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

Geometric integrators for stochastic rigid body dynamics

KAUST Repository

Tretyakov, Mikhail

2016-01-05

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

Geometric integrators for stochastic rigid body dynamics

KAUST Repository

Tretyakov, Mikhail

2016-01-01

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

Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Maejima, M.; Sato, K.

2006-01-01

The class of distributions on R generated by convolutions of Γ-distributions and the class generated by convolutions of mixtures of exponential distributions are generalized to higher dimensions and denoted by T(Rd) and B(Rd) . From the Lévy process {Xt(μ)} on Rd with distribution μ at t=1, Υ...... divisible distributions and of self-decomposable distributions on Rd , respectively. The relations with the mapping Φ from μ to the distribution at each time of the stationary process of Ornstein-Uhlenbeck type with background driving Lévy process {Xt(μ)} are studied. Developments of these results......(μ) is defined as the distribution of the stochastic integral ∫01log(1/t)dXt(μ) . This mapping is a generalization of the mapping Υ introduced by Barndorff-Nielsen and Thorbjørnsen in one dimension. It is proved that ϒ(ID(Rd))=B(Rd) and ϒ(L(Rd))=T(Rd) , where ID(Rd) and L(Rd) are the classes of infinitely...

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...

A Fractionally Integrated Wishart Stochastic Volatility Model

NARCIS (Netherlands)

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

2013-01-01

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

Integral Representations of the Catalan Numbers and Their Applications

Directory of Open Access Journals (Sweden)

Feng Qi

2017-08-01

Full Text Available In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

Ray and wave optics of integrable and stochastic systems

International Nuclear Information System (INIS)

McDonald, S.W.; Kaufman, A.N.

1979-07-01

The generalization of WKB methods to more than one dimension is discussed in terms of the integrability or non-integrability of the geometrical optics (ray Hamiltonian) system derived in the short-wave approximation. In the two-dimensional case the ray trajectories are either regular or stochastic, and the qualitative differences between these types of motion are manifested in the characteristics of the spectra and eigenfunctions. These are examined for a model system which may be integrable or stochastic, depending on a single parameter

Stochastic integration and differential equations

CERN Document Server

Protter, Philip E

2003-01-01

It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, t...

The dynamics of stochastic processes

DEFF Research Database (Denmark)

Basse-O'Connor, Andreas

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

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...

Baikov-Lee representations of cut Feynman integrals

International Nuclear Information System (INIS)

Harley, Mark; Moriello, Francesco; Schabinger, Robert M.

2017-01-01

We develop a general framework for the evaluation of d-dimensional cut Feynman integrals based on the Baikov-Lee representation of purely-virtual Feynman integrals. We implement the generalized Cutkosky cutting rule using Cauchy’s residue theorem and identify a set of constraints which determine the integration domain. The method applies equally well to Feynman integrals with a unitarity cut in a single kinematic channel and to maximally-cut Feynman integrals. Our cut Baikov-Lee representation reproduces the expected relation between cuts and discontinuities in a given kinematic channel and furthermore makes the dependence on the kinematic variables manifest from the beginning. By combining the Baikov-Lee representation of maximally-cut Feynman integrals and the properties of periods of algebraic curves, we are able to obtain complete solution sets for the homogeneous differential equations satisfied by Feynman integrals which go beyond multiple polylogarithms. We apply our formalism to the direct evaluation of a number of interesting cut Feynman integrals.

Model selection for integrated pest management with stochasticity.

Science.gov (United States)

Akman, Olcay; Comar, Timothy D; Hrozencik, Daniel

2018-04-07

In Song and Xiang (2006), an integrated pest management model with periodically varying climatic conditions was introduced. In order to address a wider range of environmental effects, the authors here have embarked upon a series of studies resulting in a more flexible modeling approach. In Akman et al. (2013), the impact of randomly changing environmental conditions is examined by incorporating stochasticity into the birth pulse of the prey species. In Akman et al. (2014), the authors introduce a class of models via a mixture of two birth-pulse terms and determined conditions for the global and local asymptotic stability of the pest eradication solution. With this work, the authors unify the stochastic and mixture model components to create further flexibility in modeling the impacts of random environmental changes on an integrated pest management system. In particular, we first determine the conditions under which solutions of our deterministic mixture model are permanent. We then analyze the stochastic model to find the optimal value of the mixing parameter that minimizes the variance in the efficacy of the pesticide. Additionally, we perform a sensitivity analysis to show that the corresponding pesticide efficacy determined by this optimization technique is indeed robust. Through numerical simulations we show that permanence can be preserved in our stochastic model. Our study of the stochastic version of the model indicates that our results on the deterministic model provide informative conclusions about the behavior of the stochastic model. Copyright © 2017 Elsevier Ltd. All rights reserved.

