucchi, C S; Cardoso, M C; Drossel, B

2016-04-07

DNA replication dynamics in cells from higher eukaryotes follows very complex but highly efficient mechanisms. However, the principles behind initiation of potential replication origins and emergence of typical patterns of nuclear replication sites remain unclear. Here, we propose a comprehensive model of DNA replication in human cells that is based on stochastic, proximity-induced replication initiation. Critical model features are: spontaneous stochastic firing of individual origins in euchromatin and facultative heterochromatin, inhibition of firing at distances below the size of chromatin loops and a domino-like effect by which replication forks induce firing of nearby origins. The model reproduces the empirical temporal and chromatin-related properties of DNA replication in human cells. We advance the one-dimensional DNA replication model to a spatial model by taking into account chromatin folding in the nucleus, and we are able to reproduce the spatial and temporal characteristics of the replication foci distribution throughout S-phase.

Doubly stochastic coherence in complex neuronal networks

Science.gov (United States)

Gao, Yang; Wang, Jianjun

2012-11-01

A system composed of coupled FitzHugh-Nagumo neurons with various topological structures is investigated under the co-presence of two independently additive and multiplicative Gaussian white noises, in which particular attention is paid to the neuronal networks spiking regularity. As the additive noise intensity and the multiplicative noise intensity are simultaneously adjusted to optimal values, the temporal periodicity of the output of the system reaches the maximum, indicating the occurrence of doubly stochastic coherence. The network topology randomness exerts different influences on the temporal coherence of the spiking oscillation for dissimilar coupling strength regimes. At a small coupling strength, the spiking regularity shows nearly no difference in the regular, small-world, and completely random networks. At an intermediate coupling strength, the temporal periodicity in a small-world neuronal network can be improved slightly by adding a small fraction of long-range connections. At a large coupling strength, the dynamical behavior of the neurons completely loses the resonance property with regard to the additive noise intensity or the multiplicative noise intensity, and the spiking regularity decreases considerably with the increase of the network topology randomness. The network topology randomness plays more of a depressed role than a favorable role in improving the temporal coherence of the spiking oscillation in the neuronal network research study.

Soil Erosion as a stochastic process

Science.gov (United States)

Casper, Markus C.

2015-04-01

corrected experimentally. To overcome this disadvantage of our actual models, soil erosion models are needed that are able to use stochastic directly variables and parameter distributions. There are only some minor approaches in this direction. The most advanced is the model "STOSEM" proposed by Sidorchuk in 2005. In this model, only a small part of the soil erosion processes is described, the aggregate detachment and the aggregate transport by flowing water. The concept is highly simplified, for example, many parameters are temporally invariant. Nevertheless, the main problem is that our existing measurements and experiments are not geared to provide stochastic parameters (e.g. as probability density functions); in the best case they deliver a statistical validation of the mean values. Again, we get effective parameters, spatially and temporally averaged. There is an urgent need for laboratory and field experiments on overland flow structure, raindrop effects and erosion rate, which deliver information on spatial and temporal structure of soil and surface properties and processes.

Stochastic flow modeling : Quasi-Geostrophy, Taylor state and torsional wave excitation

DEFF Research Database (Denmark)

Gillet, Nicolas; Jault, D.; Finlay, Chris

We reconstruct the core flow evolution over the period 1840-2010 under the quasi-geostrophic assumption, from the stochastic magnetic field model COV-OBS and its full model error covariance matrix. We make use of a prior information on the flow temporal power spectrum compatible with that of obse......We reconstruct the core flow evolution over the period 1840-2010 under the quasi-geostrophic assumption, from the stochastic magnetic field model COV-OBS and its full model error covariance matrix. We make use of a prior information on the flow temporal power spectrum compatible....... Large length-scales flow features are naturally dominated by their equatorially symmetric component from about 1900 when the symmetry constraint is relaxed. Equipartition of the kinetic energy in both symmetries coincides with the poor prediction of decadal length-of-day changes in the XIXth century. We...... interpret this as an evidence for quasi-geostrophic rapid flow changes, and the consequence of a too loose data constraint during the oldest period. We manage to retrieve rapid flow changes over the past 60 yrs, and in particular modulated torsional waves predicting correctly interannual length-of day...

Modeling stochastic lead times in multi-echelon systems

NARCIS (Netherlands)

Diks, E.B.; Heijden, van der M.C.

1996-01-01

In many multi-echelon inventory systems the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process which generates such lead times is usually not

Modeling stochastic lead times in multi-echelon systems

NARCIS (Netherlands)

Diks, E.B.; van der Heijden, M.C.

1997-01-01

In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well

Stochastic heating in the cyclotron resonance of electrons; Calentamiento estocastico en la resonancia ciclotronica de los electrones

Energy Technology Data Exchange (ETDEWEB)

Gutierrez T, C.; Hernandez A, O. [Instituto Nacional de Investigaciones Nucleares, A.P. 18-1027, 11801 Mexico D.F. (Mexico)

1999-07-01

The study of the different schemes of plasma heating by radiofrequency waves is a very actual problem related with the plasma heating in different machines and the particle acceleration mechanisms. In this work, it is obtained the expression for the temporal evolution of the energy absorbed in the cyclotron resonance of electrons where it is showed the stochastic character of the energy absorption. It is obtained the stochastic criteria in a magnetic configuration of an Ecr type plasma source. (Author)

Stochastic integration by parts and functional Itô calculus

CERN Document Server

Vives, Josep

2016-01-01

This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012). The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes. Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations. This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to pract...

Spatial and temporal variation in isotopic composition of atmospheric lead in Norwegian moss

International Nuclear Information System (INIS)

Rosman, K.J.R.; Ly, C.; Steinnes, E.

1998-01-01

Earlier studies using moss as a biomonitor of pollution have shown that long-range transport is a major source of pollution in Norway. Until now, the origin of these pollutants has been inferred from concentration measurements of various elements in moss and the climatology at each sampling site. Lead isotopes provide an opportunity to identify the sources and to quantify the contribution of each. This preliminary study reports measurements of lead isotopes in moss from selected sites along the full extent of Norway that reveal significant spatial and temporal variations. There are significant north-south trends that differ at coastal and inland sites and differ between sampling periods (1974--1994). These variations reflect the changing contributions from the different source regions as the regulation of pollution from automobiles and industry takes effect. Identifiable sources are the U.K. and possibly France, which is noticeable at coastal sites; western Europe at the southern end; and eastern Europe and Russia influencing the inland and northernmost sites

Stochastic modeling of the hypothalamic pulse generator activity.

Science.gov (United States)

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.

Noncausal stochastic calculus

CERN Document Server

Ogawa, Shigeyoshi

2017-01-01

This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...

Stochastic Spectral Descent for Discrete Graphical Models

International Nuclear Information System (INIS)

Carlson, David; Hsieh, Ya-Ping; Collins, Edo; Carin, Lawrence; Cevher, Volkan

2015-01-01

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

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

DEFF Research Database (Denmark)

Iwankiewicz, R.; Nielsen, Søren R. K.

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

Spatially heterogeneous stochasticity and the adaptive diversification of dormancy.

Science.gov (United States)

Rajon, E; Venner, S; Menu, F

2009-10-01

Diversified bet-hedging, a strategy that leads several individuals with the same genotype to express distinct phenotypes in a given generation, is now well established as a common evolutionary response to environmental stochasticity. Life-history traits defined as diversified bet-hedging (e.g. germination or diapause strategies) display marked differences between populations in spatial proximity. In order to find out whether such differences can be explained by local adaptations to spatially heterogeneous environmental stochasticity, we explored the evolution of bet-hedging dormancy strategies in a metapopulation using a two-patch model with patch differences in stochastic juvenile survival. We found that spatial differences in the level of environmental stochasticity, restricted dispersal, increased fragmentation and intermediate survival during dormancy all favour the adaptive diversification of bet-hedging dormancy strategies. Density dependency also plays a major role in the diversification of dormancy strategies because: (i) it may interact locally with environmental stochasticity and amplify its effects; however, (ii) it can also generate chaotic population dynamics that may impede diversification. Our work proposes new hypotheses to explain the spatial patterns of bet-hedging strategies that we hope will encourage new empirical studies of this topic.

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

Science.gov (United States)

Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning

2018-03-01

World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.

Stochastic generation of multi-site daily precipitation focusing on extreme events

Directory of Open Access Journals (Sweden)

G. Evin

2018-01-01

Full Text Available Many multi-site stochastic models have been proposed for the generation of daily precipitation, but they generally focus on the reproduction of low to high precipitation amounts at the stations concerned. This paper proposes significant extensions to the multi-site daily precipitation model introduced by Wilks, with the aim of reproducing the statistical features of extremely rare events (in terms of frequency and magnitude at different temporal and spatial scales. In particular, the first extended version integrates heavy-tailed distributions, spatial tail dependence, and temporal dependence in order to obtain a robust and appropriate representation of the most extreme precipitation fields. A second version enhances the first version using a disaggregation method. The performance of these models is compared at different temporal and spatial scales on a large region covering approximately half of Switzerland. While daily extremes are adequately reproduced at the stations by all models, including the benchmark Wilks version, extreme precipitation amounts at larger temporal scales (e.g., 3-day amounts are clearly underestimated when temporal dependence is ignored.

Numerical resolution of N-dimensional Fokker-Plank stochastic equations

International Nuclear Information System (INIS)

Garcia-Olivares, A.; Muoz, A.

1992-01-01

This document describes the use of a library of programs able to solve stochastic Fokker-Planck equations in a N-dimensional space. the input data are essentially: (i) the initial distribution of the stochastic variable, (ii) the drift and fluctuation coefficients as a function of the state (which can be obtained from the transition probabilities between neighboring states) and (iii) some parameters controlling the run. A last version of the library accepts sources and sinks defined in the states space. The output is the temporal evolution of the probability distribution in the space defined by a N-dimensional grid. Some applications and readings in Synergetics, Self-Organization, transport phenomena, Ecology and other fields are suggested. If the probability distribution is interpreted as a distribution of particles then the codes can be used to solve the N-dimensional problem of advection-diffusion. (author) 21 fig. 16 ref

Numerical Resolution of N-dimensional Fokker-Planck stochastic equations

International Nuclear Information System (INIS)

Garcia-Olivares, R. A.; Munoz Roldan, A.

1992-01-01

This document describes the use of a library of programs able to solve stochastic Fokker-Planck equations in a N-dimensional space. The input data are essentially: (i) the initial distribution of the stochastic variable, (ii) the drift and fluctuation coefficients as a function of the state (which can be obtained from the transition probabilities between neighboring states) and (iii) some parameters controlling the run. A last version of the library accepts sources and sinks defined in the states space. The output is the temporal evolution of the probability distribution in the space defined by a N-dimensional grid. Some applications and readings in Synergetic, Self-Organization, transport phenomena, Ecology and other fields are suggested. If the probability distribution is interpreted as a distribution of particles then the codes can be used to solve the N-dimensional problem of advection-diffusion. (Author) 16 refs

Evaluation of high resolution spatio-temporal precipitation extremes from a stochastic weather generator

DEFF Research Database (Denmark)

Sørup, Hjalte Jomo Danielsen; Christensen, O. B.; Arnbjerg-Nielsen, Karsten

gauges in the model area. The spatio-temporal performance of the model with respect to precipitation extremes is evaluated in the points of a 2x2 km regular grid covering the full model area. The model satisfactorily reproduces the extreme behaviour of the observed precipitation with respect to event...... intensity levels and unconditional spatial correlation when evaluated using an event based ranking approach at point scale and an advanced spatio-temporal coupling of extreme events. Prospectively the model can be used as a tool to evaluate the impact of climate change without relying onprecipitation output......Spatio-temporal rainfall is modelled for the North-Eastern part of Zealand (Denmark) using the Spatio-Temporal Neyman-Scott Rectangular Pulses model as implemented in the RainSim software. Hourly precipitation series for fitting the model are obtained from a dense network of tipping bucket rain...

Evoking prescribed spike times in stochastic neurons

Science.gov (United States)

Doose, Jens; Lindner, Benjamin

2017-09-01

Single cell stimulation in vivo is a powerful tool to investigate the properties of single neurons and their functionality in neural networks. We present a method to determine a cell-specific stimulus that reliably evokes a prescribed spike train with high temporal precision of action potentials. We test the performance of this stimulus in simulations for two different stochastic neuron models. For a broad range of parameters and a neuron firing with intermediate firing rates (20-40 Hz) the reliability in evoking the prescribed spike train is close to its theoretical maximum that is mainly determined by the level of intrinsic noise.

Detecting change in stochastic sound sequences.

Directory of Open Access Journals (Sweden)

Benjamin Skerritt-Davis

2018-05-01

Full Text Available Our ability to parse our acoustic environment relies on the brain's capacity to extract statistical regularities from surrounding sounds. Previous work in regularity extraction has predominantly focused on the brain's sensitivity to predictable patterns in sound sequences. However, natural sound environments are rarely completely predictable, often containing some level of randomness, yet the brain is able to effectively interpret its surroundings by extracting useful information from stochastic sounds. It has been previously shown that the brain is sensitive to the marginal lower-order statistics of sound sequences (i.e., mean and variance. In this work, we investigate the brain's sensitivity to higher-order statistics describing temporal dependencies between sound events through a series of change detection experiments, where listeners are asked to detect changes in randomness in the pitch of tone sequences. Behavioral data indicate listeners collect statistical estimates to process incoming sounds, and a perceptual model based on Bayesian inference shows a capacity in the brain to track higher-order statistics. Further analysis of individual subjects' behavior indicates an important role of perceptual constraints in listeners' ability to track these sensory statistics with high fidelity. In addition, the inference model facilitates analysis of neural electroencephalography (EEG responses, anchoring the analysis relative to the statistics of each stochastic stimulus. This reveals both a deviance response and a change-related disruption in phase of the stimulus-locked response that follow the higher-order statistics. These results shed light on the brain's ability to process stochastic sound sequences.

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

Science.gov (United States)

Ricci, F; Rica, R A; Spasenović, M; Gieseler, J; Rondin, L; Novotny, L; Quidant, R

2017-05-09

Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.

MODELLING AND SIMULATION OF A NEUROPHYSIOLOGICAL EXPERIMENT BY SPATIO-TEMPORAL POINT PROCESSES

Directory of Open Access Journals (Sweden)

Viktor Beneš

2011-05-01

Full Text Available We present a stochastic model of an experimentmonitoring the spiking activity of a place cell of hippocampus of an experimental animal moving in an arena. Doubly stochastic spatio-temporal point process is used to model and quantify overdispersion. Stochastic intensity is modelled by a Lévy based random field while the animal path is simplified to a discrete random walk. In a simulation study first a method suggested previously is used. Then it is shown that a solution of the filtering problem yields the desired inference to the random intensity. Two approaches are suggested and the new one based on finite point process density is applied. Using Markov chain Monte Carlo we obtain numerical results from the simulated model. The methodology is discussed.

Stochastic Optimal Prediction with Application to Averaged Euler Equations

Energy Technology Data Exchange (ETDEWEB)

Bell, John [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Chorin, Alexandre J. [Univ. of California, Berkeley, CA (United States); Crutchfield, William [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

2017-04-24

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.

On square-wave-driven stochastic resonance for energy harvesting in a bistable system

Energy Technology Data Exchange (ETDEWEB)

Su, Dongxu, E-mail: sudx@iis.u-tokyo.ac.jp [Graduate School of Engineering, The University of Tokyo, Tokyo 1538505 (Japan); Zheng, Rencheng; Nakano, Kimihiko [Institute of Industrial Science, The University of Tokyo, Tokyo 1538505 (Japan); Cartmell, Matthew P [Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD (United Kingdom)

2014-11-15

Stochastic resonance is a physical phenomenon through which the throughput of energy within an oscillator excited by a stochastic source can be boosted by adding a small modulating excitation. This study investigates the feasibility of implementing square-wave-driven stochastic resonance to enhance energy harvesting. The motivating hypothesis was that such stochastic resonance can be efficiently realized in a bistable mechanism. However, the condition for the occurrence of stochastic resonance is conventionally defined by the Kramers rate. This definition is inadequate because of the necessity and difficulty in estimating white noise density. A bistable mechanism has been designed using an explicit analytical model which implies a new approach for achieving stochastic resonance in the paper. Experimental tests confirm that the addition of a small-scale force to the bistable system excited by a random signal apparently leads to a corresponding amplification of the response that we now term square-wave-driven stochastic resonance. The study therefore indicates that this approach may be a promising way to improve the performance of an energy harvester under certain forms of random excitation.

On square-wave-driven stochastic resonance for energy harvesting in a bistable system

International Nuclear Information System (INIS)

Su, Dongxu; Zheng, Rencheng; Nakano, Kimihiko; Cartmell, Matthew P

2014-01-01

Stochastic resonance is a physical phenomenon through which the throughput of energy within an oscillator excited by a stochastic source can be boosted by adding a small modulating excitation. This study investigates the feasibility of implementing square-wave-driven stochastic resonance to enhance energy harvesting. The motivating hypothesis was that such stochastic resonance can be efficiently realized in a bistable mechanism. However, the condition for the occurrence of stochastic resonance is conventionally defined by the Kramers rate. This definition is inadequate because of the necessity and difficulty in estimating white noise density. A bistable mechanism has been designed using an explicit analytical model which implies a new approach for achieving stochastic resonance in the paper. Experimental tests confirm that the addition of a small-scale force to the bistable system excited by a random signal apparently leads to a corresponding amplification of the response that we now term square-wave-driven stochastic resonance. The study therefore indicates that this approach may be a promising way to improve the performance of an energy harvester under certain forms of random excitation

Structure and properties of Hughston's stochastic extension of the Schroedinger equation

International Nuclear Information System (INIS)

Adler, Stephen L.; Horwitz, Lawrence P.

2000-01-01

Hughston has recently proposed a stochastic extension of the Schroedinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston's equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston's equation to earlier work on norm-preserving stochastic equations, and show that Hughston's equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston's, suffices to give an objective interpretation of the measurement process in quantum mechanics. (c) 2000 American Institute of Physics

Evaluation of potential human health effects associated with the agricultural uses of 1,3-D: Spatial and temporal stochastic risk analysis

Energy Technology Data Exchange (ETDEWEB)

Driver, Jeffrey H., E-mail: jeff@risksciences.net [risksciences.net, LLC, 10009 Wisakon Trail, Manassas, VA 20111 (United States); Price, Paul S. [The Dow Chemical Company, 1803 Building, Midland, MI 48674 (United States); Van Wesenbeeck, Ian [Dow AgroSciences, LLC, 9330 Zionsville Road, Indianapolis, IN 46268 (United States); Ross, John H. [risksciences.net, LLC, 5150 Fair Oaks Blvd., Ste. 101-370, Carmichael, CA 95608 (United States); Gehen, Sean [Dow AgroSciences, LLC, 9330 Zionsville Road, Indianapolis, IN 46268 (United States); Holden, Larry R. [Larry R. Holden, Statistical Consulting, 1403 Post Oak Circle, College Station, TX (United States); Landenberger, Bryce [The Dow Chemical Company, 1803 Building, Midland, MI 48674 (United States); Hastings, Kerry; Yan, Zhongyu; Rasoulpour, Reza [Dow AgroSciences, LLC, 9330 Zionsville Road, Indianapolis, IN 46268 (United States)

2016-11-15

Dow AgroSciences (DAS) markets and sells 1,3-Dichloropropene (1,3-D), the active ingredient in Telone®, which is used as a pre-plant soil fumigant nematicide in economically important crops in California. 1,3-D has been regulated as a “probable human carcinogen” and the California Department of Pesticide Regulation limits use of 1,3-D based on human health risk assessments for bystanders. This paper presents a risk characterization for bystanders based on advances in the assessment of both exposure and hazard. The revised bystander risk assessment incorporates significant advances: 1) new data on residency duration and mobility in communities where 1,3-D is in high demand; 2) new information on spatial and temporal concentrations of 1,3-D in air based on multi-year modeling using a validated model; and 3) a new stochastic spatial and temporal model of long-term exposures. Predicted distributions of long-term, chronic exposures indicate that current, and anticipated uses of 1,3-D would result in lifetime average daily doses lower than 0.002 mg/kg/d, a dose associated with theoretical lifetime excess cancer risk of < 10{sup −} {sup 5} to > 95% of the local population based on a non-threshold risk assessment approach. Additionally, examination of 1,3-D toxicity studies including new chronic toxicity data and mechanism of action supports the use of a non-linear, threshold based risk assessment approach. The estimated maximum annual average daily dose of < 0.0016 mg/kg/d derived from the updated exposure assessment was then compared with a threshold point of departure. The calculated margin of exposure is > 1000-fold, a clear indication of acceptable risk for human health. In summary, the best available science supports 1,3-D's threshold nature of hazard and the revised exposure assessment supports that current agricultural uses of 1,3-D are associated with reasonable certainty of no harm, i.e., estimated long-term exposures pose insignificant health risks

STOCHASTIC FLOWS OF MAPPINGS

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.

Size and stochasticity in irrigated social-ecological systems

Science.gov (United States)

Puy, Arnald; Muneepeerakul, Rachata; Balbo, Andrea L.

2017-03-01

This paper presents a systematic study of the relation between the size of irrigation systems and the management of uncertainty. We specifically focus on studying, through a stylized theoretical model, how stochasticity in water availability and taxation interacts with the stochastic behavior of the population within irrigation systems. Our results indicate the existence of two key population thresholds for the sustainability of any irrigation system: or the critical population size required to keep the irrigation system operative, and N* or the population threshold at which the incentive to work inside the irrigation system equals the incentives to work elsewhere. Crossing irretrievably leads to system collapse. N* is the population level with a sub-optimal per capita payoff towards which irrigation systems tend to gravitate. When subjected to strong stochasticity in water availability or taxation, irrigation systems might suffer sharp population drops and irreversibly disintegrate into a system collapse, via a mechanism we dub ‘collapse trap’. Our conceptual study establishes the basis for further work aiming at appraising the dynamics between size and stochasticity in irrigation systems, whose understanding is key for devising mitigation and adaptation measures to ensure their sustainability in the face of increasing and inevitable uncertainty.

Modular invariance and stochastic quantization

International Nuclear Information System (INIS)

Ordonez, C.R.; Rubin, M.A.; Zwanziger, D.

1989-01-01

In Polyakov path integrals and covariant closed-string field theory, integration over Teichmueller parameters must be restricted by hand to a single modular region. This problem has an analog in Yang-Mills gauge theory---namely, the Gribov problem, which can be resolved by the method of stochastic gauge fixing. This method is here employed to quantize a simple modular-invariant system: the Polyakov point particle. In the limit of a large gauge-fixing force, it is shown that suitable choices for the functional form of the gauge-fixing force can lead to a restriction of Teichmueller integration to a single modular region. Modifications which arise when applying stochastic quantization to a system in which the volume of the orbits of the gauge group depends on a dynamical variable, such as a Teichmueller parameter, are pointed out, and the extension to Polyakov strings and covariant closed-string field theory is discussed

Collective, stochastic and nonequilibrium behavior of highly excited hadronic matter

Energy Technology Data Exchange (ETDEWEB)

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

1984-04-23

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

Lead Pollution Remanence in an Urban River System: A multi-scale temporal and spatial study

Directory of Open Access Journals (Sweden)

Ayrault S.

2013-04-01

Full Text Available This work aims at studying the fate of sediments contaminated with tetraethyl Pb from leaded gasoline using a two-dimension upscaling approach, from a small urban subcatchment, the Orge River (900 km2 to the whole Seine River basin (64700 km2, in France. In France, the leaded gasoline reduction started in 1986 and leaded gasoline was completely banned after 2000. This work aims at assessing whether the ban of leaded gasoline is related to changes in Pb contamination sources of these river suspended sediment particles (SPM and bed sediment. Sediment cores and samples collected in the course of previous research projects of the Seine River contamination were used as temporal archives. The study of the isotopic lead ratio showed the fast decrease of the contamination of urban river suspended particulate matter due to the “gasoline” lead source from 2000 to 2011. This source mostly disappeared in the SPM from the Seine River basin that includes urban areas but also agricultural and industrial activities. Nevertheless, it is still present in the small urban catchment of the Orge River. The results on bed sediments showed a different pattern, where the “gasoline” source is still active in densely populated areas, either in the Seine River in the 20 km downstream Paris, or along the Orge River.

Stochastic processes

CERN Document Server

Parzen, Emanuel

1962-01-01

Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine

Stochastic inflation: Quantum phase-space approach

International Nuclear Information System (INIS)

Habib, S.

1992-01-01

In this paper a quantum-mechanical phase-space picture is constructed for coarse-grained free quantum fields in an inflationary universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase-space quantum distribution function are found for the cases of power-law and exponential expansions. The expectation values of dynamical variables with respect to these solutions are compared to the corresponding cutoff regularized field-theoretic results (we do not restrict ourselves only to left-angle Φ 2 right-angle). Fair agreement is found provided the coarse-graining scale is kept within certain limits. By focusing on the full phase-space distribution function rather than a reduced distribution it is shown that the thermodynamic interpretation of the stochastic formalism faces several difficulties (e.g., there is no fluctuation-dissipation theorem). The coarse graining does not guarantee an automatic classical limit as quantum correlations turn out to be crucial in order to get results consistent with standard quantum field theory. Therefore, the method does not by itself constitute an explanation of the quantum to classical transition in the early Universe. In particular, we argue that the stochastic equations do not lead to decoherence

Stochastic sawtooth reconnection in ASDEX Upgrade

International Nuclear Information System (INIS)

Igochine, V.; Dumbrajs, O.; Zohm, H.; Flaws, A.