Random function representation of stationary stochastic vector processes for probability density evolution analysis of wind-induced structures

Science.gov (United States)

Liu, Zhangjun; Liu, Zenghui

2018-06-01

This paper develops a hybrid approach of spectral representation and random function for simulating stationary stochastic vector processes. In the proposed approach, the high-dimensional random variables, included in the original spectral representation (OSR) formula, could be effectively reduced to only two elementary random variables by introducing the random functions that serve as random constraints. Based on this, a satisfactory simulation accuracy can be guaranteed by selecting a small representative point set of the elementary random variables. The probability information of the stochastic excitations can be fully emerged through just several hundred of sample functions generated by the proposed approach. Therefore, combined with the probability density evolution method (PDEM), it could be able to implement dynamic response analysis and reliability assessment of engineering structures. For illustrative purposes, a stochastic turbulence wind velocity field acting on a frame-shear-wall structure is simulated by constructing three types of random functions to demonstrate the accuracy and efficiency of the proposed approach. Careful and in-depth studies concerning the probability density evolution analysis of the wind-induced structure have been conducted so as to better illustrate the application prospects of the proposed approach. Numerical examples also show that the proposed approach possesses a good robustness.

Application of Stochastic Sensitivity Analysis to Integrated Force Method

Directory of Open Access Journals (Sweden)

X. F. Wei

2012-01-01

Full Text Available As a new formulation in structural analysis, Integrated Force Method has been successfully applied to many structures for civil, mechanical, and aerospace engineering due to the accurate estimate of forces in computation. Right now, it is being further extended to the probabilistic domain. For the assessment of uncertainty effect in system optimization and identification, the probabilistic sensitivity analysis of IFM was further investigated in this study. A set of stochastic sensitivity analysis formulation of Integrated Force Method was developed using the perturbation method. Numerical examples are presented to illustrate its application. Its efficiency and accuracy were also substantiated with direct Monte Carlo simulations and the reliability-based sensitivity method. The numerical algorithm was shown to be readily adaptable to the existing program since the models of stochastic finite element and stochastic design sensitivity are almost identical.

Stochastic analysis in discrete and continuous settings with normal martingales

CERN Document Server

Privault, Nicolas

2009-01-01

This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.

Path integral representations on the complex sphere

International Nuclear Information System (INIS)

Grosche, C.

2007-08-01

In this paper we discuss the path integral representations for the coordinate systems on the complex sphere S 3C . The Schroedinger equation, respectively the path integral, separates in exactly 21 orthogonal coordinate systems. We enumerate these coordinate systems and we are able to present the path integral representations explicitly in the majority of the cases. In each solution the expansion into the wave-functions is stated. Also, the kernel and the corresponding Green function can be stated in closed form in terms of the invariant distance on the sphere, respectively on the hyperboloid. (orig.)

Functional representations of integrable hierarchies

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2006-01-01

We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which 'functional representations' of particular hierarchies (such as KP, discrete KP, mKP, AKNS), i.e. formulations in terms of functional equations, are systematically and quite easily obtained. The formalism genuinely applies to hierarchies where the dependent variables live in a noncommutative (typically matrix) algebra. The obtained functional representations can be understood as 'noncommutative' analogues of 'Fay identities' for the KP hierarchy

Path integral representations on the complex sphere

Energy Technology Data Exchange (ETDEWEB)

Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2007-08-15

In this paper we discuss the path integral representations for the coordinate systems on the complex sphere S{sub 3C}. The Schroedinger equation, respectively the path integral, separates in exactly 21 orthogonal coordinate systems. We enumerate these coordinate systems and we are able to present the path integral representations explicitly in the majority of the cases. In each solution the expansion into the wave-functions is stated. Also, the kernel and the corresponding Green function can be stated in closed form in terms of the invariant distance on the sphere, respectively on the hyperboloid. (orig.)

A stochastic-programming approach to integrated asset and liability ...

African Journals Online (AJOL)

This increase in complexity has provided an impetus for the investigation into integrated asset- and liability-management frameworks that could realistically address dynamic portfolio allocation in a risk-controlled way. In this paper the authors propose a multi-stage dynamic stochastic-programming model for the integrated ...