2007-01-01

In this paper we investigate non-complete sawtooth reconnection in the ASDEX Upgrade tokamak. Such reconnection phenomena are associated with internal m/n = 1/1 kink mode which does not vanish after the crash phase (as would be the case for complete reconnection). It is shown that this sawtooth cannot be fully described by pure m/n = 1/1 mode and that higher harmonics play an important role during the sawtooth crash phase. We employ the Hamiltonian formalism and reconstructed perturbations to model incomplete sawtooth reconnection. It is demonstrated that stochastization appears due to the excitation of low-order resonances which are present in the corresponding q-profiles inside the q = 1 surface which reflects the key role of the q 0 value. Depending on this value two completely different situations are possible for one and the same mode perturbations: (i) the resonant surfaces are present in the q-profile leading to stochasticity and sawtooth crash (q 0 ∼ 0.7 ± 0.1); (ii) the resonant surfaces are not present, which means no stochasticity in the system and no crash event (q 0 ∼ 0.9 ± 0.05). Accordingly the central safety factor value is always less than unity in the case of a non-complete sawtooth reconnection. Our investigations show that the stochastic model agrees well with the experimental observations and can be proposed as a promising candidate for an explanation of the sawtooth reconnection

Predicting Rift Valley Fever Inter-epidemic Activities and Outbreak Patterns: Insights from a Stochastic Host-Vector Model.

Directory of Open Access Journals (Sweden)

Sansao A Pedro

2016-12-01

Full Text Available Rift Valley fever (RVF outbreaks are recurrent, occurring at irregular intervals of up to 15 years at least in East Africa. Between outbreaks disease inter-epidemic activities exist and occur at low levels and are maintained by female Aedes mcintoshi mosquitoes which transmit the virus to their eggs leading to disease persistence during unfavourable seasons. Here we formulate and analyse a full stochastic host-vector model with two routes of transmission: vertical and horizontal. By applying branching process theory we establish novel relationships between the basic reproduction number, R0, vertical transmission and the invasion and extinction probabilities. Optimum climatic conditions and presence of mosquitoes have not fully explained the irregular oscillatory behaviour of RVF outbreaks. Using our model without seasonality and applying van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how outbreaks multi-year periodicity varies with the vertical transmission. Our theory predicts complex fluctuations with a dominant period of 1 to 10 years which essentially depends on the efficiency of vertical transmission. Our predictions are then compared to temporal patterns of disease outbreaks in Tanzania, Kenya and South Africa. Our analyses show that interaction between nonlinearity, stochasticity and vertical transmission provides a simple but plausible explanation for the irregular oscillatory nature of RVF outbreaks. Therefore, we argue that while rainfall might be the major determinant for the onset and switch-off of an outbreak, the occurrence of a particular outbreak is also a result of a build up phenomena that is correlated to vertical transmission efficiency.

A coupled stochastic inverse-management framework for dealing with nonpoint agriculture pollution under groundwater parameter uncertainty

Science.gov (United States)

Llopis-Albert, Carlos; Palacios-Marqués, Daniel; Merigó, José M.

2014-04-01

In this paper a methodology for the stochastic management of groundwater quality problems is presented, which can be used to provide agricultural advisory services. A stochastic algorithm to solve the coupled flow and mass transport inverse problem is combined with a stochastic management approach to develop methods for integrating uncertainty; thus obtaining more reliable policies on groundwater nitrate pollution control from agriculture. The stochastic inverse model allows identifying non-Gaussian parameters and reducing uncertainty in heterogeneous aquifers by constraining stochastic simulations to data. The management model determines the spatial and temporal distribution of fertilizer application rates that maximizes net benefits in agriculture constrained by quality requirements in groundwater at various control sites. The quality constraints can be taken, for instance, by those given by water laws such as the EU Water Framework Directive (WFD). Furthermore, the methodology allows providing the trade-off between higher economic returns and reliability in meeting the environmental standards. Therefore, this new technology can help stakeholders in the decision-making process under an uncertainty environment. The methodology has been successfully applied to a 2D synthetic aquifer, where an uncertainty assessment has been carried out by means of Monte Carlo simulation techniques.

Stochastic Gabor reflectivity and acoustic impedance inversion

Science.gov (United States)

Hariri Naghadeh, Diako; Morley, Christopher Keith; Ferguson, Angus John

2018-02-01

To delineate subsurface lithology to estimate petrophysical properties of a reservoir, it is possible to use acoustic impedance (AI) which is the result of seismic inversion. To change amplitude to AI, removal of wavelet effects from the seismic signal in order to get a reflection series, and subsequently transforming those reflections to AI, is vital. To carry out seismic inversion correctly it is important to not assume that the seismic signal is stationary. However, all stationary deconvolution methods are designed following that assumption. To increase temporal resolution and interpretation ability, amplitude compensation and phase correction are inevitable. Those are pitfalls of stationary reflectivity inversion. Although stationary reflectivity inversion methods are trying to estimate reflectivity series, because of incorrect assumptions their estimations will not be correct, but may be useful. Trying to convert those reflection series to AI, also merging with the low frequency initial model, can help us. The aim of this study was to apply non-stationary deconvolution to eliminate time variant wavelet effects from the signal and to convert the estimated reflection series to the absolute AI by getting bias from well logs. To carry out this aim, stochastic Gabor inversion in the time domain was used. The Gabor transform derived the signal’s time-frequency analysis and estimated wavelet properties from different windows. Dealing with different time windows gave an ability to create a time-variant kernel matrix, which was used to remove matrix effects from seismic data. The result was a reflection series that does not follow the stationary assumption. The subsequent step was to convert those reflections to AI using well information. Synthetic and real data sets were used to show the ability of the introduced method. The results highlight that the time cost to get seismic inversion is negligible related to general Gabor inversion in the frequency domain. Also

Climate, soil, and vegetation controls on the temporal variability of vadose zone transport

NARCIS (Netherlands)

Harman, C.J.; Rao, P.S.C.; Basu, N.B.; McGrath, G.S.; Kumar, P.; Sivapalan, M.

2011-01-01

Temporal patterns of solute transport and transformation through the vadose zone are driven by the stochastic variability of water fluxes. This is determined by the hydrologic filtering of precipitation variability into infiltration, storage, drainage, and evapotranspiration. In this work we develop

Stochasticity and superadiabaticity in radiofrequency plasma heating

International Nuclear Information System (INIS)

Stix, T.H.

1979-04-01

In a plasma subject to radiofrequency fields, it is only the resonant particles - comprising just a minor portion of the total velocity distribution - which are strongly affected. Under near-fusion conditions, thermalization by Coulomb collisions is slow, and noncollisional stochasticity can play an important role in reshaping f(v). It is found that the common rf interactions, including Landau, cyclotron and transit-time damping, can be fitted in a unified manner by a simple two-step one-parameter (epsilon) mapping which can display collision-free stochastic or adiabatic (also called superadiabatic) behavior, depending on the choice of epsilon. The effect on the evolution of the space averaged f (x,v,t) is reasonably well described by a pseudo-stochastic diffusion function, D/sub PS/(v,epsilon) which is the quasilinear diffusion coefficient but with appropriate widening of the delta-function spikes. Coulomb collisions, leading to D/sub Coul/(v) which may be added and directly compared to D/sub PS/(v,epsilon), are introduced by Langevin terms in the mapping equations

Stochastic phenomena in a fiber Raman amplifier

Energy Technology Data Exchange (ETDEWEB)

Kalashnikov, Vladimir [Aston Institute of Photonic Technologies, Aston University, Birmingham (United Kingdom); Institute of Photonics, Vienna University of Technology (Austria); Sergeyev, Sergey V. [Aston Institute of Photonic Technologies, Aston University, Birmingham (United Kingdom); Ania-Castanon, Juan Diego [Instituto de Optica CSIC, Madrid (Spain); Jacobsen, Gunnar [Acreo, Kista (Sweden); Popov, Sergei [Royal Institute of Technology (KTH), Stockholm (Sweden)

2017-01-15

The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of which is a key to unlocking the fiber optic systems specifications required in high resolution spectroscopy, metrology, biomedicine and telecommunications. Here, by using direct stochastic modeling, the mapping of interplay of the Raman scattering-based nonlinearity, the random birefringence of a fiber, and the pump-to-signal intensity noise transfer has been done in terms of the fiber Raman amplifier parameters, namely polarization mode dispersion, the relative intensity noise of the pump laser, fiber length, and the signal power. The obtained results reveal conditions for emergence of the random birefringence-induced resonance-like enhancement of the gain fluctuations (stochastic anti-resonance) accompanied by pulse broadening and rare events in the form of low power output signals having probability heavily deviated from the Gaussian distribution. (copyright 2016 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

A stochastic SIRS epidemic model with infectious force under intervention strategies

Science.gov (United States)

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

2015-12-01

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

Potential of stochastic cooling of heavy ions in the LHC

CERN Document Server

Schaumann, M; Blaskiewicz, M

2013-01-01

The dynamics of the high intensity lead beams in the LHC are strongly influenced by intra-beam scattering (IBS), leading to significant emittance growth and particle losses at all energies. Particle losses during collisions are dominated by nuclear electromagnetic processes and the debunching effect arising from the influence of IBS, resulting in a non-exponential intensity decay during the fill and short luminosity lifetimes. In the LHC heavy ion runs, 3 experiments will be taking data and the average fill duration will be rather short as a consequence of the high burn-off rate. The achievements with stochastic cooling at RHIC suggest that such a system at LHC could substantially reduce the emittance growth and the debunching component during injection and collisions. The luminosity lifetime and fill length could be improved to optimize the use of the limited run time of 4 weeks per year. This paper discusses the first results of a feasibility study to use stochastic cooling on the lead ion beams in the LHC....

A simulation to study the feasibility of improving the temporal resolution of LAGEOS geodynamic solutions by using a sequential process noise filter

Science.gov (United States)

Hartman, Brian Davis

1995-01-01

A key drawback to estimating geodetic and geodynamic parameters over time based on satellite laser ranging (SLR) observations is the inability to accurately model all the forces acting on the satellite. Errors associated with the observations and the measurement model can detract from the estimates as well. These 'model errors' corrupt the solutions obtained from the satellite orbit determination process. Dynamical models for satellite motion utilize known geophysical parameters to mathematically detail the forces acting on the satellite. However, these parameters, while estimated as constants, vary over time. These temporal variations must be accounted for in some fashion to maintain meaningful solutions. The primary goal of this study is to analyze the feasibility of using a sequential process noise filter for estimating geodynamic parameters over time from the Laser Geodynamics Satellite (LAGEOS) SLR data. This evaluation is achieved by first simulating a sequence of realistic LAGEOS laser ranging observations. These observations are generated using models with known temporal variations in several geodynamic parameters (along track drag and the J(sub 2), J(sub 3), J(sub 4), and J(sub 5) geopotential coefficients). A standard (non-stochastic) filter and a stochastic process noise filter are then utilized to estimate the model parameters from the simulated observations. The standard non-stochastic filter estimates these parameters as constants over consecutive fixed time intervals. Thus, the resulting solutions contain constant estimates of parameters that vary in time which limits the temporal resolution and accuracy of the solution. The stochastic process noise filter estimates these parameters as correlated process noise variables. As a result, the stochastic process noise filter has the potential to estimate the temporal variations more accurately since the constraint of estimating the parameters as constants is eliminated. A comparison of the temporal

Impurity penetration through the stochastic layer near the separatrix in tokamaks

International Nuclear Information System (INIS)

Morozov, D.K.; Herrera, J.J.E.; Rantsev-Kartinov, V.A.

1995-01-01

It is shown that a stochastic layer produced by ripple perturbations near the separatrix in tokamaks, leads to anomalous plasma flow out of the bulk plasma along perturbed field lines, which brings out impurities. This suggests that the stochastic layer may play a cleaning role. There is an opposite process of anomalous impurity diffusion into the plasma. The balance of these two processes defines the impurity concentration in the bulk plasma. copyright 1995 American Institute of Physics

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

Science.gov (United States)

Herman, Dor; Shnerb, Nadav M.

2017-08-01

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

Mean Field Games for Stochastic Growth with Relative Utility

Energy Technology Data Exchange (ETDEWEB)

Huang, Minyi, E-mail: mhuang@math.carleton.ca [Carleton University, School of Mathematics and Statistics (Canada); Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu [University of Puerto Rico, Department of Mathematics (United States)

2016-12-15

This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.

Mean Field Games for Stochastic Growth with Relative Utility

International Nuclear Information System (INIS)

Huang, Minyi; Nguyen, Son Luu

2016-01-01

This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.

Robustness of Populations in Stochastic Environments

DEFF Research Database (Denmark)

Gießen, Christian; Kötzing, Timo

2014-01-01

these results to LeadingOnes and to many different noise models, showing how the application of drift theory can significantly simplify and generalize previous analyses. Most surprisingly, even small populations (of size _(log n)) can make evolutionary algorithms perform well for high noise levels, well outside......We consider stochastic versions of OneMax and Leading-Ones and analyze the performance of evolutionary algorithms with and without populations on these problems. It is known that the (1+1) EA on OneMax performs well in the presence of very small noise, but poorly for higher noise levels. We extend...

Stochastic Modeling of Past Volcanic Crises

Science.gov (United States)

Woo, Gordon

2018-01-01

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

Acoustic wave propagation and stochastic effects in metamaterial absorbers

DEFF Research Database (Denmark)

Christensen, Johan; Willatzen, Morten

2014-01-01

We show how stochastic variations of the effective parameters of anisotropic structured metamaterials can lead to increased absorption of sound. For this, we derive an analytical model based on the Bourret approximation and illustrate the immediate connection between material disorder and attenua...

Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

NARCIS (Netherlands)

van Haastrecht, A.; Lord, R.; Pelsser, A.; Schrager, D.

2009-01-01

We consider the pricing of long-dated insurance contracts under stochastic interest rates and stochastic volatility. In particular, we focus on the valuation of insurance options with long-term equity or foreign exchange exposures. Our modeling framework extends the stochastic volatility model of

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

Science.gov (United States)

Gay-Balmaz, François; Holm, Darryl D.

2018-01-01

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

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

Science.gov (United States)

Gay-Balmaz, François; Holm, Darryl D.

2018-06-01

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

Modelling of oil spill frequency, leak sources and contamination probability in the Caspian Sea using multi-temporal SAR images 2006–2010 and stochastic modelling

Directory of Open Access Journals (Sweden)

Emil Bayramov

2016-05-01

Full Text Available The main goal of this research was to detect oil spills, to determine the oil spill frequencies and to approximate oil leak sources around the Oil Rocks Settlement, the Chilov and Pirallahi Islands in the Caspian Sea using 136 multi-temporal ENVISAT Advanced Synthetic Aperture Radar Wide Swath Medium Resolution images acquired during 2006–2010. The following oil spill frequencies were observed around the Oil Rocks Settlement, the Chilov and Pirallahi Islands: 2–10 (3471.04 sq km, 11–20 (971.66 sq km, 21–50 (692.44 sq km, 51–128 (191.38 sq km. The most critical oil leak sources with the frequency range of 41–128 were observed at the Oil Rocks Settlement. The exponential regression analysis between wind speeds and oil slick areas detected from 136 multi-temporal ENVISAT images revealed the regression coefficient equal to 63%. The regression model showed that larger oil spill areas were observed with decreasing wind speeds. The spatiotemporal patterns of currents in the Caspian Sea explained the multi-directional spatial distribution of oil spills around Oil Rocks Settlement, the Chilov and Pirallahi Islands. The linear regression analysis between detected oil spill frequencies and predicted oil contamination probability by the stochastic model showed the positive trend with the regression coefficient of 30%.

The interpolation method of stochastic functions and the stochastic variational principle

International Nuclear Information System (INIS)

Liu Xianbin; Chen Qiu

1993-01-01

Uncertainties have been attaching more importance to increasingly in modern engineering structural design. Viewed on an appropriate scale, the inherent physical attributes (material properties) of many structural systems always exhibit some patterns of random variation in space and time, generally the random variation shows a small parameter fluctuation. For a linear mechanical system, the random variation is modeled as a random one of a linear partial differential operator and, in stochastic finite element method, a random variation of a stiffness matrix. Besides the stochasticity of the structural physical properties, the influences of random loads which always represent themselves as the random boundary conditions bring about much more complexities in structural analysis. Now the stochastic finite element method or the probabilistic finite element method is used to study the structural systems with random physical parameters, whether or not the loads are random. Differing from the general finite element theory, the main difficulty which the stochastic finite element method faces is the inverse operation of stochastic operators and stochastic matrices, since the inverse operators and the inverse matrices are statistically correlated to the random parameters and random loads. So far, many efforts have been made to obtain the reasonably approximate expressions of the inverse operators and inverse matrices, such as Perturbation Method, Neumann Expansion Method, Galerkin Method (in appropriate Hilbert Spaces defined for random functions), Orthogonal Expansion Method. Among these methods, Perturbation Method appear to be the most available. The advantage of these methods is that the fairly accurate response statistics can be obtained under the condition of the finite information of the input. However, the second-order statistics obtained by use of Perturbation Method and Neumann Expansion Method are not always the appropriate ones, because the relevant second

Noise Analysis of Single-Ended Input Differential Amplifier using Stochastic Differential Equation

OpenAIRE

Tarun Kumar Rawat; Abhirup Lahiri; Ashish Gupta

2008-01-01

In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parame...

Stochastic dominance for law invariant preferences: The happy story of elliptical distributions

OpenAIRE

Matteo Del Vigna

2012-01-01

We study the connections between stochastic dominance and law invariant preferences. Whenever the functional that represents preferences depends only on the law of the random variable, we shall look for conditions that imply a ranking of distributions. In analogy with the Expected Utility paradigm, we prove that functional dominance leads to first order stochastic dominance. We analyze in details the case of Dual Theory of Choice and Cumulative Prospect Theory, including all its distinctive f...

High-resolution stochastic generation of extreme rainfall intensity for urban drainage modelling applications

Science.gov (United States)

Peleg, Nadav; Blumensaat, Frank; Molnar, Peter; Fatichi, Simone; Burlando, Paolo

2016-04-01

Urban drainage response is highly dependent on the spatial and temporal structure of rainfall. Therefore, measuring and simulating rainfall at a high spatial and temporal resolution is a fundamental step to fully assess urban drainage system reliability and related uncertainties. This is even more relevant when considering extreme rainfall events. However, the current space-time rainfall models have limitations in capturing extreme rainfall intensity statistics for short durations. Here, we use the STREAP (Space-Time Realizations of Areal Precipitation) model, which is a novel stochastic rainfall generator for simulating high-resolution rainfall fields that preserve the spatio-temporal structure of rainfall and its statistical characteristics. The model enables a generation of rain fields at 102 m and minute scales in a fast and computer-efficient way matching the requirements for hydrological analysis of urban drainage systems. The STREAP model was applied successfully in the past to generate high-resolution extreme rainfall intensities over a small domain. A sub-catchment in the city of Luzern (Switzerland) was chosen as a case study to: (i) evaluate the ability of STREAP to disaggregate extreme rainfall intensities for urban drainage applications; (ii) assessing the role of stochastic climate variability of rainfall in flow response and (iii) evaluate the degree of non-linearity between extreme rainfall intensity and system response (i.e. flow) for a small urban catchment. The channel flow at the catchment outlet is simulated by means of a calibrated hydrodynamic sewer model.

Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras

Energy Technology Data Exchange (ETDEWEB)

Dobay, M. P. D., E-mail: maria.pamela.david@physik.uni-muenchen.de; Alberola, A. Piera; Mendoza, E. R.; Raedler, J. O., E-mail: joachim.raedler@physik.uni-muenchen.de [Ludwig-Maximilians University, Faculty of Physics, Center for NanoScience (Germany)

2012-03-15

Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.

Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras

International Nuclear Information System (INIS)

Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.

2012-01-01

Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.

Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras

Science.gov (United States)

Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.

2012-03-01

Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.

Stochastic control and the second law of thermodynamics

Science.gov (United States)

Brockett, R. W.; Willems, J. C.

1979-01-01

The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average values, and not on sample path behavior. We are lead to a criterion which, when satisfied, permits one to assign a temperature to a stochastic system in such a way as to have Carnot cycles be the optimal trajectories of optimal control problems. Entropy is also defined and we are able to prove an equipartition of energy theorem using this definition of temperature. Our formulation allows one to treat irreversibility in a quite natural and completely precise way.

Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

Science.gov (United States)

Varga, Katherine Yvonne

2015-01-01

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

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas

2017-12-27

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas; Richtarik, Peter

2017-01-01

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Stochastic neuron models

CERN Document Server

Greenwood, Priscilla E

2016-01-01

This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...

Separating temporal and topological effects in walk-based network centrality.

Science.gov (United States)

Colman, Ewan R; Charlton, Nathaniel

2016-07-01

The recently introduced concept of dynamic communicability is a valuable tool for ranking the importance of nodes in a temporal network. Two metrics, broadcast score and receive score, were introduced to measure the centrality of a node with respect to a model of contagion based on time-respecting walks. This article examines the temporal and structural factors influencing these metrics by considering a versatile stochastic temporal network model. We analytically derive formulas to accurately predict the expectation of the broadcast and receive scores when one or more columns in a temporal edge-list are shuffled. These methods are then applied to two publicly available data sets and we quantify how much the centrality of each individual depends on structural or temporal influences. From our analysis, we highlight two practical contributions: a way to control for temporal variation when computing dynamic communicability and the conclusion that the broadcast and receive scores can, under a range of circumstances, be replaced by the row and column sums of the matrix exponential of a weighted adjacency matrix given by the data.

Solving simple stochastic games with few coin toss positions

DEFF Research Database (Denmark)

Ibsen-Jensen, Rasmus; Miltersen, Peter Bro

2011-01-01

Gimbert and Horn gave an algorithm for solving simple stochastic games with running time O(r! n) where n is the number of positions of the simple stochastic game and r is the number of its coin toss positions. Chatterjee et al. pointed out that a variant of strategy iteration can be implemented...... to solve this problem in time 4^r r^{O(1)} n^{O(1)}. In this paper, we show that an algorithm combining value iteration with retrograde analysis achieves a time bound of O(r 2^r (r log r + n)), thus improving both time bounds. While the algorithm is simple, the analysis leading to this time bound...

Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator

Science.gov (United States)

Zhang, Lu; Lai, Li; Peng, Hao; Tu, Zhe; Zhong, Suchuan

2018-01-01

The dynamics of many soft condensed matter and biological systems is affected by space limitations, which produce some peculiar effects on the systems' stochastic resonance (SR) behavior. In this study, we propose a model where SR can be observed: a confined overdamped harmonic oscillator that is subjected to a sinusoidal driving force and is under the influence of a multiplicative white noise. The output response of the system is a periodic signal with harmonic frequencies that are odd multiples of the driving frequency. We verify the amplitude resonances at the driving frequencies and superharmonic frequencies that are equal to three, five, and seven times the driving frequency, using a numerical method based on the stochastic Taylor expansion. The synergistic effect of the multiplicative white noise, constant boundaries, and periodic driving force that can induce a SR in the output amplitude at the driving and superharmonic frequencies is found. The SR phenomenon found in this paper is sensitive to the driving amplitude and frequency, inherent potential parameter, and boundary width, thus leading to various resonance conditions. Therefore, the mechanism found could be beneficial for the characterization of these confined systems and could constitute an important tool for controlling their basic properties.

Stochastic tools in turbulence

CERN Document Server

Lumey, John L

2012-01-01

Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the

Pricing real estate index options under stochastic interest rates

Science.gov (United States)

Gong, Pu; Dai, Jun

2017-08-01

Real estate derivatives as new financial instruments are not merely risk management tools but also provide a novel way to gain exposure to real estate assets without buying or selling the physical assets. Although real estate derivatives market has exhibited a rapid development in recent years, the valuation challenge of real estate derivatives remains a great obstacle for further development in this market. In this paper, we derive a partial differential equation contingent on a real estate index in a stochastic interest rate environment and propose a modified finite difference method that adopts the non-uniform grids to solve this problem. Numerical results confirm the efficiency of the method and indicate that constant interest rate models lead to the mispricing of options and the effects of stochastic interest rates on option prices depend on whether the term structure of interest rates is rising or falling. Finally, we have investigated and compared the different effects of stochastic interest rates on European and American option prices.

Stochastic analysis in production process and ecology under uncertainty

CERN Document Server

Bieda, Bogusław

2014-01-01

The monograph addresses a problem of stochastic analysis based on the uncertainty assessment by simulation and application of this method in ecology and steel industry under uncertainty. The first chapter defines the Monte Carlo (MC) method and random variables in stochastic models. Chapter two deals with the contamination transport in porous media. Stochastic approach for Municipal Solid Waste transit time contaminants modeling using MC simulation has been worked out. The third chapter describes the risk analysis of the waste to energy facility proposal for Konin city, including the financial aspects. Environmental impact assessment of the ArcelorMittal Steel Power Plant, in Kraków - in the chapter four - is given. Thus, four scenarios of the energy mix production processes were studied. Chapter five contains examples of using ecological Life Cycle Assessment (LCA) - a relatively new method of environmental impact assessment - which help in preparing pro-ecological strategy, and which can lead to reducing t...

Bond and CDS Pricing via the Stochastic Recovery Black-Cox Model

Directory of Open Access Journals (Sweden)

Albert Cohen

2017-04-01

Full Text Available Building on recent work incorporating recovery risk into structural models by Cohen & Costanzino (2015, we consider the Black-Cox model with an added recovery risk driver. The recovery risk driver arises naturally in the context of imperfect information implicit in the structural framework. This leads to a two-factor structural model we call the Stochastic Recovery Black-Cox model, whereby the asset risk driver At defines the default trigger and the recovery risk driver Rt defines the amount recovered in the event of default. We then price zero-coupon bonds and credit default swaps under the Stochastic Recovery Black-Cox model. Finally, we compare our results with the classic Black-Cox model, give explicit expressions for the recovery risk premium in the Stochastic Recovery Black-Cox model, and detail how the introduction of separate but correlated risk drivers leads to a decoupling of the default and recovery risk premiums in the credit spread. We conclude this work by computing the effect of adding coupons that are paid continuously until default, and price perpetual (consol bonds in our two-factor firm value model, extending calculations in the seminal paper by Leland (1994.

Extinction in neutrally stable stochastic Lotka-Volterra models

Science.gov (United States)

Dobrinevski, Alexander; Frey, Erwin

2012-05-01

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

Stochastic lag time in nucleated linear self-assembly

Energy Technology Data Exchange (ETDEWEB)

Tiwari, Nitin S. [Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Schoot, Paul van der [Group Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)

2016-06-21

Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise on account of the small system size at the cellular scale. We study the nucleated reversible self-assembly of monomeric building blocks into polymer-like aggregates using the method of kinetic Monte Carlo. Kinetic Monte Carlo, being inherently stochastic, allows us to study the impact of fluctuations on the polymerization reactions. One of the most important characteristic features in this kind of problem is the existence of a lag phase before self-assembly takes off, which is what we focus attention on. We study the associated lag time as a function of system size and kinetic pathway. We find that the leading order stochastic contribution to the lag time before polymerization commences is inversely proportional to the system volume for large-enough system size for all nine reaction pathways tested. Finite-size corrections to this do depend on the kinetic pathway.

Collective stochastic coherence in recurrent neuronal networks

Science.gov (United States)

Sancristóbal, Belén; Rebollo, Beatriz; Boada, Pol; Sanchez-Vives, Maria V.; Garcia-Ojalvo, Jordi

2016-09-01

Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can show substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. We report this behaviour in the slow oscillation regime exhibited by a cerebral cortex network under dynamical conditions resembling slow-wave sleep and anaesthesia. Computational analysis of a biologically realistic network model reveals that an intermediate level of background noise leads to quasi-regular dynamics. We verify this prediction experimentally in cortical slices subject to varying amounts of extracellular potassium, which modulates neuronal excitability and thus synaptic noise. The model also predicts that this effectively regular state should exhibit noise-induced memory of the spatial propagation profile of the collective oscillations, which is also verified experimentally. Taken together, these results allow us to construe the high regularity observed experimentally in the brain as an instance of collective stochastic coherence.

Stochastic description of heterogeneities of permeability within groundwater flow models

International Nuclear Information System (INIS)

Cacas, M.C.; Lachassagne, P.; Ledoux, E.; Marsily, G. de

1991-01-01

In order to model radionuclide migration in the geosphere realistically at the field scale, the hydrogeologist needs to be able to simulate groundwater flow in heterogeneous media. Heterogeneity of the medium can be described using a stochastic approach, that affects the way in which a flow model is formulated. In this paper, we discuss the problems that we have encountered in modelling both continuous and fractured media. The stochastic approach leads to a methodology that enables local measurements of permeability to be integrated into a model which gives a good prediction of groundwater flow on a regional scale. 5 Figs.; 8 Refs

Stochastic processes in cell biology

CERN Document Server

Bressloff, Paul C

2014-01-01

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology.  A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods.   This text is primarily...

Stochastic pump effect and geometric phases in dissipative and stochastic systems

Energy Technology Data Exchange (ETDEWEB)

Sinitsyn, Nikolai [Los Alamos National Laboratory

2008-01-01

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).

Stochastic Modeling and Simulation of Near-Fault Ground Motions for Performance-Based Earthquake Engineering

OpenAIRE

Dabaghi, Mayssa

2014-01-01

A comprehensive parameterized stochastic model of near-fault ground motions in two orthogonal horizontal directions is developed. The proposed model uniquely combines several existing and new sub-models to represent major characteristics of recorded near-fault ground motions. These characteristics include near-fault effects of directivity and fling step; temporal and spectral non-stationarity; intensity, duration and frequency content characteristics; directionality of components, as well as ...

Regime-switching stochastic volatility. Evidence from the crude oil market

International Nuclear Information System (INIS)

Vo, Minh T.

2009-01-01

This paper incorporates regime-switching into the stochastic volatility (SV) framework in an attempt to explain the behavior of crude oil prices in order to forecast their volatility. More specifically, it models the volatility of oil return as a stochastic volatility process whose mean is subject to shifts in regime. The shift is governed by a two-state first-order Markov process. The Bayesian Markov Chain Monte Carlo method is used to estimate the models. The main findings are: first, there is clear evidence of regime-switching in the oil market. Ignoring it will lead to a false impression that the volatility is highly persistent and therefore highly predictable. Second, incorporating regime-switching into the SV framework significantly enhances the forecasting power of the SV model. Third, the regime-switching stochastic volatility model does a good job in capturing major events affecting the oil market. (author)

Encoding efficiency of suprathreshold stochastic resonance on stimulus-specific information

Energy Technology Data Exchange (ETDEWEB)

Duan, Fabing, E-mail: fabing.duan@gmail.com [Institute of Complexity Science, Qingdao University, Qingdao 266071 (China); Chapeau-Blondeau, François, E-mail: chapeau@univ-angers.fr [Laboratoire Angevin de Recherche en Ingénierie des Systèmes (LARIS), Université d' Angers, 62 avenue Notre Dame du Lac, 49000 Angers (France); Abbott, Derek, E-mail: derek.abbott@adelaide.edu.au [Centre for Biomedical Engineering (CBME) and School of Electrical & Electronic Engineering, The University of Adelaide, Adelaide, SA 5005 (Australia)

2016-01-08

In this paper, we evaluate the encoding efficiency of suprathreshold stochastic resonance (SSR) based on a local information-theoretic measure of stimulus-specific information (SSI), which is the average specific information of responses associated with a particular stimulus. The theoretical and numerical analyses of SSIs reveal that noise can improve neuronal coding efficiency for a large population of neurons, which leads to produce increased information-rich responses. The SSI measure, in contrast to the global measure of average mutual information, can characterize the noise benefits in finer detail for describing the enhancement of neuronal encoding efficiency of a particular stimulus, which may be of general utility in the design and implementation of a SSR coding scheme. - Highlights: • Evaluating the noise-enhanced encoding efficiency via stimulus-specific information. • New form of stochastic resonance based on the measure of encoding efficiency. • Analyzing neural encoding schemes from suprathreshold stochastic resonance detailedly.

Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models.

Science.gov (United States)

Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi

2016-01-01

Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.

Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models.

Directory of Open Access Journals (Sweden)

Ryo Oizumi

Full Text Available Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.

Stochastic modeling concepts in groundwater and risk assessment: potential application to marine problems

International Nuclear Information System (INIS)

Hamed, Maged M.

2000-01-01

Parameter uncertainty is ubiquitous in marine environmental processes. Failure to account for this uncertainty may lead to erroneous results, and may have significant environmental and economic ramifications. Stochastic modeling of oil spill transport and fate is, therefore, central in the development of an oil spill contingency plan for new oil and gas projects. Over the past twenty years, several stochastic modeling tools have been developed for modeling parameter uncertainty, including the spectral, perturbation, and simulation methods. In this work we explore the application of a new stochastic methodology, the first-order reliability method (FORM), in oil spill modeling. FORM was originally developed in the structural reliability field and has been recently applied to various environmental problems. The method has many appealing features that makes it a powerful tool for modeling complex environmental systems. The theory of FORM is presented, identifying the features that distinguish the method from other stochastic tools. Different formulations to the reliability-based stochastic oil spill modeling are presented in a decision-analytic context. (Author)

Concurrency-Induced Transitions in Epidemic Dynamics on Temporal Networks.

Science.gov (United States)

Onaga, Tomokatsu; Gleeson, James P; Masuda, Naoki

2017-09-08

Social contact networks underlying epidemic processes in humans and animals are highly dynamic. The spreading of infections on such temporal networks can differ dramatically from spreading on static networks. We theoretically investigate the effects of concurrency, the number of neighbors that a node has at a given time point, on the epidemic threshold in the stochastic susceptible-infected-susceptible dynamics on temporal network models. We show that network dynamics can suppress epidemics (i.e., yield a higher epidemic threshold) when the node's concurrency is low, but can also enhance epidemics when the concurrency is high. We analytically determine different phases of this concurrency-induced transition, and confirm our results with numerical simulations.

Concurrency-Induced Transitions in Epidemic Dynamics on Temporal Networks

Science.gov (United States)

Onaga, Tomokatsu; Gleeson, James P.; Masuda, Naoki

2017-09-01

Social contact networks underlying epidemic processes in humans and animals are highly dynamic. The spreading of infections on such temporal networks can differ dramatically from spreading on static networks. We theoretically investigate the effects of concurrency, the number of neighbors that a node has at a given time point, on the epidemic threshold in the stochastic susceptible-infected-susceptible dynamics on temporal network models. We show that network dynamics can suppress epidemics (i.e., yield a higher epidemic threshold) when the node's concurrency is low, but can also enhance epidemics when the concurrency is high. We analytically determine different phases of this concurrency-induced transition, and confirm our results with numerical simulations.

A stochastic-field description of finite-size spiking neural networks.

Science.gov (United States)

Dumont, Grégory; Payeur, Alexandre; Longtin, André

2017-08-01

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.

Sequential stochastic optimization

CERN Document Server

Cairoli, Renzo

1996-01-01

Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet

Simple stochastic simulation.

Science.gov (United States)

Schilstra, Maria J; Martin, Stephen R

2009-01-01

Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.

Identification of AR(I)MA processes for modelling temporal correlations of GPS observations

Science.gov (United States)

Luo, X.; Mayer, M.; Heck, B.

2009-04-01

In many geodetic applications observations of the Global Positioning System (GPS) are routinely processed by means of the least-squares method. However, this algorithm delivers reliable estimates of unknown parameters und realistic accuracy measures only if both the functional and stochastic models are appropriately defined within GPS data processing. One deficiency of the stochastic model used in many GPS software products consists in neglecting temporal correlations of GPS observations. In practice the knowledge of the temporal stochastic behaviour of GPS observations can be improved by analysing time series of residuals resulting from the least-squares evaluation. This paper presents an approach based on the theory of autoregressive (integrated) moving average (AR(I)MA) processes to model temporal correlations of GPS observations using time series of observation residuals. A practicable integration of AR(I)MA models in GPS data processing requires the determination of the order parameters of AR(I)MA processes at first. In case of GPS, the identification of AR(I)MA processes could be affected by various factors impacting GPS positioning results, e.g. baseline length, multipath effects, observation weighting, or weather variations. The influences of these factors on AR(I)MA identification are empirically analysed based on a large amount of representative residual time series resulting from differential GPS post-processing using 1-Hz observation data collected within the permanent SAPOS® (Satellite Positioning Service of the German State Survey) network. Both short and long time series are modelled by means of AR(I)MA processes. The final order parameters are determined based on the whole residual database; the corresponding empirical distribution functions illustrate that multipath and weather variations seem to affect the identification of AR(I)MA processes much more significantly than baseline length and observation weighting. Additionally, the modelling

Stochastic Optimization of Wind Turbine Power Factor Using Stochastic Model of Wind Power

DEFF Research Database (Denmark)

Chen, Peiyuan; Siano, Pierluigi; Bak-Jensen, Birgitte

2010-01-01

This paper proposes a stochastic optimization algorithm that aims to minimize the expectation of the system power losses by controlling wind turbine (WT) power factors. This objective of the optimization is subject to the probability constraints of bus voltage and line current requirements....... The optimization algorithm utilizes the stochastic models of wind power generation (WPG) and load demand to take into account their stochastic variation. The stochastic model of WPG is developed on the basis of a limited autoregressive integrated moving average (LARIMA) model by introducing a crosscorrelation...... structure to the LARIMA model. The proposed stochastic optimization is carried out on a 69-bus distribution system. Simulation results confirm that, under various combinations of WPG and load demand, the system power losses are considerably reduced with the optimal setting of WT power factor as compared...

Singular stochastic differential equations

CERN Document Server

Cherny, Alexander S

2005-01-01

The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

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

Indian Academy of Sciences (India)

C Sivakumar

2017-12-11

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

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.

Science.gov (United States)

Kang, Yun; Lanchier, Nicolas

2011-06-01

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the

Groundwater Management at Varamin Plain: The Consideration of Stochastic and Environmental Effects

International Nuclear Information System (INIS)

Najafi Alamdarlo, H.; Ahmadian, M.; Khalilian, S.

2016-01-01

Groundwater is one of the common resources in Varamin Plain, but due to over extraction it has been exposed to ruin. This phenomenon will lead to economic and environmental problems. On the other hand, the world is expected to face with more stochastic events of water supply. Furthermore, incorporating stochastic consideration of water supply becomes more acute in designing water facilities. Therefore, the strategies should be applied to improve managing resources and increase the efficiency of irrigation system. Hence, in this study the effect of efficiency improvement of irrigation system on the exploitation of groundwater and cropping pattern is examined in deterministic and stochastic condition using Nash bargaining theory. The results showed that farmers in B scenario are more willing to cooperate and as a result of their cooperation, they lose only 3 percentages of their present value of the objective function. Therefore, the efficiency improvement of irrigation system can result in improving the cooperation between farmers and increasing the amount of reserves.Groundwater is one of the common resources in Varamin Plain, but due to over extraction it has been exposed to ruin. This phenomenon will lead to economic and environmental problems. On the other hand, the world is expected to face with more stochastic events of water supply. Furthermore, incorporating stochastic consideration of water supply becomes more acute in designing water facilities. Therefore, the strategies should be applied to improve managing resources and increase the efficiency of irrigation system. Hence, in this study the effect of efficiency improvement of irrigation system on the exploitation of groundwater and cropping pattern is examined in deterministic and stochastic condition using Nash bargaining theory. The results showed that farmers in B scenario are more willing to cooperate and as a result of their cooperation, they lose only 3 percentages of their present value of the

Discrete changes of current statistics in periodically driven stochastic systems

International Nuclear Information System (INIS)

Chernyak, Vladimir Y; Sinitsyn, N A

2010-01-01

We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the driving protocol. To describe this effect, we introduce a new topological phase factor in the evolution of the moment generating function which is akin to the topological geometric phase in the evolution of a periodically driven quantum mechanical system with time-reversal symmetry. This phase leads to the prediction of a sign change for the difference of the probabilities to find even and odd numbers of particles transferred in a stochastic system in response to cyclic evolution of control parameters. The driving protocols that lead to this sign change should enclose specific degeneracy points in the space of control parameters. The relation between the topology of the paths in the control parameter space and the sign changes can be described in terms of the first Stiefel–Whitney class of topological invariants. (letter)

SDE decomposition and A-type stochastic interpretation in nonequilibrium processes

Science.gov (United States)

Yuan, Ruoshi; Tang, Ying; Ao, Ping

2017-12-01

An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochastic differential equation (SDE) into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the α-type interpretation for multidimensional systems. The potential landscape serves as a Hamiltonian-like function in nonequilibrium processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel framework. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.

Collective, stochastic and nonequilibrium behavior of highly excited hadronic matter

International Nuclear Information System (INIS)

Carruthers, P.

1983-01-01

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

Treatment of constraints in the stochastic quantization method and covariantized Langevin equation

International Nuclear Information System (INIS)

Ikegami, Kenji; Kimura, Tadahiko; Mochizuki, Riuji

1993-01-01

We study the treatment of the constraints in the stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking into account the Ito calculus. Then we obtain an improved Langevin equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochastic equilibrium state. This treatment is applied to an O(N) non-linear σ model and it is shown that singular terms appearing in the improved Langevin equation cancel out the δ n (0) divergences in one loop order. We also ascertain that the above Langevin equation, rewritten in terms of independent variables, is actually equivalent to the one in the general-coordinate transformation covariant and vielbein-rotation invariant formalism. (orig.)

Quasi-continuous stochastic simulation framework for flood modelling

Science.gov (United States)

Moustakis, Yiannis; Kossieris, Panagiotis; Tsoukalas, Ioannis; Efstratiadis, Andreas

2017-04-01

Typically, flood modelling in the context of everyday engineering practices is addressed through event-based deterministic tools, e.g., the well-known SCS-CN method. A major shortcoming of such approaches is the ignorance of uncertainty, which is associated with the variability of soil moisture conditions and the variability of rainfall during the storm event.In event-based modeling, the sole expression of uncertainty is the return period of the design storm, which is assumed to represent the acceptable risk of all output quantities (flood volume, peak discharge, etc.). On the other hand, the varying antecedent soil moisture conditions across the basin are represented by means of scenarios (e.g., the three AMC types by SCS),while the temporal distribution of rainfall is represented through standard deterministic patterns (e.g., the alternative blocks method). In order to address these major inconsistencies,simultaneously preserving the simplicity and parsimony of the SCS-CN method, we have developed a quasi-continuous stochastic simulation approach, comprising the following steps: (1) generation of synthetic daily rainfall time series; (2) update of potential maximum soil moisture retention, on the basis of accumulated five-day rainfall; (3) estimation of daily runoff through the SCS-CN formula, using as inputs the daily rainfall and the updated value of soil moisture retention;(4) selection of extreme events and application of the standard SCS-CN procedure for each specific event, on the basis of synthetic rainfall.This scheme requires the use of two stochastic modelling components, namely the CastaliaR model, for the generation of synthetic daily data, and the HyetosMinute model, for the disaggregation of daily rainfall to finer temporal scales. Outcomes of this approach are a large number of synthetic flood events, allowing for expressing the design variables in statistical terms and thus properly evaluating the flood risk.

Initiating stochastic maintenance optimization at Candu Power Plants

International Nuclear Information System (INIS)

Doyle, E.K.

2003-01-01

As previously reported at ICONE 6 in New Orleans (1996), the use of various innovative maintenance optimization techniques at Bruce has lead to cost effective preventive maintenance applications for complex systems. Further cost refinement of the station maintenance strategy is being evaluated via the applicability of statistical analysis of historical failure data. Since the statistical evaluation was initiated in 1999 significant progress has been made in demonstrating the viability of stochastic methods in Candu maintenance. Some of the relevant results were presented at ICONE 10 in Washington DC (2002). Success with the graphical displays and the relatively easy to implement stochastic computer programs was sufficient to move the program along to the next significant phase. This next phase consists of investigating the validity of using subjective elicitation techniques to obtain component lifetime distributions. This technique provides access to the elusive failure statistics, the lack of which is often referred to in the literature as the principle impediment preventing the use of stochastic methods in large industry. At the same time the technique allows very valuable information to be captured from the fast retiring 'baby boom generation'. Initial indications have been quite positive. (author)

Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Veraart, Almut

Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on genera...

Functional Abstraction of Stochastic Hybrid Systems

NARCIS (Netherlands)

Bujorianu, L.M.; Blom, Henk A.P.; Hermanns, H.

2006-01-01

The verification problem for stochastic hybrid systems is quite difficult. One method to verify these systems is stochastic reachability analysis. Concepts of abstractions for stochastic hybrid systems are needed to ease the stochastic reachability analysis. In this paper, we set up different ways

Stochastic quantisation: theme and variation

International Nuclear Information System (INIS)

Klauder, J.R.; Kyoto Univ.

1987-01-01

The paper on stochastic quantisation is a contribution to the book commemorating the sixtieth birthday of E.S. Fradkin. Stochastic quantisation reformulates Euclidean quantum field theory in the language of Langevin equations. The generalised free field is discussed from the viewpoint of stochastic quantisation. An artificial family of highly singular model theories wherein the space-time derivatives are dropped altogether is also examined. Finally a modified form of stochastic quantisation is considered. (U.K.)

Discrimination of acoustic communication signals by grasshoppers (Chorthippus biguttulus): temporal resolution, temporal integration, and the impact of intrinsic noise.

Science.gov (United States)

Ronacher, Bernhard; Wohlgemuth, Sandra; Vogel, Astrid; Krahe, Rüdiger

2008-08-01

A characteristic feature of hearing systems is their ability to resolve both fast and subtle amplitude modulations of acoustic signals. This applies also to grasshoppers, which for mate identification rely mainly on the characteristic temporal patterns of their communication signals. Usually the signals arriving at a receiver are contaminated by various kinds of noise. In addition to extrinsic noise, intrinsic noise caused by stochastic processes within the nervous system contributes to making signal recognition a difficult task. The authors asked to what degree intrinsic noise affects temporal resolution and, particularly, the discrimination of similar acoustic signals. This study aims at exploring the neuronal basis for sexual selection, which depends on exploiting subtle differences between basically similar signals. Applying a metric, by which the similarities of spike trains can be assessed, the authors investigated how well the communication signals of different individuals of the same species could be discriminated and correctly classified based on the responses of auditory neurons. This spike train metric yields clues to the optimal temporal resolution with which spike trains should be evaluated. (c) 2008 APA, all rights reserved

STOCHASTIC ASSESSMENT OF NIGERIAN STOCHASTIC ...

African Journals Online (AJOL)

eobe

STOCHASTIC ASSESSMENT OF NIGERIAN WOOD FOR BRIDGE DECKS ... abandoned bridges with defects only in their decks in both rural and urban locations can be effectively .... which can be seen as the detection of rare physical.

Temporal self-splitting of optical pulses

Science.gov (United States)

Ding, Chaoliang; Koivurova, Matias; Turunen, Jari; Pan, Liuzhan

2018-05-01

We present mathematical models for temporally and spectrally partially coherent pulse trains with Laguerre-Gaussian and Hermite-Gaussian Schell-model statistics as extensions of the standard Gaussian Schell model for pulse trains. We derive propagation formulas of both classes of pulsed fields in linearly dispersive media and in temporal optical systems. It is found that, in general, both types of fields exhibit time-domain self-splitting upon propagation. The Laguerre-Gaussian model leads to multiply peaked pulses, while the Hermite-Gaussian model leads to doubly peaked pulses, in the temporal far field (in dispersive media) or at the Fourier plane of a temporal system. In both model fields the character of the self-splitting phenomenon depends both on the degree of temporal and spectral coherence and on the power spectrum of the field.

Stochastic quantization and gravity

International Nuclear Information System (INIS)

Rumpf, H.

1984-01-01

We give a preliminary account of the application of stochastic quantization to the gravitational field. We start in Section I from Nelson's formulation of quantum mechanics as Newtonian stochastic mechanics and only then introduce the Parisi-Wu stochastic quantization scheme on which all the later discussion will be based. In Section II we present a generalization of the scheme that is applicable to fields in physical (i.e. Lorentzian) space-time and treat the free linearized gravitational field in this manner. The most remarkable result of this is the noncausal propagation of conformal gravitons. Moreover the concept of stochastic gauge-fixing is introduced and a complete discussion of all the covariant gauges is given. A special symmetry relating two classes of covariant gauges is exhibited. Finally Section III contains some preliminary remarks on full nonlinear gravity. In particular we argue that in contrast to gauge fields the stochastic gravitational field cannot be transformed to a Gaussian process. (Author)

Predicting population extinction or disease outbreaks with stochastic models

Directory of Open Access Journals (Sweden)

Linda J. S. Allen

2017-01-01

Full Text Available Models of exponential growth, logistic growth and epidemics are common applications in undergraduate differential equation courses. The corresponding stochastic models are not part of these courses, although when population sizes are small their behaviour is often more realistic and distinctly different from deterministic models. For example, the randomness associated with births and deaths may lead to population extinction even in an exponentially growing population. Some background in continuous-time Markov chains and applications to populations, epidemics and cancer are presented with a goal to introduce this topic into the undergraduate mathematics curriculum that will encourage further investigation into problems on conservation, infectious diseases and cancer therapy. MATLAB programs for graphing sample paths of stochastic models are provided in the Appendix.

Stochastic climate theory

NARCIS (Netherlands)

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

2017-01-01

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

Anomalous scaling of stochastic processes and the Moses effect.

Science.gov (United States)

Chen, Lijian; Bassler, Kevin E; McCauley, Joseph L; Gunaratne, Gemunu H

2017-04-01

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t^{1/2}. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

Anomalous scaling of stochastic processes and the Moses effect

Science.gov (United States)

Chen, Lijian; Bassler, Kevin E.; McCauley, Joseph L.; Gunaratne, Gemunu H.

2017-04-01

The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t1/2. However, processes in which the probability distribution is not normal and the scaling exponent differs from 1/2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, autocorrelations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect and the Noah effect, respectively. If the increments are nonstationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data are analyzed, revealing that their anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

Chance Constrained Input Relaxation to Congestion in Stochastic DEA. An Application to Iranian Hospitals.

Science.gov (United States)

Kheirollahi, Hooshang; Matin, Behzad Karami; Mahboubi, Mohammad; Alavijeh, Mehdi Mirzaei

2015-01-01

This article developed an approached model of congestion, based on relaxed combination of inputs, in stochastic data envelopment analysis (SDEA) with chance constrained programming approaches. Classic data envelopment analysis models with deterministic data have been used by many authors to identify congestion and estimate its levels; however, data envelopment analysis with stochastic data were rarely used to identify congestion. This article used chance constrained programming approaches to replace stochastic models with "deterministic equivalents". This substitution leads us to non-linear problems that should be solved. Finally, the proposed method based on relaxed combination of inputs was used to identify congestion input in six Iranian hospital with one input and two outputs in the period of 2009 to 2012.

2–stage stochastic Runge–Kutta for stochastic delay differential equations

Energy Technology Data Exchange (ETDEWEB)

Rosli, Norhayati; Jusoh Awang, Rahimah [Faculty of Industrial Science and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300, Gambang, Pahang (Malaysia); Bahar, Arifah; Yeak, S. H. [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)

2015-05-15

This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.

Space-time-modulated stochastic processes

Science.gov (United States)

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.

RES: Regularized Stochastic BFGS Algorithm

Science.gov (United States)

Mokhtari, Aryan; Ribeiro, Alejandro

2014-12-01

RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second order methods, on the other hand, is impracticable because computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both, the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian egeinvalues of the sample functions are sufficient to guarantee convergence to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.

PARAMETRIC IDENTIFICATION OF STOCHASTIC SYSTEM BY NON-GRADIENT RANDOM SEARCHING

Directory of Open Access Journals (Sweden)

A. A. Lobaty

2017-01-01

Full Text Available At this moment we know a great variety of identification objects, tasks and methods and its significance is constantly increasing in various fields of science and technology.  The identification problem is dependent on a priori information about identification object, besides that  the existing approaches and methods of identification are determined by the form of mathematical models (deterministic, stochastic, frequency, temporal, spectral etc.. The paper considers a problem for determination of system parameters  (identification object which is assigned by the stochastic mathematical model including random functions of time. It has been shown  that while making optimization of the stochastic systems subject to random actions deterministic methods can be applied only for a limited approximate optimization of the system by taking into account average random effects and fixed structure of the system. The paper proposes an algorithm for identification of  parameters in a mathematical model of  the stochastic system by non-gradient random searching. A specific  feature  of the algorithm is its applicability  practically to mathematic models of any type because the applied algorithm does not depend on linearization and differentiability of functions included in the mathematical model of the system. The proposed algorithm  ensures searching of  an extremum for the specified quality criteria in terms of external uncertainties and limitations while using random searching of parameters for a mathematical model of the system. The paper presents results of the investigations on operational capability of the considered identification method  while using mathematical simulation of hypothetical control system with a priori unknown parameter values of the mathematical model. The presented results of the mathematical simulation obviously demonstrate the operational capability of the proposed identification method.

Elitism and Stochastic Dominance

OpenAIRE

Bazen, Stephen; Moyes, Patrick

2011-01-01

Stochastic dominance has typically been used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adpations be made. We apply in the paper the stochastic dominance approach to the measurment of elitism which may be considered the opposite of egalitarianism. While the...

Stochastic clustering of material surface under high-heat plasma load

Science.gov (United States)

Budaev, Viacheslav P.

2017-11-01

The results of a study of a surface formed by high-temperature plasma loads on various materials such as tungsten, carbon and stainless steel are presented. High-temperature plasma irradiation leads to an inhomogeneous stochastic clustering of the surface with self-similar granularity - fractality on the scale from nanoscale to macroscales. Cauliflower-like structure of tungsten and carbon materials are formed under high heat plasma load in fusion devices. The statistical characteristics of hierarchical granularity and scale invariance are estimated. They differ qualitatively from the roughness of the ordinary Brownian surface, which is possibly due to the universal mechanisms of stochastic clustering of material surface under the influence of high-temperature plasma.

Stochastic analytic regularization

International Nuclear Information System (INIS)

Alfaro, J.

1984-07-01

Stochastic regularization is reexamined, pointing out a restriction on its use due to a new type of divergence which is not present in the unregulated theory. Furthermore, we introduce a new form of stochastic regularization which permits the use of a minimal subtraction scheme to define the renormalized Green functions. (author)

On Stochastic Dependence

Science.gov (United States)

Meyer, Joerg M.

2018-01-01

The contrary of stochastic independence splits up into two cases: pairs of events being favourable or being unfavourable. Examples show that both notions have quite unexpected properties, some of them being opposite to intuition. For example, transitivity does not hold. Stochastic dependence is also useful to explain cases of Simpson's paradox.

Stochastic massless fields I: Integer spin

International Nuclear Information System (INIS)

Lim, S.C.

1981-04-01

Nelson's stochastic quantization scheme is applied to classical massless tensor potential in ''Coulomb'' gauge. The relationship between stochastic potential field in various gauges is discussed using the case of vector potential as an illustration. It is possible to identify the Euclidean tensor potential with the corresponding stochastic field in physical Minkowski space-time. Stochastic quantization of massless fields can also be carried out in terms of field strength tensors. An example of linearized stochastic gravitational field in vacuum is given. (author)

Evaluation of potential human health effects associated with the agricultural uses of 1,3-D: Spatial and temporal stochastic risk analysis.

Science.gov (United States)

Driver, Jeffrey H; Price, Paul S; Van Wesenbeeck, Ian; Ross, John H; Gehen, Sean; Holden, Larry R; Landenberger, Bryce; Hastings, Kerry; Yan, Zhongyu June; Rasoulpour, Reza

2016-11-15

Dow AgroSciences (DAS) markets and sells 1,3-Dichloropropene (1,3-D), the active ingredient in Telone®, which is used as a pre-plant soil fumigant nematicide in economically important crops in California. 1,3-D has been regulated as a "probable human carcinogen" and the California Department of Pesticide Regulation limits use of 1,3-D based on human health risk assessments for bystanders. This paper presents a risk characterization for bystanders based on advances in the assessment of both exposure and hazard. The revised bystander risk assessment incorporates significant advances: 1) new data on residency duration and mobility in communities where 1,3-D is in high demand; 2) new information on spatial and temporal concentrations of 1,3-D in air based on multi-year modeling using a validated model; and 3) a new stochastic spatial and temporal model of long-term exposures. Predicted distributions of long-term, chronic exposures indicate that current, and anticipated uses of 1,3-D would result in lifetime average daily doses lower than 0.002mg/kg/d, a dose associated with theoretical lifetime excess cancer risk of 95% of the local population based on a non-threshold risk assessment approach. Additionally, examination of 1,3-D toxicity studies including new chronic toxicity data and mechanism of action supports the use of a non-linear, threshold based risk assessment approach. The estimated maximum annual average daily dose of 1000-fold, a clear indication of acceptable risk for human health. In summary, the best available science supports 1,3-D's threshold nature of hazard and the revised exposure assessment supports that current agricultural uses of 1,3-D are associated with reasonable certainty of no harm, i.e., estimated long-term exposures pose insignificant health risks to bystanders even when the non-threshold approach is assumed. Copyright © 2016 Elsevier B.V. All rights reserved.

Dynamic Stochastic Superresolution of sparsely observed turbulent systems

International Nuclear Information System (INIS)

Branicki, M.; Majda, A.J.

2013-01-01

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

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

International Nuclear Information System (INIS)

Pham, H.

2002-01-01

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

Quantum stochastics

CERN Document Server

Chang, Mou-Hsiung

2015-01-01

The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...

Stochastic cooling

International Nuclear Information System (INIS)

Bisognano, J.; Leemann, C.

1982-03-01

Stochastic cooling is the damping of betatron oscillations and momentum spread of a particle beam by a feedback system. In its simplest form, a pickup electrode detects the transverse positions or momenta of particles in a storage ring, and the signal produced is amplified and applied downstream to a kicker. The time delay of the cable and electronics is designed to match the transit time of particles along the arc of the storage ring between the pickup and kicker so that an individual particle receives the amplified version of the signal it produced at the pick-up. If there were only a single particle in the ring, it is obvious that betatron oscillations and momentum offset could be damped. However, in addition to its own signal, a particle receives signals from other beam particles. In the limit of an infinite number of particles, no damping could be achieved; we have Liouville's theorem with constant density of the phase space fluid. For a finite, albeit large number of particles, there remains a residue of the single particle damping which is of practical use in accumulating low phase space density beams of particles such as antiprotons. It was the realization of this fact that led to the invention of stochastic cooling by S. van der Meer in 1968. Since its conception, stochastic cooling has been the subject of much theoretical and experimental work. The earliest experiments were performed at the ISR in 1974, with the subsequent ICE studies firmly establishing the stochastic cooling technique. This work directly led to the design and construction of the Antiproton Accumulator at CERN and the beginnings of p anti p colliding beam physics at the SPS. Experiments in stochastic cooling have been performed at Fermilab in collaboration with LBL, and a design is currently under development for a anti p accumulator for the Tevatron

Spatio-Temporal Rule Mining

DEFF Research Database (Denmark)

Gidofalvi, Gyozo; Pedersen, Torben Bach

2005-01-01

Recent advances in communication and information technology, such as the increasing accuracy of GPS technology and the miniaturization of wireless communication devices pave the road for Location-Based Services (LBS). To achieve high quality for such services, spatio-temporal data mining techniques...... are needed. In this paper, we describe experiences with spatio-temporal rule mining in a Danish data mining company. First, a number of real world spatio-temporal data sets are described, leading to a taxonomy of spatio-temporal data. Second, the paper describes a general methodology that transforms...... the spatio-temporal rule mining task to the traditional market basket analysis task and applies it to the described data sets, enabling traditional association rule mining methods to discover spatio-temporal rules for LBS. Finally, unique issues in spatio-temporal rule mining are identified and discussed....

Stochastic Analysis with Financial Applications

CERN Document Server

Kohatsu-Higa, Arturo; Sheu, Shuenn-Jyi

2011-01-01

Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. This book also covers the areas of backward stochastic differential equations via the (non-li

Stochastic and deterministic processes regulate spatio-temporal variation in seed bank diversity

Science.gov (United States)

Alejandro A. Royo; Todd E. Ristau

2013-01-01

Seed banks often serve as reservoirs of taxonomic and genetic diversity that buffer plant populations and influence post-disturbance vegetation trajectories; yet evaluating their importance requires understanding how their composition varies within and across spatial and temporal scales (α- and β-diversity). Shifts in seed bank diversity are strongly...

Stochastic Reachability Analysis of Hybrid Systems

CERN Document Server

Bujorianu, Luminita Manuela

2012-01-01

Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then...

Stochastic Estimation via Polynomial Chaos

Science.gov (United States)

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Stochastic population dynamics in spatially extended predator-prey systems

Science.gov (United States)

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

2018-02-01

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

Remarks on stochastic acceleration

International Nuclear Information System (INIS)

Graeff, P.

1982-12-01

Stochastic acceleration and turbulent diffusion are strong turbulence problems since no expansion parameter exists. Hence the problem of finding rigorous results is of major interest both for checking approximations and for reference models. Since we have found a way of constructing such models in the turbulent diffusion case the question of the extension to stochastic acceleration now arises. The paper offers some possibilities illustrated by the case of 'stochastic free fall' which may be particularly interesting in the context of linear response theory. (orig.)

Fock space, symbolic algebra, and analytical solutions for small stochastic systems.

Science.gov (United States)

Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A

2015-12-01

Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

Stochastic parameterizing manifolds and non-Markovian reduced equations stochastic manifolds for nonlinear SPDEs II

CERN Document Server

Chekroun, Mickaël D; Wang, Shouhong

2015-01-01

In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.

Stochastic spin-one massive field

International Nuclear Information System (INIS)

Lim, S.C.

1984-01-01

Stochastic quantization schemes of Nelson and Parisi and Wu are applied to a spin-one massive field. Unlike the scalar case Nelson's stochastic spin-one massive field cannot be identified with the corresponding euclidean field even if the fourth component of the euclidean coordinate is taken as equal to the real physical time. In the Parisi-Wu quantization scheme the stochastic Proca vector field has a similar property as the scalar field; which has an asymptotically stationary part and a transient part. The large equal-time limit of the expectation values of the stochastic Proca field are equal to the expectation values of the corresponding euclidean field. In the Stueckelberg formalism the Parisi-Wu scheme gives rise to a stochastic vector field which differs from the massless gauge field in that the gauge cannot be fixed by the choice of boundary condition. (orig.)

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

Energy Technology Data Exchange (ETDEWEB)

Hosking, John Joseph Absalom, E-mail: j.j.a.hosking@cma.uio.no [University of Oslo, Centre of Mathematics for Applications (CMA) (Norway)

2012-12-15

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

International Nuclear Information System (INIS)

Hosking, John Joseph Absalom

2012-01-01

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966–979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197–216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

Stochastic TDHF and the Boltzman-Langevin equation

International Nuclear Information System (INIS)

Suraud, E.; Reinhard, P.G.

1991-01-01

Outgoing from a time-dependent theory of correlations, we present a stochastic differential equation for the propagation of ensembles of Slater determinants, called Stochastic Time-Dependent Hartree-Fock (Stochastic TDHF). These ensembles are allowed to develop large fluctuations in the Hartree-Fock mean fields. An alternative stochastic differential equation, the Boltzmann-Langevin equation, can be derived from Stochastic TDHF by averaging over subensembles with small fluctuations

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

Science.gov (United States)

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

2011-08-01

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

A stochastic cloud model for cloud and ozone retrievals from UV measurements

International Nuclear Information System (INIS)

Efremenko, Dmitry S.; Schüssler, Olena; Doicu, Adrian; Loyola, Diego

2016-01-01

The new generation of satellite instruments provides measurements in and around the Oxygen A-band on a global basis and with a relatively high spatial resolution. These data are commonly used for the determination of cloud properties. A stochastic model and radiative transfer model, previously developed by the authors, is used as the forward model component in retrievals of cloud parameters and ozone total and partial columns. The cloud retrieval algorithm combines local and global optimization routines, and yields a retrieval accuracy of about 1% and a fast computational time. Retrieved parameters are the cloud optical thickness and the cloud-top height. It was found that the use of the independent pixel approximation instead of the stochastic cloud model leads to large errors in the retrieved cloud parameters, as well as, in the retrieved ozone height resolved partial columns. The latter can be reduced by using the stochastic cloud model to compute the optimal value of the regularization parameter in the framework of Tikhonov regularization. - Highlights: • A stochastic radiative transfer model for retrieving clouds/ozone is designed. • Errors of independent pixel approximation (IPA) for O3 total column are small. • The error of IPA for ozone profile retrieval may become large. • The use of stochastic model reduces the error of ozone profile retrieval.

Stochastic resonance in a stochastic bistable system with additive noises and square–wave signal

International Nuclear Information System (INIS)

Feng, Guo; Xiang-Dong, Luo; Shao-Fu, Li; Yu-Rong, Zhou

2010-01-01

This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio. It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as a function of the system parameters, or as a function of the static force. Moreover, the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise on the signal-to-noise ratio is investigated. (general)

Stochastic quantization of Proca field

International Nuclear Information System (INIS)

Lim, S.C.

1981-03-01

We discuss the complications that arise in the application of Nelson's stochastic quantization scheme to classical Proca field. One consistent way to obtain spin-one massive stochastic field is given. It is found that the result of Guerra et al on the connection between ground state stochastic field and the corresponding Euclidean-Markov field extends to the spin-one case. (author)

Stochastic optimization methods

CERN Document Server

Marti, Kurt

2005-01-01

Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

KAUST Repository

Woolley, Thomas E.; Baker, Ruth E.; Gaffney, Eamonn A.; Maini, Philip K.; Seirin-Lee, Sungrim

2012-01-01

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

KAUST Repository

Woolley, Thomas E.

2012-05-22

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

Domain decomposition method of stochastic PDEs: a two-level scalable preconditioner

International Nuclear Information System (INIS)

Subber, Waad; Sarkar, Abhijit

2012-01-01

For uncertainty quantification in many practical engineering problems, the stochastic finite element method (SFEM) may be computationally challenging. In SFEM, the size of the algebraic linear system grows rapidly with the spatial mesh resolution and the order of the stochastic dimension. In this paper, we describe a non-overlapping domain decomposition method, namely the iterative substructuring method to tackle the large-scale linear system arising in the SFEM. The SFEM is based on domain decomposition in the geometric space and a polynomial chaos expansion in the probabilistic space. In particular, a two-level scalable preconditioner is proposed for the iterative solver of the interface problem for the stochastic systems. The preconditioner is equipped with a coarse problem which globally connects the subdomains both in the geometric and probabilistic spaces via their corner nodes. This coarse problem propagates the information quickly across the subdomains leading to a scalable preconditioner. For numerical illustrations, a two-dimensional stochastic elliptic partial differential equation (SPDE) with spatially varying non-Gaussian random coefficients is considered. The numerical scalability of the the preconditioner is investigated with respect to the mesh size, subdomain size, fixed problem size per subdomain and order of polynomial chaos expansion. The numerical experiments are performed on a Linux cluster using MPI and PETSc parallel libraries.

Robust lane detection and tracking using multiple visual cues under stochastic lane shape conditions

Science.gov (United States)

Huang, Zhi; Fan, Baozheng; Song, Xiaolin

2018-03-01

As one of the essential components of environment perception techniques for an intelligent vehicle, lane detection is confronted with challenges including robustness against the complicated disturbance and illumination, also adaptability to stochastic lane shapes. To overcome these issues, we proposed a robust lane detection method named classification-generation-growth-based (CGG) operator to the detected lines, whereby the linear lane markings are identified by synergizing multiple visual cues with the a priori knowledge and spatial-temporal information. According to the quality of linear lane fitting, the linear and linear-parabolic models are dynamically switched to describe the actual lane. The Kalman filter with adaptive noise covariance and the region of interests (ROI) tracking are applied to improve the robustness and efficiency. Experiments were conducted with images covering various challenging scenarios. The experimental results evaluate the effectiveness of the presented method for complicated disturbances, illumination, and stochastic lane shapes.

Phenomenology of stochastic exponential growth

Science.gov (United States)

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

2017-06-01

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

The two-regime method for optimizing stochastic reaction-diffusion simulations

KAUST Repository

Flegg, M. B.

2011-10-19

Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less detailed compartment-based simulations. Compartment-based approaches yield quick and accurate mesoscopic results, but lack the level of detail that is characteristic of the computationally intensive molecular-based models. Often microscopic detail is only required in a small region (e.g. close to the cell membrane). Currently, the best way to achieve microscopic detail is to use a resource-intensive simulation over the whole domain. We develop the two-regime method (TRM) in which a molecular-based algorithm is used where desired and a compartment-based approach is used elsewhere. We present easy-to-implement coupling conditions which ensure that the TRM results have the same accuracy as a detailed molecular-based model in the whole simulation domain. Therefore, the TRM combines strengths of previously developed stochastic reaction-diffusion software to efficiently explore the behaviour of biological models. Illustrative examples and the mathematical justification of the TRM are also presented.

Evidence for Neural Computations of Temporal Coherence in an Auditory Scene and Their Enhancement during Active Listening.

Science.gov (United States)

O'Sullivan, James A; Shamma, Shihab A; Lalor, Edmund C

2015-05-06

The human brain has evolved to operate effectively in highly complex acoustic environments, segregating multiple sound sources into perceptually distinct auditory objects. A recent theory seeks to explain this ability by arguing that stream segregation occurs primarily due to the temporal coherence of the neural populations that encode the various features of an individual acoustic source. This theory has received support from both psychoacoustic and functional magnetic resonance imaging (fMRI) studies that use stimuli which model complex acoustic environments. Termed stochastic figure-ground (SFG) stimuli, they are composed of a "figure" and background that overlap in spectrotemporal space, such that the only way to segregate the figure is by computing the coherence of its frequency components over time. Here, we extend these psychoacoustic and fMRI findings by using the greater temporal resolution of electroencephalography to investigate the neural computation of temporal coherence. We present subjects with modified SFG stimuli wherein the temporal coherence of the figure is modulated stochastically over time, which allows us to use linear regression methods to extract a signature of the neural processing of this temporal coherence. We do this under both active and passive listening conditions. Our findings show an early effect of coherence during passive listening, lasting from ∼115 to 185 ms post-stimulus. When subjects are actively listening to the stimuli, these responses are larger and last longer, up to ∼265 ms. These findings provide evidence for early and preattentive neural computations of temporal coherence that are enhanced by active analysis of an auditory scene. Copyright © 2015 the authors 0270-6474/15/357256-08$15.00/0.

Optimal Control for Stochastic Delay Evolution Equations

Energy Technology Data Exchange (ETDEWEB)

Meng, Qingxin, E-mail: mqx@hutc.zj.cn [Huzhou University, Department of Mathematical Sciences (China); Shen, Yang, E-mail: skyshen87@gmail.com [York University, Department of Mathematics and Statistics (Canada)

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.

Introduction to stochastic calculus

CERN Document Server

Karandikar, Rajeeva L

2018-01-01

This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level stud...

Approaching complexity by stochastic methods: From biological systems to turbulence

Energy Technology Data Exchange (ETDEWEB)

Friedrich, Rudolf [Institute for Theoretical Physics, University of Muenster, D-48149 Muenster (Germany); Peinke, Joachim [Institute of Physics, Carl von Ossietzky University, D-26111 Oldenburg (Germany); Sahimi, Muhammad [Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA 90089-1211 (United States); Reza Rahimi Tabar, M., E-mail: mohammed.r.rahimi.tabar@uni-oldenburg.de [Department of Physics, Sharif University of Technology, Tehran 11155-9161 (Iran, Islamic Republic of); Institute of Physics, Carl von Ossietzky University, D-26111 Oldenburg (Germany); Fachbereich Physik, Universitaet Osnabrueck, Barbarastrasse 7, 49076 Osnabrueck (Germany)

2011-09-15

This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science, turbulence, seismic time series and epileptic brain dynamics, to name but a few. Furthermore, it has been recognized that a similar approach can be applied to the data that depend on a length scale, such as velocity increments in fully developed turbulent flow, or height increments that characterize rough surfaces. A basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale. This scale is referred to as the Markov-Einstein (ME) scale, and has turned out to be a useful characteristic of complex systems. We provide a review of the operational methods that have been developed for analyzing stochastic data in time and scale. We address in detail the following issues: (i) reconstruction of stochastic evolution equations from data in terms of the Langevin equations or the corresponding Fokker-Planck equations and (ii) intermittency, cascades, and multiscale correlation functions.

Approaching complexity by stochastic methods: From biological systems to turbulence

International Nuclear Information System (INIS)

Friedrich, Rudolf; Peinke, Joachim; Sahimi, Muhammad; Reza Rahimi Tabar, M.

2011-01-01

This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science, turbulence, seismic time series and epileptic brain dynamics, to name but a few. Furthermore, it has been recognized that a similar approach can be applied to the data that depend on a length scale, such as velocity increments in fully developed turbulent flow, or height increments that characterize rough surfaces. A basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale. This scale is referred to as the Markov-Einstein (ME) scale, and has turned out to be a useful characteristic of complex systems. We provide a review of the operational methods that have been developed for analyzing stochastic data in time and scale. We address in detail the following issues: (i) reconstruction of stochastic evolution equations from data in terms of the Langevin equations or the corresponding Fokker-Planck equations and (ii) intermittency, cascades, and multiscale correlation functions.

Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem

Directory of Open Access Journals (Sweden)

V. Charles

2011-01-01

Full Text Available In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP problem approach is proposed, which strikes the balance between previous models available in the literature.

Brownian motion, martingales, and stochastic calculus

CERN Document Server

Le Gall, Jean-François

2016-01-01

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...

Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models

International Nuclear Information System (INIS)

Eyink, Gregory L.

2009-01-01

We prove that smooth solutions of nonideal (viscous and resistive) incompressible magnetohydrodynamic (MHD) equations satisfy a stochastic law of flux conservation. This property implies that the magnetic flux through a surface is equal to the average of the magnetic fluxes through an ensemble of surfaces advected backward in time by the plasma velocity perturbed with a random white noise. Our result is an analog of the well-known Alfven theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein and Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the nonideal MHD equations but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall MHD and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux conservation remains stochastic in that limit.

Evaluation of high resolution spatio-temporal precipitation extremes from a stochastic weather generator

DEFF Research Database (Denmark)

Sørup, Hjalte Jomo Danielsen; Christensen, O. B.; Arnbjerg-Nielsen, Karsten

2017-01-01

Spatio-temporal rainfall is modelled for the North-Eastern part of Zealand (Denmark) using the Spatio-Temporal Neyman-Scott Rectangular Pulses model as implemented in the RainSim software. Hourly precipitation series for fitting the model are obtained from a dense network of tipping bucket rain...... gauges in the model area. The spatiotemporal performance of the model with respect to precipitation extremes is evaluated in the points of a 2x2 km regular grid covering the full model area. The model satisfactorily reproduces the extreme behaviour of the observed precipitation with respect to event...... intensity levels and unconditional spatial correlation when evaluated using an event based ranking approach at point scale and an advanced spatiotemporal coupling of extreme events. Prospectively the model can be used as a tool to evaluate the impact of climate change without relying on precipitation output...

Brownian motion and stochastic calculus

CERN Document Server

Karatzas, Ioannis

1998-01-01

This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...

Variance decomposition in stochastic simulators.

Science.gov (United States)

Le Maître, O P; Knio, O M; Moraes, A

2015-06-28

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

Variance decomposition in stochastic simulators

Science.gov (United States)

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

2015-06-01

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

Variance decomposition in stochastic simulators

Energy Technology Data Exchange (ETDEWEB)

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

2015-06-28

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

Variance decomposition in stochastic simulators

KAUST Repository

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

2015-01-01

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

Stochastic synaptic plasticity with memristor crossbar arrays

KAUST Repository

Naous, Rawan

2016-11-01

Memristive devices have been shown to exhibit slow and stochastic resistive switching behavior under low-voltage, low-current operating conditions. Here we explore such mechanisms to emulate stochastic plasticity in memristor crossbar synapse arrays. Interfaced with integrate-and-fire spiking neurons, the memristive synapse arrays are capable of implementing stochastic forms of spike-timing dependent plasticity which parallel mean-rate models of stochastic learning with binary synapses. We present theory and experiments with spike-based stochastic learning in memristor crossbar arrays, including simplified modeling as well as detailed physical simulation of memristor stochastic resistive switching characteristics due to voltage and current induced filament formation and collapse. © 2016 IEEE.

Stochastic synaptic plasticity with memristor crossbar arrays

KAUST Repository

Naous, Rawan; Al-Shedivat, Maruan; Neftci, Emre; Cauwenberghs, Gert; Salama, Khaled N.

2016-01-01

Memristive devices have been shown to exhibit slow and stochastic resistive switching behavior under low-voltage, low-current operating conditions. Here we explore such mechanisms to emulate stochastic plasticity in memristor crossbar synapse arrays. Interfaced with integrate-and-fire spiking neurons, the memristive synapse arrays are capable of implementing stochastic forms of spike-timing dependent plasticity which parallel mean-rate models of stochastic learning with binary synapses. We present theory and experiments with spike-based stochastic learning in memristor crossbar arrays, including simplified modeling as well as detailed physical simulation of memristor stochastic resistive switching characteristics due to voltage and current induced filament formation and collapse. © 2016 IEEE.

An introduction to probability and stochastic processes

CERN Document Server

Melsa, James L

2013-01-01

Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.

Research on nonlinear stochastic dynamical price model

International Nuclear Information System (INIS)

Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng

2008-01-01

In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies

An Approach to Stochastic Peridynamic Theory.

Energy Technology Data Exchange (ETDEWEB)

Demmie, Paul N.

2018-04-01

In many material systems, man-made or natural, we have an incomplete knowledge of geometric or material properties, which leads to uncertainty in predicting their performance under dynamic loading. Given the uncertainty and a high degree of spatial variability in properties of materials subjected to impact, a stochastic theory of continuum mechanics would be useful for modeling dynamic response of such systems. Peridynamic theory is such a theory. It is formulated as an integro- differential equation that does not employ spatial derivatives, and provides for a consistent formulation of both deformation and failure of materials. We discuss an approach to stochastic peridynamic theory and illustrate the formulation with examples of impact loading of geological materials with uncorrelated or correlated material properties. We examine wave propagation and damage to the material. The most salient feature is the absence of spallation, referred to as disorder toughness, which generalizes similar results from earlier quasi-static damage mechanics. Acknowledgements This research was made possible by the support from DTRA grant HDTRA1-08-10-BRCWM. I thank Dr. Martin Ostoja-Starzewski for introducing me to the mechanics of random materials and collaborating with me throughout and after this DTRA project.

Comparison of deterministic and stochastic techniques for estimation of design basis floods for nuclear power plants

International Nuclear Information System (INIS)

Solomon, S.I.; Harvey, K.D.

1982-12-01

The IAEA Safety Guide 50-SG-S10A recommends that design basis floods be estimated by deterministic techniques using probable maximum precipitation and a rainfall runoff model to evaluate the corresponding flood. The Guide indicates that stochastic techniques are also acceptable in which case floods of very low probability have to be estimated. The paper compares the results of applying the two techniques in two river basins at a number of locations and concludes that the uncertainty of the results of both techniques is of the same order of magnitude. However, the use of the unit hydrograph as the rainfall runoff model may lead in some cases to nonconservative estimates. A distributed non-linear rainfall runoff model leads to estimates of probable maximum flood flows which are very close to values of flows having a 10 6 - 10 7 years return interval estimated using a conservative and relatively simple stochastic technique. Recommendations on the practical application of Safety Guide 50-SG-10A are made and the extension of the stochastic technique to ungauged sites and other design parameters is discussed

Stochastic Systems Uncertainty Quantification and Propagation

CERN Document Server

Grigoriu, Mircea

2012-01-01

Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents: ·         A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis   ·          Probabilistic models for random variables an...

Stochastic-field cavitation model

International Nuclear Information System (INIS)

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

2013-01-01

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

Stochastic-field cavitation model

Science.gov (United States)

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

2013-07-01

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

Stochastic Model of Vesicular Sorting in Cellular Organelles

Science.gov (United States)

Vagne, Quentin; Sens, Pierre

2018-02-01

The proper sorting of membrane components by regulated exchange between cellular organelles is crucial to intracellular organization. This process relies on the budding and fusion of transport vesicles, and should be strongly influenced by stochastic fluctuations, considering the relatively small size of many organelles. We identify the perfect sorting of two membrane components initially mixed in a single compartment as a first passage process, and we show that the mean sorting time exhibits two distinct regimes as a function of the ratio of vesicle fusion to budding rates. Low ratio values lead to fast sorting but result in a broad size distribution of sorted compartments dominated by small entities. High ratio values result in two well-defined sorted compartments but sorting is exponentially slow. Our results suggest an optimal balance between vesicle budding and fusion for the rapid and efficient sorting of membrane components and highlight the importance of stochastic effects for the steady-state organization of intracellular compartments.

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

Science.gov (United States)

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

2011-11-01

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

Magnetic Tunnel Junction Based Long-Term Short-Term Stochastic Synapse for a Spiking Neural Network with On-Chip STDP Learning

Science.gov (United States)

Srinivasan, Gopalakrishnan; Sengupta, Abhronil; Roy, Kaushik

2016-07-01

Spiking Neural Networks (SNNs) have emerged as a powerful neuromorphic computing paradigm to carry out classification and recognition tasks. Nevertheless, the general purpose computing platforms and the custom hardware architectures implemented using standard CMOS technology, have been unable to rival the power efficiency of the human brain. Hence, there is a need for novel nanoelectronic devices that can efficiently model the neurons and synapses constituting an SNN. In this work, we propose a heterostructure composed of a Magnetic Tunnel Junction (MTJ) and a heavy metal as a stochastic binary synapse. Synaptic plasticity is achieved by the stochastic switching of the MTJ conductance states, based on the temporal correlation between the spiking activities of the interconnecting neurons. Additionally, we present a significance driven long-term short-term stochastic synapse comprising two unique binary synaptic elements, in order to improve the synaptic learning efficiency. We demonstrate the efficacy of the proposed synaptic configurations and the stochastic learning algorithm on an SNN trained to classify handwritten digits from the MNIST dataset, using a device to system-level simulation framework. The power efficiency of the proposed neuromorphic system stems from the ultra-low programming energy of the spintronic synapses.

Joint Bayesian Stochastic Inversion of Well Logs and Seismic Data for Volumetric Uncertainty Analysis

Directory of Open Access Journals (Sweden)

Moslem Moradi

2015-06-01

Full Text Available Here in, an application of a new seismic inversion algorithm in one of Iran’s oilfields is described. Stochastic (geostatistical seismic inversion, as a complementary method to deterministic inversion, is perceived as contribution combination of geostatistics and seismic inversion algorithm. This method integrates information from different data sources with different scales, as prior information in Bayesian statistics. Data integration leads to a probability density function (named as a posteriori probability that can yield a model of subsurface. The Markov Chain Monte Carlo (MCMC method is used to sample the posterior probability distribution, and the subsurface model characteristics can be extracted by analyzing a set of the samples. In this study, the theory of stochastic seismic inversion in a Bayesian framework was described and applied to infer P-impedance and porosity models. The comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more detailed information of subsurface character. Since multiple realizations are extracted by this method, an estimation of pore volume and uncertainty in the estimation were analyzed.

Stochastic Pi-calculus Revisited

DEFF Research Database (Denmark)

Cardelli, Luca; Mardare, Radu Iulian

2013-01-01

We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...

A stochastic Galerkin method for the Euler equations with Roe variable transformation

KAUST Repository

Pettersson, Per; Iaccarino, Gianluca; Nordströ m, Jan

2014-01-01

The Euler equations subject to uncertainty in the initial and boundary conditions are investigated via the stochastic Galerkin approach. We present a new fully intrusive method based on a variable transformation of the continuous equations. Roe variables are employed to get quadratic dependence in the flux function and a well-defined Roe average matrix that can be determined without matrix inversion.In previous formulations based on generalized polynomial chaos expansion of the physical variables, the need to introduce stochastic expansions of inverse quantities, or square roots of stochastic quantities of interest, adds to the number of possible different ways to approximate the original stochastic problem. We present a method where the square roots occur in the choice of variables, resulting in an unambiguous problem formulation.The Roe formulation saves computational cost compared to the formulation based on expansion of conservative variables. Moreover, the Roe formulation is more robust and can handle cases of supersonic flow, for which the conservative variable formulation fails to produce a bounded solution. For certain stochastic basis functions, the proposed method can be made more effective and well-conditioned. This leads to increased robustness for both choices of variables. We use a multi-wavelet basis that can be chosen to include a large number of resolution levels to handle more extreme cases (e.g. strong discontinuities) in a robust way. For smooth cases, the order of the polynomial representation can be increased for increased accuracy. © 2013 Elsevier Inc.

Lead isotope ratios in artists' lead white: a progress report

Energy Technology Data Exchange (ETDEWEB)

Keisch, B; Callahan, R C [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

1976-07-01

The lead isotope ratios in over four hundred samples of lead white have been determined. The samples represent various geographical sources and dates from the thirteenth century to the present. A new method for organizing this large volume of data is described which helps with the visualization of temporal and geographic patterns. A number of interesting relationships between lead isotope ratio and date or source are shown to exist. Some examples of successful applications of this methodology are described.

Stochastic volatility of volatility in continuous time

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole; Veraart, Almut

This paper introduces the concept of stochastic volatility of volatility in continuous time and, hence, extends standard stochastic volatility (SV) models to allow for an additional source of randomness associated with greater variability in the data. We discuss how stochastic volatility...... of volatility can be defined both non-parametrically, where we link it to the quadratic variation of the stochastic variance process, and parametrically, where we propose two new SV models which allow for stochastic volatility of volatility. In addition, we show that volatility of volatility can be estimated...

Considering inventory distributions in a stochastic periodic inventory routing system

Science.gov (United States)

Yadollahi, Ehsan; Aghezzaf, El-Houssaine

2017-07-01

Dealing with the stochasticity of parameters is one of the critical issues in business and industry nowadays. Supply chain planners have difficulties in forecasting stochastic parameters of a distribution system. Demand rates of customers during their lead time are one of these parameters. In addition, holding a huge level of inventory at the retailers is costly and inefficient. To cover the uncertainty of forecasting demand rates, researchers have proposed the usage of safety stock to avoid stock-out. However, finding the precise level of safety stock depends on forecasting the statistical distribution of demand rates and their variations in different settings among the planning horizon. In this paper the demand rate distributions and its parameters are taken into account for each time period in a stochastic periodic IRP. An analysis of the achieved statistical distribution of the inventory and safety stock level is provided to measure the effects of input parameters on the output indicators. Different values for coefficient of variation are applied to the customers' demand rate in the optimization model. The outcome of the deterministic equivalent model of SPIRP is simulated in form of an illustrative case.

Quantum stochastic calculus associated with quadratic quantum noises

International Nuclear Information System (INIS)

Ji, Un Cig; Sinha, Kalyan B.

2016-01-01

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 calculus extends the Hudson-Parthasarathy quantum stochastic calculus

Quantum stochastic calculus associated with quadratic quantum noises

Energy Technology Data Exchange (ETDEWEB)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, Chungbuk 28644 (Korea, Republic of); Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in [Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-64, India and Department of Mathematics, Indian Institute of Science, Bangalore-12 (India)

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 calculus extends the Hudson-Parthasarathy quantum stochastic calculus.

Set-Valued Stochastic Lebesque Integral and Representation Theorems

Directory of Open Access Journals (Sweden)

Jungang Li

2008-06-01

Full Text Available In this paper, we shall firstly illustrate why we should introduce set-valued stochastic integrals, and then we shall discuss some properties of set-valued stochastic processes and the relation between a set-valued stochastic process and its selection set. After recalling the Aumann type definition of stochastic integral, we shall introduce a new definition of Lebesgue integral of a set-valued stochastic process with respect to the time t . Finally we shall prove the presentation theorem of set-valued stochastic integral and dis- cuss further properties that will be useful to study set-valued stochastic differential equations with their applications.

Being First Matters: Topographical Representational Similarity Analysis of ERP Signals Reveals Separate Networks for Audiovisual Temporal Binding Depending on the Leading Sense.

Science.gov (United States)

Cecere, Roberto; Gross, Joachim; Willis, Ashleigh; Thut, Gregor

2017-05-24

In multisensory integration, processing in one sensory modality is enhanced by complementary information from other modalities. Intersensory timing is crucial in this process because only inputs reaching the brain within a restricted temporal window are perceptually bound. Previous research in the audiovisual field has investigated various features of the temporal binding window, revealing asymmetries in its size and plasticity depending on the leading input: auditory-visual (AV) or visual-auditory (VA). Here, we tested whether separate neuronal mechanisms underlie this AV-VA dichotomy in humans. We recorded high-density EEG while participants performed an audiovisual simultaneity judgment task including various AV-VA asynchronies and unisensory control conditions (visual-only, auditory-only) and tested whether AV and VA processing generate different patterns of brain activity. After isolating the multisensory components of AV-VA event-related potentials (ERPs) from the sum of their unisensory constituents, we ran a time-resolved topographical representational similarity analysis (tRSA) comparing the AV and VA ERP maps. Spatial cross-correlation matrices were built from real data to index the similarity between the AV and VA maps at each time point (500 ms window after stimulus) and then correlated with two alternative similarity model matrices: AV maps = VA maps versus AV maps ≠ VA maps The tRSA results favored the AV maps ≠ VA maps model across all time points, suggesting that audiovisual temporal binding (indexed by synchrony perception) engages different neural pathways depending on the leading sense. The existence of such dual route supports recent theoretical accounts proposing that multiple binding mechanisms are implemented in the brain to accommodate different information parsing strategies in auditory and visual sensory systems. SIGNIFICANCE STATEMENT Intersensory timing is a crucial aspect of multisensory integration, determining whether and how

Instantaneous stochastic perturbation theory

International Nuclear Information System (INIS)

Lüscher, Martin

2015-01-01

A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.

A retrodictive stochastic simulation algorithm

International Nuclear Information System (INIS)

Vaughan, T.G.; Drummond, P.D.; Drummond, A.J.

2010-01-01

In this paper we describe a simple method for inferring the initial states of systems evolving stochastically according to master equations, given knowledge of the final states. This is achieved through the use of a retrodictive stochastic simulation algorithm which complements the usual predictive stochastic simulation approach. We demonstrate the utility of this new algorithm by applying it to example problems, including the derivation of likely ancestral states of a gene sequence given a Markovian model of genetic mutation.

Stochastic processes and quantum theory

International Nuclear Information System (INIS)

Klauder, J.R.

1975-01-01

The author analyses a variety of stochastic processes, namely real time diffusion phenomena, which are analogues of imaginary time quantum theory and convariant imaginary time quantum field theory. He elaborates some standard properties involving probability measures and stochastic variables and considers a simple class of examples. Finally he develops the fact that certain stochastic theories actually exhibit divergences that simulate those of covariant quantum field theory and presents examples of both renormaizable and unrenormalizable behavior. (V.J.C.)

Advances in temporal logic

CERN Document Server

Fisher, Michael; Gabbay, Dov; Gough, Graham

2000-01-01

Time is a fascinating subject that has captured mankind's imagination from ancient times to the present. It has been, and continues to be studied across a wide range of disciplines, from the natural sciences to philosophy and logic. More than two decades ago, Pnueli in a seminal work showed the value of temporal logic in the specification and verification of computer programs. Today, a strong, vibrant international research community exists in the broad community of computer science and AI. This volume presents a number of articles from leading researchers containing state-of-the-art results in such areas as pure temporal/modal logic, specification and verification, temporal databases, temporal aspects in AI, tense and aspect in natural language, and temporal theorem proving. Earlier versions of some of the articles were given at the most recent International Conference on Temporal Logic, University of Manchester, UK. Readership: Any student of the area - postgraduate, postdoctoral or even research professor ...

Stochastic Still Water Response Model

DEFF Research Database (Denmark)

Friis-Hansen, Peter; Ditlevsen, Ove Dalager

2002-01-01

In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model is...... out that an important parameter of the stochastic cargo field model is the mean number of containers delivered by each customer.......In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...

Stochastic quantization of Einstein gravity

International Nuclear Information System (INIS)

Rumpf, H.

1986-01-01

We determine a one-parameter family of covariant Langevin equations for the metric tensor of general relativity corresponding to DeWitt's one-parameter family of supermetrics. The stochastic source term in these equations can be expressed in terms of a Gaussian white noise upon the introduction of a stochastic tetrad field. The only physically acceptable resolution of a mathematical ambiguity in the ansatz for the source term is the adoption of Ito's calculus. By taking the formal equilibrium limit of the stochastic metric a one-parameter family of covariant path-integral measures for general relativity is obtained. There is a unique parameter value, distinguished by any one of the following three properties: (i) the metric is harmonic with respect to the supermetric, (ii) the path-integral measure is that of DeWitt, (iii) the supermetric governs the linearized Einstein dynamics. Moreover the Feynman propagator corresponding to this parameter is causal. Finally we show that a consistent stochastic perturbation theory gives rise to a new type of diagram containing ''stochastic vertices.''

Momentum Maps and Stochastic Clebsch Action Principles

Science.gov (United States)

Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S.

2018-01-01

We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into Itô form. In comparing the Stratonovich and Itô forms of the stochastic dynamical equations governing the components of the momentum map, we find that the Itô contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.

Spatial and temporal variability of chorus and hiss

Science.gov (United States)

Santolik, O.; Hospodarsky, G. B.; Kurth, W. S.; Kletzing, C.

2017-12-01

Whistler-mode electromagnetic waves, especially natural emissions of chorus and hiss, have been shown to influence the dynamics of the Van Allen radiation belts via quasi-linear or nonlinear wave particle interactions, transferring energy between different electron populations. Average intensities of chorus and hiss emissions have been found to increase with increasing levels of geomagnetic activity but their stochastic variations in individual spacecraft measurements are usually larger these large-scale temporal effects. To separate temporal and spatial variations of wave characteristics, measurements need to be simultaneously carried out in different locations by identical and/or well calibrated instrumentation. We use two-point survey measurements of the Waves instruments of the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) onboard two Van Allen Probes to asses spatial and temporal variability of chorus and hiss. We take advantage of a systematic analysis of this large data set which has been collected during 2012-2017 over a range of separation vectors of the two spacecraft. We specifically address the question whether similar variations occur at different places at the same time. Our results indicate that power variations are dominated by separations in MLT at scales larger than 0.5h.

Identification of appropriate lags and temporal resolutions for low flow indicators in the River Rhine to forecast low flows with different lead times

NARCIS (Netherlands)

Demirel, M.C.; Booij, Martijn J.; Hoekstra, Arjen Ysbert

2013-01-01

The aim of this paper is to assess the relative importance of low flow indicators for the River Rhine and to identify their appropriate temporal lag and resolution. This is done in the context of low flow forecasting with lead times of 14 and 90 days. First, the Rhine basin is subdivided into seven

Stochastic biomathematical models with applications to neuronal modeling

CERN Document Server

Batzel, Jerry; Ditlevsen, Susanne

2013-01-01

Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.

Introduction to stochastic dynamic programming

CERN Document Server

Ross, Sheldon M; Lukacs, E

1983-01-01

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

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...

BRST stochastic quantization

International Nuclear Information System (INIS)

Hueffel, H.

1990-01-01

After a brief review of the BRST formalism and of the Parisi-Wu stochastic quantization method we introduce the BRST stochastic quantization scheme. It allows the second quantization of constrained Hamiltonian systems in a manifestly gauge symmetry preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed by a discussion on the interacting field theory associated to the relativistic point particle system. 58 refs. (Author)

Stochastic models, estimation, and control

CERN Document Server

Maybeck, Peter S

1982-01-01

This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.

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

Directory of Open Access Journals (Sweden)

Simon Rosenfeld

2009-01-01

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

New "Tau-Leap" Strategy for Accelerated Stochastic Simulation.

Science.gov (United States)

Ramkrishna, Doraiswami; Shu, Che-Chi; Tran, Vu

2014-12-10

The "Tau-Leap" strategy for stochastic simulations of chemical reaction systems due to Gillespie and co-workers has had considerable impact on various applications. This strategy is reexamined with Chebyshev's inequality for random variables as it provides a rigorous probabilistic basis for a measured τ-leap thus adding significantly to simulation efficiency. It is also shown that existing strategies for simulation times have no probabilistic assurance that they satisfy the τ-leap criterion while the use of Chebyshev's inequality leads to a specified degree of certainty with which the τ-leap criterion is satisfied. This reduces the loss of sample paths which do not comply with the τ-leap criterion. The performance of the present algorithm is assessed, with respect to one discussed by Cao et al. ( J. Chem. Phys. 2006 , 124 , 044109), a second pertaining to binomial leap (Tian and Burrage J. Chem. Phys. 2004 , 121 , 10356; Chatterjee et al. J. Chem. Phys. 2005 , 122 , 024112; Peng et al. J. Chem. Phys. 2007 , 126 , 224109), and a third regarding the midpoint Poisson leap (Peng et al., 2007; Gillespie J. Chem. Phys. 2001 , 115 , 1716). The performance assessment is made by estimating the error in the histogram measured against that obtained with the so-called stochastic simulation algorithm. It is shown that the current algorithm displays notably less histogram error than its predecessor for a fixed computation time and, conversely, less computation time for a fixed accuracy. This computational advantage is an asset in repetitive calculations essential for modeling stochastic systems. The importance of stochastic simulations is derived from diverse areas of application in physical and biological sciences, process systems, and economics, etc. Computational improvements such as those reported herein are therefore of considerable significance.

Stochastic theories of quantum mechanics

International Nuclear Information System (INIS)

De la Pena, L.; Cetto, A.M.

1991-01-01

The material of this article is organized into five sections. In Sect. I the basic characteristics of quantum systems are briefly discussed, with emphasis on their stochastic properties. In Sect. II a version of stochastic quantum mechanics is presented, to conclude that the quantum formalism admits an interpretation in terms of stochastic processes. In Sect. III the elements of stochastic electrodynamics are described, and its possibilities and limitations as a fundamental theory of quantum systems are discussed. Section IV contains a recent reformulation that overcomes the limitations of the theory discussed in the foregoing section. Finally, in Sect. V the theorems of EPR, Von Neumann and Bell are discussed briefly. The material is pedagogically presented and includes an ample list of references, but the details of the derivations are generally omitted. (Author)

Lead isotope ratios in artists' lead white: a progress report

International Nuclear Information System (INIS)

Keisch, B.; Callahan, R.C.

1976-01-01

The lead isotope ratios in over four hundred samples of lead white have been determined. The samples represent various geographical sources and dates from the thirteenth century to the present. A new method for organizing this large volume of data is described which helps with the visualization of temporal and geographic patterns. A number of interesting relationships between lead isotope ratio and date or source are shown to exist. Some examples of successful applications of this methodology are described. (author)

A heterogeneous stochastic FEM framework for elliptic PDEs

International Nuclear Information System (INIS)

Hou, Thomas Y.; Liu, Pengfei

2015-01-01

We introduce a new concept of sparsity for the stochastic elliptic operator −div(a(x,ω)∇(⋅)), which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially heterogeneous stochastic structure. This new concept of sparsity motivates a heterogeneous stochastic finite element method (HSFEM) framework for linear elliptic equations, which discretizes the equations using the heterogeneous coupling of spatial basis with local stochastic basis to exploit the local stochastic structure of the solution space. We also provide a sampling method to construct the local stochastic basis for this framework using the randomized range finding techniques. The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions. An online error estimation and correction procedure through Monte Carlo sampling is given. Numerical results for several problems with high dimensional stochastic input are presented to demonstrate the efficiency of the HSFEM in the online stage

Separable quadratic stochastic operators

International Nuclear Information System (INIS)

Rozikov, U.A.; Nazir, S.

2009-04-01

We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)

Trajectory averaging for stochastic approximation MCMC algorithms

KAUST Repository

Liang, Faming

2010-01-01

to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic

Dynamical and hamiltonian dilations of stochastic processes

International Nuclear Information System (INIS)

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

1982-01-01

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

Transport in Stochastic Media

International Nuclear Information System (INIS)

Haran, O.; Shvarts, D.; Thieberger, R.

1998-01-01

Classical transport of neutral particles in a binary, scattering, stochastic media is discussed. It is assumed that the cross-sections of the constituent materials and their volume fractions are known. The inner structure of the media is stochastic, but there exist a statistical knowledge about the lump sizes, shapes and arrangement. The transmission through the composite media depends on the specific heterogeneous realization of the media. The current research focuses on the averaged transmission through an ensemble of realizations, frm which an effective cross-section for the media can be derived. The problem of one dimensional transport in stochastic media has been studied extensively [1]. In the one dimensional description of the problem, particles are transported along a line populated with alternating material segments of random lengths. The current work discusses transport in two-dimensional stochastic media. The phenomenon that is unique to the multi-dimensional description of the problem is obstacle bypassing. Obstacle bypassing tends to reduce the opacity of the media, thereby reducing its effective cross-section. The importance of this phenomenon depends on the manner in which the obstacles are arranged in the media. Results of transport simulations in multi-dimensional stochastic media are presented. Effective cross-sections derived from the simulations are compared against those obtained for the one-dimensional problem, and against those obtained from effective multi-dimensional models, which are partially based on a Markovian assumption

Stochastic Stability of Endogenous Growth: Theory and Applications

OpenAIRE

Boucekkine, Raouf; Pintus, Patrick; Zou, Benteng

2015-01-01

We examine the issue of stability of stochastic endogenous growth. First, stochastic stability concepts are introduced and applied to stochastic linear homogenous differen- tial equations to which several stochastic endogenous growth models reduce. Second, we apply the mathematical theory to two models, starting with the stochastic AK model. It’s shown that in this case exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncerta...

Stochastic models: theory and simulation.

Energy Technology Data Exchange (ETDEWEB)

Field, Richard V., Jr.

2008-03-01

Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.

An extension of clarke's model with stochastic amplitude flip processes

KAUST Repository

Hoel, Hakon

2014-07-01

Stochastic modeling is an essential tool for studying statistical properties of wireless channels. In multipath fading channel (MFC) models, the signal reception is modeled by a sum of wave path contributions, and Clarke\\'s model is an important example of such which has been widely accepted in many wireless applications. However, since Clarke\\'s model is temporally deterministic, Feng and Field noted that it does not model real wireless channels with time-varying randomness well. Here, we extend Clarke\\'s model to a novel time-varying stochastic MFC model with scatterers randomly flipping on and off. Statistical properties of the MFC model are analyzed and shown to fit well with real signal measurements, and a limit Gaussian process is derived from the model when the number of active wave paths tends to infinity. A second focus of this work is a comparison study of the error and computational cost of generating signal realizations from the MFC model and from its limit Gaussian process. By rigorous analysis and numerical studies, we show that in many settings, signal realizations are generated more efficiently by Gaussian process algorithms than by the MFC model\\'s algorithm. Numerical examples that strengthen these observations are also presented. © 2014 IEEE.

Stochastic diffusion models for substitutable technological innovations

NARCIS (Netherlands)

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

2004-01-01

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

Stochasticity in the Josephson map

International Nuclear Information System (INIS)

Nomura, Y.; Ichikawa, Y.H.; Filippov, A.T.

1996-04-01

The Josephson map describes nonlinear dynamics of systems characterized by standard map with the uniform external bias superposed. The intricate structures of the phase space portrait of the Josephson map are examined on the basis of the tangent map associated with the Josephson map. Numerical observation of the stochastic diffusion in the Josephson map is examined in comparison with the renormalized diffusion coefficient calculated by the method of characteristic function. The global stochasticity of the Josephson map occurs at the values of far smaller stochastic parameter than the case of the standard map. (author)

An Optogenetic Platform for Real-Time, Single-Cell Interrogation of Stochastic Transcriptional Regulation.

Science.gov (United States)

Rullan, Marc; Benzinger, Dirk; Schmidt, Gregor W; Milias-Argeitis, Andreas; Khammash, Mustafa

2018-05-17

Transcription is a highly regulated and inherently stochastic process. The complexity of signal transduction and gene regulation makes it challenging to analyze how the dynamic activity of transcriptional regulators affects stochastic transcription. By combining a fast-acting, photo-regulatable transcription factor with nascent RNA quantification in live cells and an experimental setup for precise spatiotemporal delivery of light inputs, we constructed a platform for the real-time, single-cell interrogation of transcription in Saccharomyces cerevisiae. We show that transcriptional activation and deactivation are fast and memoryless. By analyzing the temporal activity of individual cells, we found that transcription occurs in bursts, whose duration and timing are modulated by transcription factor activity. Using our platform, we regulated transcription via light-driven feedback loops at the single-cell level. Feedback markedly reduced cell-to-cell variability and led to qualitative differences in cellular transcriptional dynamics. Our platform establishes a flexible method for studying transcriptional dynamics in single cells. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

Modeling the photochemical attenuation of down-the-drain chemicals during river transport by stochastic methods and field measurements of pharmaceuticals and personal care products.

Science.gov (United States)

Hanamoto, Seiya; Nakada, Norihide; Yamashita, Naoyuki; Tanaka, Hiroaki

2013-01-01

Existing stochastic models for predicting concentrations of down-the-drain chemicals in aquatic environments do not account for the diurnal variation of direct photolysis by sunlight, despite its being an important factor in natural attenuation. To overcome this limitation, we developed a stochastic model incorporating temporal variations in direct photolysis. To verify the model, we measured 57 pharmaceuticals and personal care products (PPCPs) in a 7.6-km stretch of an urban river, and determined their physical and biological properties in laboratory experiments. During transport along the river, 8 PPCPs, including ketoprofen and azithromycin, were attenuated by >20%, mainly owing to direct photolysis and adsorption to sediments. The photolabile PPCPs attenuated significantly in the daytime but persisted in the nighttime. The observations were similar to the values predicted by the photolysis model for the photolabile PPCPs (i.e., ketoprofen, diclofenac and furosemide) but not by the existing model. The stochastic model developed in this study was suggested to be a novel and useful stochastic model for evaluating direct photolysis of down-the-drain chemicals, which occurs during the river transport.

Numerical Simulation of the Heston Model under Stochastic Correlation

Directory of Open Access Journals (Sweden)

Long Teng

2017-12-01

Full Text Available Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.

Nonlinear signaling on biological networks: The role of stochasticity and spectral clustering

Science.gov (United States)

Hernandez-Hernandez, Gonzalo; Myers, Jesse; Alvarez-Lacalle, Enrique; Shiferaw, Yohannes

2017-03-01

Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different conformational states. Signaling is typically a cooperative process which requires the occurrence of multiple binding events so that reaction rates have a nonlinear dependence on the amount of signaling molecule. It is this nonlinearity that endows biological signaling networks with robust switchlike properties which are critical to their biological function. In this study we investigate how the properties of these signaling systems depend on the network architecture. Our main result is that these nonlinear networks exhibit bistability where the network activity can switch between states that correspond to a low and high activity level. We show that this bistable regime emerges at a critical coupling strength that is determined by the spectral structure of the network. In particular, the set of nodes that correspond to large components of the leading eigenvector of the adjacency matrix determines the onset of bistability. Above this transition the eigenvectors of the adjacency matrix determine a hierarchy of clusters, defined by its spectral properties, which are activated sequentially with increasing network activity. We argue further that the onset of bistability occurs either continuously or discontinuously depending upon whether the leading eigenvector is localized or delocalized. Finally, we show that at low network coupling stochastic transitions to the active branch are also driven by the set of nodes that contribute more strongly to the leading eigenvector. However, at high coupling, transitions are insensitive to network structure since the network can be activated by stochastic transitions of a few nodes. Thus this work identifies important features of biological signaling networks that may underlie their biological

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

1995-01-01

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...... to optimization variables can be performed. A computer implementation is described and an illustrative example is given....

Comparison of deterministic and stochastic techniques for estimation of design basis floods for nuclear power plants

International Nuclear Information System (INIS)

Solomon, S.I.; Harvey, K.D.; Asmis, G.J.K.

1983-01-01

The IAEA Safety Guide 50-SG-S10A recommends that design basis floods be estimated by deterministic techniques using probable maximum precipitation and a rainfall runoff model to evaluate the corresponding flood. The Guide indicates that stochastic techniques are also acceptable in which case floods of very low probability have to be estimated. The paper compares the results of applying the two techniques in two river basins at a number of locations and concludes that the uncertainty of the results of both techniques is of the same order of magnitude. However, the use of the unit hydrograph as the rain fall runoff model may lead in some cases to non-conservative estimates. A distributed non-linear rainfall runoff model leads to estimates of probable maximum flood flows which are very close to values of flows having a 10 6 to 10 7 years return interval estimated using a conservative and relatively simple stochastic technique. Recommendations on the practical application of Safety Guide 50-SG-10A are made and the extension of the stochastic technique to ungauged sites and other design parameters is discussed

Multiple-scale stochastic processes: Decimation, averaging and beyond

Energy Technology Data Exchange (ETDEWEB)

Bo, Stefano, E-mail: stefano.bo@nordita.org [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Celani, Antonio [Quantitative Life Sciences, The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151 - Trieste (Italy)

2017-02-07

The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This has provided fruitful applications for established stochastic methods and motivated further developments. These systems often involve processes taking place on widely separated time scales. For an efficient modeling one usually focuses on the slower degrees of freedom and it is of great importance to accurately eliminate the fast variables in a controlled fashion, carefully accounting for their net effect on the slower dynamics. This procedure in general requires to perform two different operations: decimation and coarse-graining. We introduce the asymptotic methods that form the basis of this procedure and discuss their application to a series of physical, biological and chemical examples. We then turn our attention to functionals of the stochastic trajectories such as residence times, counting statistics, fluxes, entropy production, etc. which have been increasingly studied in recent years. For such functionals, the elimination of the fast degrees of freedom can present additional difficulties and naive procedures can lead to blatantly inconsistent results. Homogenization techniques for functionals are less covered in the literature and we will pedagogically present them here, as natural extensions of the ones employed for the trajectories. We will also discuss recent applications of these techniques to the thermodynamics of small systems and their interpretation in terms of information-theoretic concepts.

Dynamic analysis of a stochastic rumor propagation model

Science.gov (United States)

Jia, Fangju; Lv, Guangying

2018-01-01

The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. In this paper, we are concerned with a stochastic rumor propagation model. Sufficient conditions for extinction and persistence in the mean of the rumor are established. The threshold between persistence in the mean and extinction of the rumor is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.

Basic aspects of stochastic reliability analysis for redundancy systems

International Nuclear Information System (INIS)

Doerre, P.

1989-01-01

Much confusion has been created by trying to establish common cause failure (CCF) as an extra phenomenon which has to be treated with extra methods in reliability and data analysis. This paper takes another approach which can be roughly described by the statement that dependent failure is the basic phenomenon, while 'independent failure' refers to a special limiting case, namely the perfectly homogeneous population. This approach is motivated by examples demonstrating that common causes do not lead to dependent failure, so far as physical dependencies like shared components are excluded, and that stochastic dependencies are not related to common causes. The possibility to select more than one failure behaviour from an inhomogeneous population is identified as an additional random process which creates stochastic dependence. However, this source of randomness is usually treated in the deterministic limit, which destroys dependence and hence yields incorrect multiple failure frequencies for redundancy structures, thus creating the need for applying corrective CCF models. (author)

Environmental vs Demographic Stochasticity in Population Growth

OpenAIRE

Braumann, C. A.

2010-01-01

Compares the effect on population growth of envinonmental stochasticity (random environmental variations described by stochastic differential equations) with demographic stochasticity (random variations in births and deaths described by branching processes and birth-and-death processes), in the density-independent and the density-dependent cases.

Deterministic and stochastic analysis of size effects and damage evolution in quasi-brittle materials

NARCIS (Netherlands)

Gutiérrez, M.A.; Borst, R. de

1999-01-01

This study presents some recent results on damage evolution in quasi-brittle materials including stochastic imperfections. The material strength is described as a random field and coupled to the response. The most probable configurations of imperfections leading to failure are sought by means of an

Alternative Asymmetric Stochastic Volatility Models

NARCIS (Netherlands)

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

2010-01-01

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

Transport stochastic multi-dimensional media

International Nuclear Information System (INIS)

Haran, O.; Shvarts, D.

1996-01-01

Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors)

Transport stochastic multi-dimensional media

Energy Technology Data Exchange (ETDEWEB)

Haran, O; Shvarts, D [Israel Atomic Energy Commission, Beersheba (Israel). Nuclear Research Center-Negev; Thiberger, R [Ben-Gurion Univ. of the Negev, Beersheba (Israel)

1996-12-01

Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors).

Modelling and application of stochastic processes

CERN Document Server

1986-01-01

The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza­ tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef­ ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...

Turbulent response in a stochastic regime

International Nuclear Information System (INIS)

Molvig, K.; Freidberg, J.P.; Potok, R.; Hirshman, S.P.; Whitson, J.C.; Tajima, T.

1981-06-01

The theory for the non-linear, turbulent response in a system with intrinsic stochasticity is considered. It is argued that perturbative Eulerian theories, such as the Direct Interaction Approximation (DIA), are inherently unsuited to describe such a system. The exponentiation property that characterizes stochasticity appears in the Lagrangian picture and cannot even be defined in the Eulerian representation. An approximation for stochastic systems - the Normal Stochastic Approximation - is developed and states that the perturbed orbit functions (Lagrangian fluctuations) behave as normally distributed random variables. This is independent of the Eulerian statistics and, in fact, we treat the Eulerian fluctuations as fixed. A simple model problem (appropriate for the electron response in the drift wave) is subjected to a series of computer experiments. To within numerical noise the results are in agreement with the Normal Stochastic Approximation. The predictions of the DIA for this mode show substantial qualitative and quantitative departures from the observations

Stochastic modeling and analysis of telecoms networks

CERN Document Server

Decreusefond, Laurent

2012-01-01

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

Treatment of the response of a reactor to stochastic reactivity input

International Nuclear Information System (INIS)

Bansal, N.K.

1977-08-01

One of the important applications of reactor noise theory, which relies on the methematical methods for treating stochastic processes, is to determine either the confidence limits for the allowed deviations of the measured signals during normal reactor operation, or the statistical properties of their respective expectation values. In this report, we stress mainly the general mathematical aspects for treating this problem. A global description of a reactor system, perturbed by stochastic reactivity input, leads to a stochastic differential equation with parametric excitation. A discrepancy exists in literature about obtaining the correct solution of such an equation in its general frame. We discuss this discrepancy and review the work done for solving such an equation. Some recent work indicates that linearisation of system's equations is justified in most cases of reactor operations. We develop a general scheme for calculating the various covariances and correlation functions in a stable and stationary system, which is perturbed by various noise sources and where linearisation of system's equations is justified. The formulation is easily extendable to an unstable, nonstationary system, like an uncontrolled critical reactor as demonstrated. (orig.) [de

Stochastic maintenance optimization at Candu power plants

International Nuclear Information System (INIS)

Doyle, E.K.; Duchesne, T.; Lee, C.G.; Cho, D.I.

2004-01-01

The use of various innovative maintenance optimization techniques at Bruce has lead to cost effective preventive maintenance applications for complex systems as previously reported at ICONE 6 in New Orleans (1996). Further refinement of the station maintenance strategy was evaluated via the applicability of statistical analysis of historical failure data. The viability of stochastic methods in Candu maintenance was illustrated at ICONE 10 in Washington DC (2002). The next phase consists of investigating the validity of using subjective elicitation techniques to obtain component lifetime distributions. This technique provides access to the elusive failure statistics, the lack of which is often referred to in the literature as the principal impediment preventing the use of stochastic methods in large industry. At the same time the technique allows very valuable information to be captured from the fast retiring 'baby boom generation'. Initial indications have been quite positive. The current reality of global competition necessitates the pursuit of all financial optimizers. The next construction phase in the power generation industry will soon begin on a worldwide basis. With the relatively high initial capital cost of new nuclear generation all possible avenues of financial optimization must be evaluated and implemented. (authors)

A stochastic model for the probability of malaria extinction by mass drug administration.

Science.gov (United States)

Pemberton-Ross, Peter; Chitnis, Nakul; Pothin, Emilie; Smith, Thomas A

2017-09-18

Mass drug administration (MDA) has been proposed as an intervention to achieve local extinction of malaria. Although its effect on the reproduction number is short lived, extinction may subsequently occur in a small population due to stochastic fluctuations. This paper examines how the probability of stochastic extinction depends on population size, MDA coverage and the reproduction number under control, R c . A simple compartmental model is developed which is used to compute the probability of extinction using probability generating functions. The expected time to extinction in small populations after MDA for various scenarios in this model is calculated analytically. The results indicate that mass drug administration (Firstly, R c must be sustained at R c  95% to have a non-negligible probability of successful elimination. Stochastic fluctuations only significantly affect the probability of extinction in populations of about 1000 individuals or less. The expected time to extinction via stochastic fluctuation is less than 10 years only in populations less than about 150 individuals. Clustering of secondary infections and of MDA distribution both contribute positively to the potential probability of success, indicating that MDA would most effectively be administered at the household level. There are very limited circumstances in which MDA will lead to local malaria elimination with a substantial probability.

Stochastic resonance in a delayed triple-well potential driven by correlated noises.

Science.gov (United States)

Xu, Pengfei; Jin, Yanfei; Xiao, Shaomin

2017-11-01

In this paper, we investigate stochastic resonance (SR) in a delayed triple-well potential subject to correlated noises and a harmonic signal. The stationary probability density, together with the response amplitude of the system, is obtained by using the small time delay approximation. It is found that the time delay, noise intensities, and the cross-correlation between noises can induce the occurrence of the transition. Moreover, the appropriate choice of noise intensities and time delay can improve the output of the system, enhance the SR effect, and lead to the phenomenon of noise enhanced stability. Especially, the stochastic multi-resonance phenomenon is observed when the multiplicative and additive noises are correlated. Finally, the theoretical results are well verified through numerical simulations.

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

International Nuclear Information System (INIS)

Bokanowski, Olivier; Picarelli, Athena; Zidani, Hasnaa

2015-01-01

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

Energy Technology Data Exchange (ETDEWEB)

Bokanowski, Olivier, E-mail: boka@math.jussieu.fr [Laboratoire Jacques-Louis Lions, Université Paris-Diderot (Paris 7) UFR de Mathématiques - Bât. Sophie Germain (France); Picarelli, Athena, E-mail: athena.picarelli@inria.fr [Projet Commands, INRIA Saclay & ENSTA ParisTech (France); Zidani, Hasnaa, E-mail: hasnaa.zidani@ensta.fr [Unité de Mathématiques appliquées (UMA), ENSTA ParisTech (France)

2015-02-15

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.

Transport of radionuclides in stochastic media. Pt. 1: The quasi-asymptotic approximation

International Nuclear Information System (INIS)

Devooght, J.; Smidts, O.F.

1996-01-01

A three-dimensional quasi-asymptotic approximate equation is developed for the transport of radionuclides in a stochastic velocity field. This approximation is derived from an integro-differential equation of transport in stochastic media, commonly encountered in hydrogeology. The quasi-asymptotic equation turns out to be a generalised Telegrapher's equation as found by Williams in the particular context of fractured media. We obtain the Telegrapher's equation without specifying the causes responsible for the random velocity field. Our model may thus be applied in porous media as well as in fractured media. We give the developments leading to the analytical solution of the three-dimensional Telegrapher's equation for constant parameters. This solution is then visualised for a source in the form of a square wave. (Author)

Trajectory averaging for stochastic approximation MCMC algorithms

KAUST Repository

Liang, Faming

2010-10-01

The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.

Stochastic resonance during a polymer translocation process

International Nuclear Information System (INIS)

Mondal, Debasish; Muthukumar, M.

2016-01-01

We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

Is human failure a stochastic process?

International Nuclear Information System (INIS)

Dougherty, Ed M.

1997-01-01

Human performance results in failure events that occur with a risk-significant frequency. System analysts have taken for granted the random (stochastic) nature of these events in engineering assessments such as risk assessment. However, cognitive scientists and error technologists, at least those who have interest in human reliability, have, over the recent years, claimed that human error does not need this stochastic framework. Yet they still use the language appropriate to stochastic processes. This paper examines the potential for the stochastic nature of human failure production as the basis for human reliability analysis. It distinguishes and leaves to others, however, the epistemic uncertainties over the possible probability models for the real variability of human performance

Stochastic Switching Dynamics

DEFF Research Database (Denmark)

Simonsen, Maria

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

Stochastic singular optics

CSIR Research Space (South Africa)

Roux, FS

2013-09-01

Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic... of vortices: topological charge ±1 (higher order are unstable). Positive and negative vortex densities np(x, y, z) and nn(x, y, z) ⊲ Vortex density: V = np + nn ⊲ Topological charge density: T = np − nn – p. 4/24 Subfields of SSO ⊲ Homogeneous, normally...

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

OpenAIRE

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

2017-01-01

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

Born's reciprocity principle in stochastic phase space

International Nuclear Information System (INIS)

Prugovecki, E.

1981-01-01

It is shown that the application of Born's reciprocity principle to relativistic quantum mechanics in stochastic phase space (by the requirement that the proper wave functions of extended particles satisfy the Born-Lande as well as the Klein-Gordon equation) leads to the unique determination of these functions for any given value of their rms radius. The resulting particle propagators display not only Lorentz but also reciprocal invariance. This feature remains true even in the case of mass-zero particles, such as photons, when their localization is achieved by means of extended test particles whose proper wave functions obey the reciprocity principle. (author)

Dynamics of non-holonomic systems with stochastic transport

Science.gov (United States)

Holm, D. D.; Putkaradze, V.

2018-01-01

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

Addressing model error through atmospheric stochastic physical parametrizations: impact on the coupled ECMWF seasonal forecasting system

Science.gov (United States)

Weisheimer, Antje; Corti, Susanna; Palmer, Tim; Vitart, Frederic

2014-01-01

The finite resolution of general circulation models of the coupled atmosphere–ocean system and the effects of sub-grid-scale variability present a major source of uncertainty in model simulations on all time scales. The European Centre for Medium-Range Weather Forecasts has been at the forefront of developing new approaches to account for these uncertainties. In particular, the stochastically perturbed physical tendency scheme and the stochastically perturbed backscatter algorithm for the atmosphere are now used routinely for global numerical weather prediction. The European Centre also performs long-range predictions of the coupled atmosphere–ocean climate system in operational forecast mode, and the latest seasonal forecasting system—System 4—has the stochastically perturbed tendency and backscatter schemes implemented in a similar way to that for the medium-range weather forecasts. Here, we present results of the impact of these schemes in System 4 by contrasting the operational performance on seasonal time scales during the retrospective forecast period 1981–2010 with comparable simulations that do not account for the representation of model uncertainty. We find that the stochastic tendency perturbation schemes helped to reduce excessively strong convective activity especially over the Maritime Continent and the tropical Western Pacific, leading to reduced biases of the outgoing longwave radiation (OLR), cloud cover, precipitation and near-surface winds. Positive impact was also found for the statistics of the Madden–Julian oscillation (MJO), showing an increase in the frequencies and amplitudes of MJO events. Further, the errors of El Niño southern oscillation forecasts become smaller, whereas increases in ensemble spread lead to a better calibrated system if the stochastic tendency is activated. The backscatter scheme has overall neutral impact. Finally, evidence for noise-activated regime transitions has been found in a cluster analysis of mid

The origin of the algebra of quantum operators in the stochastic formulation of quantum mechanics

International Nuclear Information System (INIS)

Davidson, M.

1979-01-01

The origin of the algebra of the non-commuting operators of quantum mechanics is explained in the general Fenyes-Nelson stochastic models in which the diffusion constant is a free parameter. This is achieved by continuing the diffusion constant to imaginary values, a continuation which destroys the physical interpretation, but does not affect experimental predictions. This continuation leads to great mathematical simplification in the stochastic theory, and to an understanding of the entire mathematical formalism of quantum mechanics. It is more than a formal construction because the diffusion parameter is not an observable in these theories. (Auth.)

Stochastic cooling at Fermilab

International Nuclear Information System (INIS)

Marriner, J.

1986-08-01

The topics discussed are the stochastic cooling systems in use at Fermilab and some of the techniques that have been employed to meet the particular requirements of the anti-proton source. Stochastic cooling at Fermilab became of paramount importance about 5 years ago when the anti-proton source group at Fermilab abandoned the electron cooling ring in favor of a high flux anti-proton source which relied solely on stochastic cooling to achieve the phase space densities necessary for colliding proton and anti-proton beams. The Fermilab systems have constituted a substantial advance in the techniques of cooling including: large pickup arrays operating at microwave frequencies, extensive use of cryogenic techniques to reduce thermal noise, super-conducting notch filters, and the development of tools for controlling and for accurately phasing the system

Quantization of dynamical systems and stochastic control theory

International Nuclear Information System (INIS)

Guerra, F.; Morato, L.M.

1982-09-01

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

On Lipschitzian quantum stochastic differential inclusions

International Nuclear Information System (INIS)

Ekhaguere, G.O.S.

1990-12-01

Quantum stochastic differential inclusions are introduced and studied within the framework of the Hudson-Parthasarathy formulation of quantum stochastic calculus. Results concerning the existence of solutions of a Lipschitzian quantum stochastic differential inclusion and the relationship between the solutions of such an inclusion and those of its convexification are presented. These generalize the Filippov existence theorem and the Filippov-Wazewski Relaxation Theorem for classical differential inclusions to the present noncommutative setting. (author). 9 refs

Stochastic temperature and the Nicolai map

International Nuclear Information System (INIS)

Hueffel, H.

1989-01-01

Just as standard temperature can be related to the time coordinate of Euclidean space, a new concept of 'stochastic temperature' may be introduced by associating it to the Parisi-Wu time of stochastic quantization. The perturbative equilibrium limit for a self-interacting scalar field is studied, and a 'thermal' mass shift to one loop is shown. In addition one may interpret the underlying stochastic process as a Nicolai map at nonzero 'temperature'. 22 refs. (Author)

Stochastic Linear Quadratic Optimal Control Problems

International Nuclear Information System (INIS)

Chen, S.; Yong, J.

2001-01-01

This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well

Stochastic modeling for time series InSAR: with emphasis on atmospheric effects

Science.gov (United States)

Cao, Yunmeng; Li, Zhiwei; Wei, Jianchao; Hu, Jun; Duan, Meng; Feng, Guangcai

2018-02-01

Despite the many applications of time series interferometric synthetic aperture radar (TS-InSAR) techniques in geophysical problems, error analysis and assessment have been largely overlooked. Tropospheric propagation error is still the dominant error source of InSAR observations. However, the spatiotemporal variation of atmospheric effects is seldom considered in the present standard TS-InSAR techniques, such as persistent scatterer interferometry and small baseline subset interferometry. The failure to consider the stochastic properties of atmospheric effects not only affects the accuracy of the estimators, but also makes it difficult to assess the uncertainty of the final geophysical results. To address this issue, this paper proposes a network-based variance-covariance estimation method to model the spatiotemporal variation of tropospheric signals, and to estimate the temporal variance-covariance matrix of TS-InSAR observations. The constructed stochastic model is then incorporated into the TS-InSAR estimators both for parameters (e.g., deformation velocity, topography residual) estimation and uncertainty assessment. It is an incremental and positive improvement to the traditional weighted least squares methods to solve the multitemporal InSAR time series. The performance of the proposed method is validated by using both simulated and real datasets.

Investor preferences for oil spot and futures based on mean-variance and stochastic dominance

NARCIS (Netherlands)

H.H. Lean (Hooi Hooi); M.J. McAleer (Michael); W.-K. Wong (Wing-Keung)

2010-01-01

textabstractThis paper examines investor preferences for oil spot and futures based on mean-variance (MV) and stochastic dominance (SD). The mean-variance criterion cannot distinct the preferences of spot and market whereas SD tests leads to the conclusion that spot dominates futures in the downside

Stochastic programming with integer recourse

NARCIS (Netherlands)

van der Vlerk, Maarten Hendrikus

1995-01-01

In this thesis we consider two-stage stochastic linear programming models with integer recourse. Such models are at the intersection of two different branches of mathematical programming. On the one hand some of the model parameters are random, which places the problem in the field of stochastic

Stochastic-hydrodynamic model of halo formation in charged particle beams

Directory of Open Access Journals (Sweden)

Nicola Cufaro Petroni

2003-03-01

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

Modelling estimation and analysis of dynamic processes from image sequences using temporal random closed sets and point processes with application to the cell exocytosis and endocytosis

OpenAIRE

Díaz Fernández, Ester

2010-01-01

In this thesis, new models and methodologies are introduced for the analysis of dynamic processes characterized by image sequences with spatial temporal overlapping. The spatial temporal overlapping exists in many natural phenomena and should be addressed properly in several Science disciplines such as Microscopy, Material Sciences, Biology, Geostatistics or Communication Networks. This work is related to the Point Process and Random Closed Set theories, within Stochastic Ge...

Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD

International Nuclear Information System (INIS)

Morningstar, C.; Lenkner, D.; Wong, C.H.; Bulava, J.; Foley, J.; Juge, K.J.; Peardon, M.

2011-08-01

A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multi-hadron operators in lattice QCD. The method is well suited for calculations in large volumes. Contributions involving quark propagation connecting hadron sink operators at the same final time can be handled in a straightforward manner, even for a large number of final time slices. The method exploits Laplacian Heaviside (LapH) smearing. Z N noise is introduced in a novel way, and variance reduction is achieved using judiciously-chosen noise dilution projectors. The method is tested using isoscalar mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin I=0,1,2 on large anisotropic 24 3 x 128 lattices with spatial spacing a s ∝0.12 fm and temporal spacing a t ∝0.034 fm for pion masses m π ∼ 390 and 240 MeV. (orig.)

Optimizing continuous cover management of boreal forest when timber prices and tree growth are stochastic

Directory of Open Access Journals (Sweden)

Timo Pukkala

2015-03-01

Full Text Available Background Decisions on forest management are made under risk and uncertainty because the stand development cannot be predicted exactly and future timber prices are unknown. Deterministic calculations may lead to biased advice on optimal forest management. The study optimized continuous cover management of boreal forest in a situation where tree growth, regeneration, and timber prices include uncertainty. Methods Both anticipatory and adaptive optimization approaches were used. The adaptive approach optimized the reservation price function instead of fixed cutting years. The future prices of different timber assortments were described by cross-correlated auto-regressive models. The high variation around ingrowth model was simulated using a model that describes the cross- and autocorrelations of the regeneration results of different species and years. Tree growth was predicted with individual tree models, the predictions of which were adjusted on the basis of a climate-induced growth trend, which was stochastic. Residuals of the deterministic diameter growth model were also simulated. They consisted of random tree factors and cross- and autocorrelated temporal terms. Results Of the analyzed factors, timber price caused most uncertainty in the calculation of the net present value of a certain management schedule. Ingrowth and climate trend were less significant sources of risk and uncertainty than tree growth. Stochastic anticipatory optimization led to more diverse post-cutting stand structures than obtained in deterministic optimization. Cutting interval was shorter when risk and uncertainty were included in the analyses. Conclusions Adaptive optimization and management led to 6%–14% higher net present values than obtained in management that was based on anticipatory optimization. Increasing risk aversion of the forest landowner led to earlier cuttings in a mature stand. The effect of risk attitude on optimization results was small.

A stochastic model with a low-frequency amplification feedback for the stratospheric northern annular mode

Science.gov (United States)

Yu, Yueyue; Cai, Ming; Ren, Rongcai

2017-08-01

We consider three indices to measure the polar stratospheric mass and stratospheric meridional mass circulation variability: anomalies of (1) total mass in the polar stratospheric cap (60-90°N, above the isentropic surface 400 K, PSM), (2) total adiabatic mass transport across 60°N into the polar stratosphere cap (AMT), (3) and total diabetic mass transport across 400 K from the polar stratosphere into the troposphere below (DMT). It is confirmed that the negative stratospheric Northern Annular Mode (NAM) and PSM indices have a nearly indistinguishable temporal evolution and a similar red-noise-like spectrum with a de-correlation timescale of 4 weeks. This enables us to examine the low-frequency nature of the NAM in the framework of mass circulation, namely, d/{dt}{PSM}={AMT} - {DMT} . The DMT index tends to be positively correlated with the PSM with a red-noise-like spectrum, representing slow radiative cooling processes giving rise to a de-correlation timescale of 3-4 weeks. The AMT is nearly perfectly correlated with the day-to-day tendency of PSM, reflecting a robust quasi 90° out-of-phase relation between the AMT and PSM at all frequency bands. Variations of vertically westward tilting of planetary waves contribute mainly to the high-frequency portion of AMT. It is the wave amplitude's slow vacillation that plays the leading role in the quasi 90° out-of-phase relation between the AMT and PSM. Based on this, we put forward a linear stochastic model with a low-frequency amplification feedback from low-frequency amplitude vacillations of planetary waves to explain the amplified low-frequency response of PSM/NAM to a stochastic forcing from the westward tilting variability.

Stochastic quantization of gravity and string fields

International Nuclear Information System (INIS)

Rumpf, H.

1986-01-01

The stochastic quantization method of Parisi and Wu is generalized so as to make it applicable to Einstein's theory of gravitation. The generalization is based on the existence of a preferred metric in field configuration space, involves Ito's calculus, and introduces a complex stochastic process adapted to Lorentzian spacetime. It implies formally the path integral measure of DeWitt, a causual Feynman propagator, and a consistent stochastic perturbation theory. The lineraized version of the theory is also obtained from the stochastic quantization of the free string field theory of Siegel and Zwiebach. (Author)

The propagation of stochastic pixel noise into magnitude and phase values in the Fourier analysis of digital images

International Nuclear Information System (INIS)

Holden, J.E.; Halama, J.R.; Hasegawa, B.H.

1986-01-01

The use of Fourier analysis in nuclear medicine gated blood ventriculography provides a useful example of the application of Fourier methods to digital medical imaging. In particular, the nuclear medicine experience demonstrates that there is diagnostic significance not only in the pixel averages of temporal Fourier magnitude and phase computed in various image regions, but also in the distributions of the individual pixel values about those averages. However, a region containing pixels that are perfectly synchronous on average would still yield a finite distribution of calculated Fourier coefficients due to the propagation of stochastic pixel noise into the calculated values. The authors have studied this noise component of both the magnitude and phase distributions using phantom studies and computer simulation. In both approaches, several thousand one-pixel 'ventriculograms' were generated, all identical to each other except for stochastic noise. Fourier magnitudes and phases at several frequencies were calculated and histograms generated. A theoretical prediction of the distributions was developed and shown to fit the experimental results well. The authors' formalism can be used to estimate study count requirements or, for fixed study counts, to assess the stochastic noise contribution in the interpretation of measured phase and magnitude distributions. (author)

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

Directory of Open Access Journals (Sweden)

Shaolin Ji

2013-01-01

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

Thermal mixtures in stochastic mechanics

Energy Technology Data Exchange (ETDEWEB)

Guerra, F [Rome Univ. (Italy). Ist. di Matematica; Loffredo, M I [Salerno Univ. (Italy). Ist. di Fisica

1981-01-17

Stochastic mechanics is extended to systems in thermal equilibrium. The resulting stochastic processes are mixtures of Nelson processes. Their Markov property is investigated in some simple cases. It is found that in order to inforce Markov property the algebra of observable associated to the present must be suitably enlarged.

Universal Temporal Profile of Replication Origin Activation in Eukaryotes

Science.gov (United States)

Goldar, Arach

2011-03-01

The complete and faithful transmission of eukaryotic genome to daughter cells involves the timely duplication of mother cell's DNA. DNA replication starts at multiple chromosomal positions called replication origin. From each activated replication origin two replication forks progress in opposite direction and duplicate the mother cell's DNA. While it is widely accepted that in eukaryotic organisms replication origins are activated in a stochastic manner, little is known on the sources of the observed stochasticity. It is often associated to the population variability to enter S phase. We extract from a growing Saccharomyces cerevisiae population the average rate of origin activation in a single cell by combining single molecule measurements and a numerical deconvolution technique. We show that the temporal profile of the rate of origin activation in a single cell is similar to the one extracted from a replicating cell population. Taking into account this observation we exclude the population variability as the origin of observed stochasticity in origin activation. We confirm that the rate of origin activation increases in the early stage of S phase and decreases at the latter stage. The population average activation rate extracted from single molecule analysis is in prefect accordance with the activation rate extracted from published micro-array data, confirming therefore the homogeneity and genome scale invariance of dynamic of replication process. All these observations point toward a possible role of replication fork to control the rate of origin activation.

The Robustness of Stochastic Switching Networks

OpenAIRE

Loh, Po-Ling; Zhou, Hongchao; Bruck, Jehoshua

2009-01-01

Many natural systems, including chemical and biological systems, can be modeled using stochastic switching circuits. These circuits consist of stochastic switches, called pswitches, which operate with a fixed probability of being open or closed. We study the effect caused by introducing an error of size ∈ to each pswitch in a stochastic circuit. We analyze two constructions – simple series-parallel and general series-parallel circuits – and prove that simple series-parallel circuits are robus...

Polarization of the vacuum by a stochastic external field

International Nuclear Information System (INIS)

Krive, I.V.; Pastur, L.A.; Rozhavskii, A.S.

1988-01-01

The effect of disorder, realized in the form of a fluctuating extra mass term, on the bosonic vacuum and fermionic vacuum of models of quantum field theory is studied. A method is developed for calculating the mean effective potential in the stochastic external field. For a model of interacting scalar and fermion fields in (3+1)-dimensional space-time it is shown that random fluctuations of the mass lead to an increase of the equilibrium mean scalar field in the system

The intrinsic stochasticity of near-integrable Hamiltonian systems

Energy Technology Data Exchange (ETDEWEB)

Krlin, L [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu

1989-09-01

Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolmogorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The paper discusses the relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem, and describes some numerical experiments on related astrophysical and high-temperature plasma problems. Some open questions are mentioned in conclusion. (author).

Entropy Production in Stochastics

Directory of Open Access Journals (Sweden)

Demetris Koutsoyiannis

2017-10-01

Full Text Available While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT or conditionally on the past and present having been observed (CEPLT. We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed.

Stochastic modeling of wetland-groundwater systems

Science.gov (United States)

Bertassello, Leonardo Enrico; Rao, P. Suresh C.; Park, Jeryang; Jawitz, James W.; Botter, Gianluca

2018-02-01

Modeling and data analyses were used in this study to examine the temporal hydrological variability in geographically isolated wetlands (GIWs), as influenced by hydrologic connectivity to shallow groundwater, wetland bathymetry, and subject to stochastic hydro-climatic forcing. We examined the general case of GIWs coupled to shallow groundwater through exfiltration or infiltration across wetland bottom. We also examined limiting case with the wetland stage as the local expression of the shallow groundwater. We derive analytical expressions for the steady-state probability density functions (pdfs) for wetland water storage and stage using few, scaled, physically-based parameters. In addition, we analyze the hydrologic crossing time properties of wetland stage, and the dependence of the mean hydroperiod on climatic and wetland morphologic attributes. Our analyses show that it is crucial to account for shallow groundwater connectivity to fully understand the hydrologic dynamics in wetlands. The application of the model to two different case studies in Florida, jointly with a detailed sensitivity analysis, allowed us to identify the main drivers of hydrologic dynamics in GIWs under different climate and morphologic conditions.

Stochastic models for structured populations scaling limits and long time behavior

CERN Document Server

Meleard, Sylvie

2015-01-01

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

Markov stochasticity coordinates

International Nuclear Information System (INIS)

Eliazar, Iddo

2017-01-01

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

Markov stochasticity coordinates

Energy Technology Data Exchange (ETDEWEB)

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

2017-01-15

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

A DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model

Science.gov (United States)

Hozman, J.; Tichý, T.

2017-12-01

Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.

Approximating Preemptive Stochastic Scheduling

OpenAIRE

Megow Nicole; Vredeveld Tjark

2009-01-01

We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...

The stochastic goodwill problem

OpenAIRE

Marinelli, Carlo

2003-01-01

Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for some classes of stochastic perturbations of the classical Nerlove-Arrow dynamics. We also consider some generalizations such as problems with constrained budget and with discretionar...

Optimal base-stock policy for the inventory system with periodic review, backorders and sequential lead times

DEFF Research Database (Denmark)

Johansen, Søren Glud; Thorstenson, Anders

2008-01-01

We extend well-known formulae for the optimal base stock of the inventory system with continuous review and constant lead time to the case with periodic review and stochastic, sequential lead times. Our extension uses the notion of the 'extended lead time'. The derived performance measures...

Sequential neural models with stochastic layers

DEFF Research Database (Denmark)

Fraccaro, Marco; Sønderby, Søren Kaae; Paquet, Ulrich

2016-01-01

How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural...... generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over...

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

Directory of Open Access Journals (Sweden)

Anqi Miao

2017-01-01

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

History-dependent stochastic Petri nets

NARCIS (Netherlands)

Schonenberg, H.; Sidorova, N.; Aalst, van der W.M.P.; Hee, van K.M.; Pnueli, A.; Virbitskaite, I.; Voronkov, A.

2010-01-01

Stochastic Petri Nets are a useful and well-known tool for performance analysis. However, an implicit assumption in the different types of Stochastic Petri Nets is the Markov property. It is assumed that a choice in the Petri net only depends on the current state and not on earlier choices. For many

Stochastic ferromagnetism analysis and numerics

CERN Document Server

Brzezniak, Zdzislaw; Neklyudov, Mikhail; Prohl, Andreas

2013-01-01

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

Modelling Cow Behaviour Using Stochastic Automata

DEFF Research Database (Denmark)

Jónsson, Ragnar Ingi

This report covers an initial study on the modelling of cow behaviour using stochastic automata with the aim of detecting lameness. Lameness in cows is a serious problem that needs to be dealt with because it results in less profitable production units and in reduced quality of life...... for the affected livestock. By featuring training data consisting of measurements of cow activity, three different models are obtained, namely an autonomous stochastic automaton, a stochastic automaton with coinciding state and output and an autonomous stochastic automaton with coinciding state and output, all...... of which describe the cows' activity in the two regarded behavioural scenarios, non-lame and lame. Using the experimental measurement data the different behavioural relations for the two regarded behavioural scenarios are assessed. The three models comprise activity within last hour, activity within last...

Rainfall Stochastic models

Science.gov (United States)

Campo, M. A.; Lopez, J. J.; Rebole, J. P.

2012-04-01

This work was carried out in north of Spain. San Sebastian A meteorological station, where there are available precipitation records every ten minutes was selected. Precipitation data covers from October of 1927 to September of 1997. Pulse models describe the temporal process of rainfall as a succession of rainy cells, main storm, whose origins are distributed in time according to a Poisson process and a secondary process that generates a random number of cells of rain within each storm. Among different pulse models, the Bartlett-Lewis was used. On the other hand, alternative renewal processes and Markov chains describe the way in which the process will evolve in the future depending only on the current state. Therefore they are nor dependant on past events. Two basic processes are considered when describing the occurrence of rain: the alternation of wet and dry periods and temporal distribution of rainfall in each rain event, which determines the rainwater collected in each of the intervals that make up the rain. This allows the introduction of alternative renewal processes and Markov chains of three states, where interstorm time is given by either of the two dry states, short or long. Thus, the stochastic model of Markov chains tries to reproduce the basis of pulse models: the succession of storms, each one composed for a series of rain, separated by a short interval of time without theoretical complexity of these. In a first step, we analyzed all variables involved in the sequential process of the rain: rain event duration, event duration of non-rain, average rainfall intensity in rain events, and finally, temporal distribution of rainfall within the rain event. Additionally, for pulse Bartlett-Lewis model calibration, main descriptive statistics were calculated for each month, considering the process of seasonal rainfall in each month. In a second step, both models were calibrated. Finally, synthetic series were simulated with calibration parameters; series

Stochastic processes dominate during boreal bryophyte community assembly.

Science.gov (United States)

Fenton, Nicole J; Bergeron, Yves

2013-09-01

Why are plant species found in certain locations and not in others? The study of community assembly rules has attempted to answer this question, and many studies articulate the historic dichotomy of deterministic (predictable niches) vs. stochastic (random or semi-random processes). The study of successional sequences to determine whether they converge, as would be expected by deterministic theory, or diverge, as stochastic theory would suggest, has been one method used to investigate this question. In this article we ask the question: Do similar boreal bryophyte communities develop in the similar habitat created by convergent succession after fires of different severities? Or do the stochastic processes generated by fires of different severity lead to different communities? Specifically we predict that deterministic structure will be more important for large forest-floor species than stochastic processes, and that the inverse will be true for small bryophyte species. We used multivariate regression trees and model selection to determine the relative weight of structure (forest structure, substrates, soil structure) and processes (fire severity) for two groups of bryophyte species sampled in 12 sites (seven high-severity and five low-severity fires). Contrary to our first hypothesis, processes were as important for large forest-floor bryophytes as for small pocket species. Fire severity, its interaction with the quality of available habitat, and its impact on the creation of biological legacies played dominant roles in determining community structure. In this study, sites with nearly identical forest structure, generated via convergent succession after high- and low-severity fire, were compared to see whether these sites supported similar bryophyte communities. While similar to some degree, both the large forest-floor species and the pocket species differed after high-severity fire compared to low-severity fire. This result suggests that the "how," or process of

Explicit calibration and simulation of stochastic fields by low-order ARMA processes

DEFF Research Database (Denmark)

Krenk, Steen

2011-01-01

A simple framework for autoregressive simulation of stochastic fields is presented. The autoregressive format leads to a simple exponential correlation structure in the time-dimension. In the case of scalar processes a more detailed correlation structure can be obtained by adding memory...... to the process via an extension to autoregressive moving average (ARMA) processes. The ARMA format incorporates a more detailed correlation structure by including previous values of the simulated process. Alternatively, a more detailed correlation structure can be obtained by including additional 'state......-space' variables in the simulation. For a scalar process this would imply an increase of the dimension of the process to be simulated. In the case of a stochastic field the correlation in the time-dimension is represented, although indirectly, in the simultaneous spatial correlation. The model with the shortest...

Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves

DEFF Research Database (Denmark)

Eldeberky, Y.; Madsen, Per A.

1999-01-01

and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...

Sliding mode control-based linear functional observers for discrete-time stochastic systems

Science.gov (United States)

Singh, Satnesh; Janardhanan, Sivaramakrishnan

2017-11-01

Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method.

Exact Algorithms for Solving Stochastic Games

DEFF Research Database (Denmark)

Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels

2012-01-01

Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....

Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity

International Nuclear Information System (INIS)

Lee, Kok Foong; Patterson, Robert I.A.; Wagner, Wolfgang; Kraft, Markus

2015-01-01

Graphical abstract: -- Highlights: •Problems concerning multi-compartment population balance equations are studied. •A class of fragmentation weight transfer functions is presented. •Three stochastic weighted algorithms are compared against the direct simulation algorithm. •The numerical errors of the stochastic solutions are assessed as a function of fragmentation rate. •The algorithms are applied to a multi-dimensional granulation model. -- Abstract: This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. The weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.

Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity

Energy Technology Data Exchange (ETDEWEB)

Lee, Kok Foong [Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA (United Kingdom); Patterson, Robert I.A.; Wagner, Wolfgang [Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin (Germany); Kraft, Markus, E-mail: mk306@cam.ac.uk [Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA (United Kingdom); School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, Singapore, 637459 (Singapore)

2015-12-15

Graphical abstract: -- Highlights: •Problems concerning multi-compartment population balance equations are studied. •A class of fragmentation weight transfer functions is presented. •Three stochastic weighted algorithms are compared against the direct simulation algorithm. •The numerical errors of the stochastic solutions are assessed as a function of fragmentation rate. •The algorithms are applied to a multi-dimensional granulation model. -- Abstract: This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. The weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.

Statistical Methods for Stochastic Differential Equations

CERN Document Server

Kessler, Mathieu; Sorensen, Michael

2012-01-01

The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a sp

Stochastic quantization of general relativity

International Nuclear Information System (INIS)

Rumpf, H.

1986-01-01

Following an elementary exposition of the basic mathematical concepts used in the theory of stochastic relaxation processes the stochastic quantization method of Parisi and Wu is briefly reviewed. The method is applied to Einstein's theory of gravitation using a formalism that is manifestly covariant with respect to field redefinitions. This requires the adoption of Ito's calculus and the introduction of a metric in field configuration space, for which there is a unique candidate. Due to the indefiniteness of the Euclidean Einstein-Hilbert action stochastic quantization is generalized to the pseudo-Riemannian case. It is formally shown to imply the DeWitt path integral measure. Finally a new type of perturbation theory is developed. (Author)

Stochastic estimation of electricity consumption

International Nuclear Information System (INIS)

Kapetanovic, I.; Konjic, T.; Zahirovic, Z.

1999-01-01

Electricity consumption forecasting represents a part of the stable functioning of the power system. It is very important because of rationality and increase of control process efficiency and development planning of all aspects of society. On a scientific basis, forecasting is a possible way to solve problems. Among different models that have been used in the area of forecasting, the stochastic aspect of forecasting as a part of quantitative models takes a very important place in applications. ARIMA models and Kalman filter as stochastic estimators have been treated together for electricity consumption forecasting. Therefore, the main aim of this paper is to present the stochastic forecasting aspect using short time series. (author)

Stochastic dynamics and irreversibility

CERN Document Server

Tomé, Tânia

2015-01-01

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

Integrated capacity and inventory management with capacity acquisition lead times

NARCIS (Netherlands)

Mincsovics, G.Z.; Tan, T.; Alp, O.

2009-01-01

We model a make-to-stock production system that utilizes permanent and contingent capacity to meet non-stationary stochastic demand, where a constant lead time is associated with the acquisition of contingent capacity. We determine the structure of the optimal solution concerning both the

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

International Nuclear Information System (INIS)

Volchenkov, D.

2009-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2009-03-15

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

Automated Flight Routing Using Stochastic Dynamic Programming

Science.gov (United States)

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

2010-01-01

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

Transport properties of stochastic Lorentz models

NARCIS (Netherlands)

Beijeren, H. van

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

Stochastic gene expression in Arabidopsis thaliana.

Science.gov (United States)

Araújo, Ilka Schultheiß; Pietsch, Jessica Magdalena; Keizer, Emma Mathilde; Greese, Bettina; Balkunde, Rachappa; Fleck, Christian; Hülskamp, Martin

2017-12-14

Although plant development is highly reproducible, some stochasticity exists. This developmental stochasticity may be caused by noisy gene expression. Here we analyze the fluctuation of protein expression in Arabidopsis thaliana. Using the photoconvertible KikGR marker, we show that the protein expressions of individual cells fluctuate over time. A dual reporter system was used to study extrinsic and intrinsic noise of marker gene expression. We report that extrinsic noise is higher than intrinsic noise and that extrinsic noise in stomata is clearly lower in comparison to several other tissues/cell types. Finally, we show that cells are coupled with respect to stochastic protein expression in young leaves, hypocotyls and roots but not in mature leaves. Our data indicate that stochasticity of gene expression can vary between tissues/cell types and that it can be coupled in a non-cell-autonomous manner.

Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise.

KAUST Repository

Bressloff, Paul C

2011-05-03

We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen so that deterministic Wilson-Cowan rate equations are recovered in the mean-field limit. We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source. We illustrate our analysis by considering one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I) subpopulations. We show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of the population oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. Finally, we show how a similar analysis can be carried out for another simple population model that exhibits limit cycle oscillations in the deterministic limit, namely, a recurrent excitatory network with synaptic depression; inclusion of synaptic depression into the neural master equation now generates a stochastic hybrid system.

Stochastic deformation of a thermodynamic symplectic structure

OpenAIRE

Kazinski, P. O.

2008-01-01

A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transform...

Stochastic differential equations and diffusion processes

CERN Document Server

Ikeda, N

1989-01-01

Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sectio

Modeling and analysis of stochastic systems

CERN Document Server

Kulkarni, Vidyadhar G

2011-01-01

Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edi

Stochastic resonance: noise-enhanced order

International Nuclear Information System (INIS)

Anishchenko, Vadim S; Neiman, Arkady B; Moss, F; Shimansky-Geier, L

1999-01-01

Stochastic resonance (SR) provides a glaring example of a noise-induced transition in a nonlinear system driven by an information signal and noise simultaneously. In the regime of SR some characteristics of the information signal (amplification factor, signal-to-noise ratio, the degrees of coherence and of order, etc.) at the output of the system are significantly improved at a certain optimal noise level. SR is realized only in nonlinear systems for which a noise-intensity-controlled characteristic time becomes available. In the present review the physical mechanism and methods of theoretical description of SR are briefly discussed. SR features determined by the structure of the information signal, noise statistics and properties of particular systems with SR are studied. A nontrivial phenomenon of stochastic synchronization defined as locking of the instantaneous phase and switching frequency of a bistable system by external periodic force is analyzed in detail. Stochastic synchronization is explored in single and coupled bistable oscillators, including ensembles. The effects of SR and stochastic synchronization of ensembles of stochastic resonators are studied both with and without coupling between the elements. SR is considered in dynamical and nondynamical (threshold) systems. The SR effect is analyzed from the viewpoint of information and entropy characteristics of the signal, which determine the degree of order or self-organization in the system. Applications of the SR concept to explaining the results of a series of biological experiments are discussed. (reviews of topical problems)

Stochastic resonance: noise-enhanced order

Energy Technology Data Exchange (ETDEWEB)

Anishchenko, Vadim S; Neiman, Arkady B [N.G. Chernyshevskii Saratov State University, Saratov (Russian Federation); Moss, F [Department of Physics and Astronomy, University of Missouri at St. Louis (United States); Shimansky-Geier, L [Humboldt University at Berlin (Germany)

1999-01-31

Stochastic resonance (SR) provides a glaring example of a noise-induced transition in a nonlinear system driven by an information signal and noise simultaneously. In the regime of SR some characteristics of the information signal (amplification factor, signal-to-noise ratio, the degrees of coherence and of order, etc.) at the output of the system are significantly improved at a certain optimal noise level. SR is realized only in nonlinear systems for which a noise-intensity-controlled characteristic time becomes available. In the present review the physical mechanism and methods of theoretical description of SR are briefly discussed. SR features determined by the structure of the information signal, noise statistics and properties of particular systems with SR are studied. A nontrivial phenomenon of stochastic synchronization defined as locking of the instantaneous phase and switching frequency of a bistable system by external periodic force is analyzed in detail. Stochastic synchronization is explored in single and coupled bistable oscillators, including ensembles. The effects of SR and stochastic synchronization of ensembles of stochastic resonators are studied both with and without coupling between the elements. SR is considered in dynamical and nondynamical (threshold) systems. The SR effect is analyzed from the viewpoint of information and entropy characteristics of the signal, which determine the degree of order or self-organization in the system. Applications of the SR concept to explaining the results of a series of biological experiments are discussed. (reviews of topical problems)

Stochastic Community Assembly: Does It Matter in Microbial Ecology?

Science.gov (United States)

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.

Stochastic processes

CERN Document Server

Borodin, Andrei N

2017-01-01

This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.

Stochastic chaos in a Duffing oscillator and its control

International Nuclear Information System (INIS)

Wu Cunli; Lei Youming; Fang Tong

2006-01-01

Stochastic chaos discussed here means a kind of chaotic responses in a Duffing oscillator with bounded random parameters under harmonic excitations. A system with random parameters is usually called a stochastic system. The modifier 'stochastic' here implies dependent on some random parameter. As the system itself is stochastic, so is the response, even under harmonic excitations alone. In this paper stochastic chaos and its control are verified by the top Lyapunov exponent of the system. A non-feedback control strategy is adopted here by adding an adjustable noisy phase to the harmonic excitation, so that the control can be realized by adjusting the noise level. It is found that by this control strategy stochastic chaos can be tamed down to the small neighborhood of a periodic trajectory or an equilibrium state. In the analysis the stochastic Duffing oscillator is first transformed into an equivalent deterministic nonlinear system by the Gegenbauer polynomial approximation, so that the problem of controlling stochastic chaos can be reduced into the problem of controlling deterministic chaos in the equivalent system. Then the top Lyapunov exponent of the equivalent system is obtained by Wolf's method to examine the chaotic behavior of the response. Numerical simulations show that the random phase control strategy is an effective way to control stochastic chaos

Stochastic stability and bifurcation in a macroeconomic model

International Nuclear Information System (INIS)

Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei

2007-01-01

On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis

Modeling delay in genetic networks: from delay birth-death processes to delay stochastic differential equations.

Science.gov (United States)

Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Bennett, Matthew R; Josić, Krešimir; Ott, William

2014-05-28

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.

Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

Energy Technology Data Exchange (ETDEWEB)

Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William [Department of Mathematics, University of Houston, Houston, Texas 77004 (United States); Bennett, Matthew R. [Department of Biochemistry and Cell Biology, Rice University, Houston, Texas 77204, USA and Institute of Biosciences and Bioengineering, Rice University, Houston, Texas 77005 (United States); Josić, Krešimir [Department of Mathematics, University of Houston, Houston, Texas 77004 (United States); Department of Biology and Biochemistry, University of Houston, Houston, Texas 77204 (United States)

2014-05-28

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.

Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

International Nuclear Information System (INIS)

Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William; Bennett, Matthew R.; Josić, Krešimir

2014-01-01

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay

Stochasticity Modeling in Memristors

KAUST Repository

Naous, Rawan

2015-10-26

Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.

Stochasticity Modeling in Memristors

KAUST Repository

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

2015-01-01

Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.

Stochasticity and transport in Hamiltonian systems

International Nuclear Information System (INIS)

MacKay, R.S.; Meiss, J.D.; Percival, I.C.

1983-08-01

The theory of transport in nonlinear dynamics is developed in terms of leaky barriers which remain when invariant tori are destroyed. We describe the organization of stochastic motion by these barriers and give an explanation of long-time correlations in the stochastic regime

Developing a stochastic parameterization to incorporate plant trait variability into ecohydrologic modeling

Science.gov (United States)

Liu, S.; Ng, G. H. C.

2017-12-01

The global plant database has revealed that plant traits can vary more within a plant functional type (PFT) than among different PFTs, indicating that the current paradigm in ecohydrogical models of specifying fixed parameters based solely on plant functional type (PFT) could potentially bias simulations. Although some recent modeling studies have attempted to incorporate this observed plant trait variability, many failed to consider uncertainties due to sparse global observation, or they omitted spatial and/or temporal variability in the traits. Here we present a stochastic parameterization for prognostic vegetation simulations that are stochastic in time and space in order to represent plant trait plasticity - the process by which trait differences arise. We have developed the new PFT parameterization within the Community Land Model 4.5 (CLM 4.5) and tested the method for a desert shrubland watershed in the Mojave Desert, where fixed parameterizations cannot represent acclimation to desert conditions. Spatiotemporally correlated plant trait parameters were first generated based on TRY statistics and were then used to implement ensemble runs for the study area. The new PFT parameterization was then further conditioned on field measurements of soil moisture and remotely sensed observations of leaf-area-index to constrain uncertainties in the sparse global database. Our preliminary results show that incorporating data-conditioned, variable PFT parameterizations strongly affects simulated soil moisture and water fluxes, compared with default simulations. The results also provide new insights about correlations among plant trait parameters and between traits and environmental conditions in the desert shrubland watershed. Our proposed stochastic PFT parameterization method for ecohydrological models has great potential in advancing our understanding of how terrestrial ecosystems are predicted to adapt to variable environmental conditions.

Stochastic quantization

International Nuclear Information System (INIS)

Klauder, J.R.

1983-01-01

The author provides an introductory survey to stochastic quantization in which he outlines this new approach for scalar fields, gauge fields, fermion fields, and condensed matter problems such as electrons in solids and the statistical mechanics of quantum spins. (Auth.)

Long-time correlations in the stochastic regime

International Nuclear Information System (INIS)

Karney, C.F.F.

1982-11-01

The phase space for Hamiltonians of two degrees of freedom is usually divided into stochastic and integrable components. Even when well into the stochastic regime, integrable orbits may surround small stable regions or islands. The effect of these islands on the correlation function for the stochastic trajectories is examined. Depending on the value of the parameter describing the rotation number for the elliptic fixed point at the center of the island, the long-time correlation function may decay as t -5 or exponentially, but more commonly it decays much more slowly (roughly as t -1 ). As a consequence these small islands may have a profound effect on the properties such as the diffusion coefficient, of the stochastic orbits

Stochastic development regression using method of moments

DEFF Research Database (Denmark)

Kühnel, Line; Sommer, Stefan Horst

2017-01-01

This paper considers the estimation problem arising when inferring parameters in the stochastic development regression model for manifold valued non-linear data. Stochastic development regression captures the relation between manifold-valued response and Euclidean covariate variables using...... the stochastic development construction. It is thereby able to incorporate several covariate variables and random effects. The model is intrinsically defined using the connection of the manifold, and the use of stochastic development avoids linearizing the geometry. We propose to infer parameters using...... the Method of Moments procedure that matches known constraints on moments of the observations conditional on the latent variables. The performance of the model is investigated in a simulation example using data on finite dimensional landmark manifolds....

Introduction to stochastic analysis integrals and differential equations

CERN Document Server

Mackevicius, Vigirdas

2013-01-01

This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion pro

Memristor-based neural networks: Synaptic versus neuronal stochasticity

KAUST Repository

Naous, Rawan

2016-11-02

In neuromorphic circuits, stochasticity in the cortex can be mapped into the synaptic or neuronal components. The hardware emulation of these stochastic neural networks are currently being extensively studied using resistive memories or memristors. The ionic process involved in the underlying switching behavior of the memristive elements is considered as the main source of stochasticity of its operation. Building on its inherent variability, the memristor is incorporated into abstract models of stochastic neurons and synapses. Two approaches of stochastic neural networks are investigated. Aside from the size and area perspective, the impact on the system performance, in terms of accuracy, recognition rates, and learning, among these two approaches and where the memristor would fall into place are the main comparison points to be considered.

Estimation of local concentration from measurements of stochastic adsorption dynamics using carbon nanotube-based sensors

International Nuclear Information System (INIS)

Jang, Hong; Lee, Jay H.; Braatz, Richard D.

2016-01-01

This paper proposes a maximum likelihood estimation (MLE) method for estimating time varying local concentration of the target molecule proximate to the sensor from the time profile of monomolecular adsorption and desorption on the surface of the sensor at nanoscale. Recently, several carbon nanotube sensors have been developed that can selectively detect target molecules at a trace concentration level. These sensors use light intensity changes mediated by adsorption or desorption phenomena on their surfaces. The molecular events occurring at trace concentration levels are inherently stochastic, posing a challenge for optimal estimation. The stochastic behavior is modeled by the chemical master equation (CME), composed of a set of ordinary differential equations describing the time evolution of probabilities for the possible adsorption states. Given the significant stochastic nature of the underlying phenomena, rigorous stochastic estimation based on the CME should lead to an improved accuracy over than deterministic estimation formulated based on the continuum model. Motivated by this expectation, we formulate the MLE based on an analytical solution of the relevant CME, both for the constant and the time-varying local concentrations, with the objective of estimating the analyte concentration field in real time from the adsorption readings of the sensor array. The performances of the MLE and the deterministic least squares are compared using data generated by kinetic Monte Carlo (KMC) simulations of the stochastic process. Some future challenges are described for estimating and controlling the concentration field in a distributed domain using the sensor technology.

Time-ordered product expansions for computational stochastic system biology

International Nuclear Information System (INIS)

Mjolsness, Eric

2013-01-01

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie’s stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems. (paper)

American option pricing with stochastic volatility processes

Directory of Open Access Journals (Sweden)

Ping LI

2017-12-01

Full Text Available In order to solve the problem of option pricing more perfectly, the option pricing problem with Heston stochastic volatility model is considered. The optimal implementation boundary of American option and the conditions for its early execution are analyzed and discussed. In view of the fact that there is no analytical American option pricing formula, through the space discretization parameters, the stochastic partial differential equation satisfied by American options with Heston stochastic volatility is transformed into the corresponding differential equations, and then using high order compact finite difference method, numerical solutions are obtained for the option price. The numerical experiments are carried out to verify the theoretical results and simulation. The two kinds of optimal exercise boundaries under the conditions of the constant volatility and the stochastic volatility are compared, and the results show that the optimal exercise boundary also has stochastic volatility. Under the setting of parameters, the behavior and the nature of volatility are analyzed, the volatility curve is simulated, the calculation results of high order compact difference method are compared, and the numerical option solution is obtained, so that the method is verified. The research result provides reference for solving the problems of option pricing under stochastic volatility such as multiple underlying asset option pricing and barrier option pricing.

Foundations of stochastic analysis

CERN Document Server

Rao, M M; Lukacs, E

1981-01-01

Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and mea

Spatial stochasticity and non-continuum effects in gas flows

Energy Technology Data Exchange (ETDEWEB)

Dadzie, S. Kokou, E-mail: k.dadzie@glyndwr.ac.uk [Mechanical and Aeronautical Engineering, Glyndwr University, Mold Road, Wrexham LL11 2AW (United Kingdom); Reese, Jason M., E-mail: jason.reese@strath.ac.uk [Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ (United Kingdom)

2012-02-06

We investigate the relationship between spatial stochasticity and non-continuum effects in gas flows. A kinetic model for a dilute gas is developed using strictly a stochastic molecular model reasoning, without primarily referring to either the Liouville or the Boltzmann equations for dilute gases. The kinetic equation, a stochastic version of the well-known deterministic Boltzmann equation for dilute gas, is then associated with a set of macroscopic equations for the case of a monatomic gas. Tests based on a heat conduction configuration and sound wave dispersion show that spatial stochasticity can explain some non-continuum effects seen in gases. -- Highlights: ► We investigate effects of molecular spatial stochasticity in non-continuum regime. ► Present a simplify spatial stochastic kinetic equation. ► Present a spatial stochastic macroscopic flow equations. ► Show effects of the new model on sound wave dispersion prediction. ► Show effects of the new approach in density profiles in a heat conduction.

Universality in stochastic exponential growth.

Science.gov (United States)

Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

2014-07-11

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Double diffusivity model under stochastic forcing

Science.gov (United States)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into

High-speed Stochastic Fatigue Testing

DEFF Research Database (Denmark)

Brincker, Rune; Sørensen, John Dalsgaard

1990-01-01

Good stochastic fatigue tests are difficult to perform. One of the major reasons is that ordinary servohydraulic loading systems realize the prescribed load history accurately at very low testing speeds only. If the speeds used for constant amplitude testing are applied to stochastic fatigue...

Stochastic analysis of complex reaction networks using binomial moment equations.

Science.gov (United States)

Barzel, Baruch; Biham, Ofer

2012-09-01

The stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species. Direct integration of the master equation is thus infeasible and is most often replaced by Monte Carlo simulations. While Monte Carlo simulations are a highly effective tool, equation-based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network. Here, we present a highly efficient equation-based method for the analysis of stochastic reaction networks. The method is based on the recently introduced binomial moment equations [Barzel and Biham, Phys. Rev. Lett. 106, 150602 (2011)]. The binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species. They capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure. This leads to a simple and transparent form of the equations, and allows a highly efficient and surprisingly simple truncation scheme. Unlike ordinary moment equations, in which the inclusion of high order moments is prohibitively complicated, the binomial moment equations can be easily constructed up to any desired order. The result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions. The number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial (and often quadratic) dependence on the number of reactive species in the binomial moment equations. The aim of this paper is twofold: to present a complete derivation of the binomial moment equations; to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role.

Full particle orbit effects in regular and stochastic magnetic fields

Energy Technology Data Exchange (ETDEWEB)

Ogawa, Shun, E-mail: shun.ogawa@cpt.univ-mrs.fr [Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille (France); CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex (France); Cambon, Benjamin; Leoncini, Xavier; Vittot, Michel [Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille (France); Castillo-Negrete, Diego del [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6169 (United States); Dif-Pradalier, Guilhem; Garbet, Xavier [CEA, IRFM, F-13108 St. Paul-lez-Durance Cedex (France)

2016-07-15

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the

Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry

DEFF Research Database (Denmark)

Sommer, Stefan Horst; Svane, Anne Marie

2017-01-01

distributions. We discuss a factorization of the frame bundle projection map through this bundle, the natural sub-Riemannian structure of the frame bundle, the effect of holonomy, and the existence of subbundles where the Hormander condition is satisfied such that the Brownian motions have smooth transition......We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed...... in the frame bundle lead to a family of probability distributions on the manifold. We explain how data mean and covariance can be interpreted as points in the frame bundle or, more precisely, in the bundle of symmetric positive definite 2-tensors analogously to the parameters describing Euclidean normal...

STOCHASTIC GRADIENT METHODS FOR UNCONSTRAINED OPTIMIZATION

Directory of Open Access Journals (Sweden)

Nataša Krejić

2014-12-01

Full Text Available This papers presents an overview of gradient based methods for minimization of noisy functions. It is assumed that the objective functions is either given with error terms of stochastic nature or given as the mathematical expectation. Such problems arise in the context of simulation based optimization. The focus of this presentation is on the gradient based Stochastic Approximation and Sample Average Approximation methods. The concept of stochastic gradient approximation of the true gradient can be successfully extended to deterministic problems. Methods of this kind are presented for the data fitting and machine learning problems.

SATA II - Stochastic Algebraic Topology and Applications

Science.gov (United States)

2017-01-30

AFRL-AFOSR-UK-TR-2017-0018 SATA II - Stochastic Algebraic Topology and Applications 150032 Robert Adler TECHNION ISRAEL INSTITUTE OF TECHNOLOGY Final...REPORT TYPE Final 3. DATES COVERED (From - To) 15 Dec 2014 to 14 Dec 2016 4. TITLE AND SUBTITLE SATA II - Stochastic Algebraic Topology and Applications... Topology and Applications Continuation of, and associated with SATA: Stochastic Algebraic Topology and Applications FA8655-11-1-3039, 09/1/2011–08/31/2014

Stochastic growth of localized plasma waves

International Nuclear Information System (INIS)

Robinson, P.A.; Cairns, Iver H.

2001-01-01

Localized bursty plasma waves are detected by spacecraft in many space plasmas. The large spatiotemporal scales involved imply that beam and other instabilities relax to marginal stability and that mean wave energies are low. Stochastic wave growth occurs when ambient fluctuations perturb the system, causing fluctuations about marginal stability. This yields regions where growth is enhanced and others where damping is increased; bursts are associated with enhanced growth and can occur even when the mean growth rate is negative. In stochastic growth, energy loss from the source is suppressed relative to secular growth, preserving it far longer than otherwise possible. Linear stochastic growth can operate at wave levels below thresholds of nonlinear wave-clumping mechanisms such as strong-turbulence modulational instability and is not subject to their coherence and wavelength limits. These mechanisms can be distinguished by statistics of the fields, whose strengths are lognormally distributed if stochastically growing and power-law distributed in strong turbulence. Recent applications of stochastic growth theory (SGT) are described, involving bursty plasma waves and unstable particle distributions in type III solar radio sources, the Earth's foreshock, magnetosheath, and polar cap regions. It is shown that when combined with wave-wave processes, SGT also accounts for associated radio emissions

Memristors Empower Spiking Neurons With Stochasticity

KAUST Repository

Al-Shedivat, Maruan

2015-06-01

Recent theoretical studies have shown that probabilistic spiking can be interpreted as learning and inference in cortical microcircuits. This interpretation creates new opportunities for building neuromorphic systems driven by probabilistic learning algorithms. However, such systems must have two crucial features: 1) the neurons should follow a specific behavioral model, and 2) stochastic spiking should be implemented efficiently for it to be scalable. This paper proposes a memristor-based stochastically spiking neuron that fulfills these requirements. First, the analytical model of the memristor is enhanced so it can capture the behavioral stochasticity consistent with experimentally observed phenomena. The switching behavior of the memristor model is demonstrated to be akin to the firing of the stochastic spike response neuron model, the primary building block for probabilistic algorithms in spiking neural networks. Furthermore, the paper proposes a neural soma circuit that utilizes the intrinsic nondeterminism of memristive switching for efficient spike generation. The simulations and analysis of the behavior of a single stochastic neuron and a winner-take-all network built of such neurons and trained on handwritten digits confirm that the circuit can be used for building probabilistic sampling and pattern adaptation machinery in spiking networks. The findings constitute an important step towards scalable and efficient probabilistic neuromorphic platforms. © 2011 IEEE.

Stochasticity in materials structure, properties, and processing—A review

Science.gov (United States)

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.

Relevance of control theory to design and maintenance problems in time-variant reliability: The case of stochastic viability

International Nuclear Information System (INIS)

Rougé, Charles; Mathias, Jean-Denis; Deffuant, Guillaume

2014-01-01

The goal of this paper is twofold: (1) to show that time-variant reliability and a branch of control theory called stochastic viability address similar problems with different points of view, and (2) to demonstrate the relevance of concepts and methods from stochastic viability in reliability problems. On the one hand, reliability aims at evaluating the probability of failure of a system subjected to uncertainty and stochasticity. On the other hand, viability aims at maintaining a controlled dynamical system within a survival set. When the dynamical system is stochastic, this work shows that a viability problem belongs to a specific class of design and maintenance problems in time-variant reliability. Dynamic programming, which is used for solving Markovian stochastic viability problems, then yields the set of design states for which there exists a maintenance strategy which guarantees reliability with a confidence level β for a given period of time T. Besides, it leads to a straightforward computation of the date of the first outcrossing, informing on when the system is most likely to fail. We illustrate this approach with a simple example of population dynamics, including a case where load increases with time. - Highlights: • Time-variant reliability tools cannot devise complex maintenance strategies. • Stochastic viability is a control theory that computes a probability of failure. • Some design and maintenance problems are stochastic viability problems. • Used in viability, dynamic programming can find reliable maintenance actions. • Confronting reliability and control theories such as viability is promising

Theory, technology, and technique of stochastic cooling

International Nuclear Information System (INIS)

Marriner, J.

1993-10-01

The theory and technological implementation of stochastic cooling is described. Theoretical and technological limitations are discussed. Data from existing stochastic cooling systems are shown to illustrate some useful techniques

Stochasticity induced by coherent wavepackets

International Nuclear Information System (INIS)

Fuchs, V.; Krapchev, V.; Ram, A.; Bers, A.

1983-02-01

We consider the momentum transfer and diffusion of electrons periodically interacting with a coherent longitudinal wavepacket. Such a problem arises, for example, in lower-hybrid current drive. We establish the stochastic threshold, the stochastic region δv/sub stoch/ in velocity space, the associated momentum transfer j, and the diffusion coefficient D. We concentrate principally on the weak-field regime, tau/sub autocorrelation/ < tau/sub bounce/

Stochastic efficiency: five case studies

International Nuclear Information System (INIS)

Proesmans, Karel; Broeck, Christian Van den

2015-01-01

Stochastic efficiency is evaluated in five case studies: driven Brownian motion, effusion with a thermo-chemical and thermo-velocity gradient, a quantum dot and a model for information to work conversion. The salient features of stochastic efficiency, including the maximum of the large deviation function at the reversible efficiency, are reproduced. The approach to and extrapolation into the asymptotic time regime are documented. (paper)

Stochastic optimization: beyond mathematical programming

CERN Multimedia

CERN. Geneva

2015-01-01

Stochastic optimization, among which bio-inspired algorithms, is gaining momentum in areas where more classical optimization algorithms fail to deliver satisfactory results, or simply cannot be directly applied. This presentation will introduce baseline stochastic optimization algorithms, and illustrate their efficiency in different domains, from continuous non-convex problems to combinatorial optimization problem, to problems for which a non-parametric formulation can help exploring unforeseen possible solution spaces.

Stochastic quantization and gauge invariance

International Nuclear Information System (INIS)

Viana, R.L.

1987-01-01

A survey of the fundamental ideas about Parisi-Wu's Stochastic Quantization Method, with applications to Scalar, Gauge and Fermionic theories, is done. In particular, the Analytic Stochastic Regularization Scheme is used to calculate the polarization tensor for Quantum Electrodynamics with Dirac bosons or Fermions. The regularization influence is studied for both theories and an extension of this method for some supersymmetrical models is suggested. (author)

Temporal genetic structure in a poecilogonous polychaete: the interplay of developmental mode and environmental stochasticity

DEFF Research Database (Denmark)

Hansen, Benni Winding; Kesäniemi, Jenni E; Mustonen, Marina

2014-01-01

elegans, a poecilogonous polychaete with within-species variation in developmental mode. P. elegans produces either planktonic, benthic, or intermediate larvae, varying both among and within populations, providing a within-species test of the generality of a relationship between temporal genetic variation...

Stochastic Thermodynamics: A Dynamical Systems Approach

Directory of Open Access Journals (Sweden)

Tanmay Rajpurohit

2017-12-01

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

Double stochastic matrices in quantum mechanics

International Nuclear Information System (INIS)

Louck, J.D.

1997-01-01

The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Lande's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n'-space is subjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices

Stochastic space-time and quantum theory

International Nuclear Information System (INIS)