Continuous local martingales and stochastic integration in UMD Banach spaces

NARCIS (Netherlands)

Veraar, M.C.

2007-01-01

Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator is an

Stochastic simulation of PWR vessel integrity for pressurized thermal shock conditions

International Nuclear Information System (INIS)

Jackson, P.S.; Moelling, D.S.

1984-01-01

A stochastic simulation methodology is presented for performing probabilistic analyses of Pressurized Water Reactor vessel integrity. Application of the methodology to vessel-specific integrity analyses is described in the context of Pressurized Thermal Shock (PTS) conditions. A Bayesian method is described for developing vessel-specific models of the density of undetected volumetric flaws from ultrasonic inservice inspection results. Uncertainty limits on the probabilistic results due to sampling errors are determined from the results of the stochastic simulation. An example is provided to illustrate the methodology

Use of stratigraphic models as soft information to constrain stochastic modeling of rock properties: Development of the GSLIB-Lynx integration module

International Nuclear Information System (INIS)

Cromer, M.V.; Rautman, C.A.

1995-10-01

Rock properties in volcanic units at Yucca Mountain are controlled largely by relatively deterministic geologic processes related to the emplacement, cooling, and alteration history of the tuffaceous lithologic sequence. Differences in the lithologic character of the rocks have been used to subdivide the rock sequence into stratigraphic units, and the deterministic nature of the processes responsible for the character of the different units can be used to infer the rock material properties likely to exist in unsampled regions. This report proposes a quantitative, theoretically justified method of integrating interpretive geometric models, showing the three-dimensional distribution of different stratigraphic units, with numerical stochastic simulation techniques drawn from geostatistics. This integration of soft, constraining geologic information with hard, quantitative measurements of various material properties can produce geologically reasonable, spatially correlated models of rock properties that are free from stochastic artifacts for use in subsequent physical-process modeling, such as the numerical representation of ground-water flow and radionuclide transport. Prototype modeling conducted using the GSLIB-Lynx Integration Module computer program, known as GLINTMOD, has successfully demonstrated the proposed integration technique. The method involves the selection of stratigraphic-unit-specific material-property expected values that are then used to constrain the probability function from which a material property of interest at an unsampled location is simulated

Stochastic Integration H∞ Filter for Rapid Transfer Alignment of INS.

Science.gov (United States)

Zhou, Dapeng; Guo, Lei

2017-11-18

The performance of an inertial navigation system (INS) operated on a moving base greatly depends on the accuracy of rapid transfer alignment (RTA). However, in practice, the coexistence of large initial attitude errors and uncertain observation noise statistics poses a great challenge for the estimation accuracy of misalignment angles. This study aims to develop a novel robust nonlinear filter, namely the stochastic integration H ∞ filter (SIH ∞ F) for improving both the accuracy and robustness of RTA. In this new nonlinear H ∞ filter, the stochastic spherical-radial integration rule is incorporated with the framework of the derivative-free H ∞ filter for the first time, and the resulting SIH ∞ F simultaneously attenuates the negative effect in estimations caused by significant nonlinearity and large uncertainty. Comparisons between the SIH ∞ F and previously well-known methodologies are carried out by means of numerical simulation and a van test. The results demonstrate that the newly-proposed method outperforms the cubature H ∞ filter. Moreover, the SIH ∞ F inherits the benefit of the traditional stochastic integration filter, but with more robustness in the presence of uncertainty.

Weighted -Integral Representations of -Functions in

Directory of Open Access Journals (Sweden)

Arman H. Karapetyan

2012-01-01

Full Text Available For 1-functions , given in the complex space , integral representations of the form =(−( are obtained. Here, is the orthogonal projector of the space 2{;−||||(} onto its subspace of entire functions and the integral operator appears by means of explicitly constructed kernel Φ which is investigated in detail.

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...

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

Stochastic programming problems with generalized integrated chance constraints

Czech Academy of Sciences Publication Activity Database

Branda, Martin

2012-01-01

Roč. 61, č. 8 (2012), s. 949-968 ISSN 0233-1934 R&D Projects: GA ČR GAP402/10/1610 Grant - others:SVV(CZ) 261315/2010 Institutional support: RVO:67985556 Keywords : chance constraints * integrated chance constraints * penalty functions * sample approximations * blending problem Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.707, year: 2012 http://library.utia.cas.cz/separaty/2012/E/branda-stochastic programming problems with generalized integrated.pdf

On the Riesz representation theorem and integral operators ...

African Journals Online (AJOL)

We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...

Stochastic integration in Banach spaces theory and applications

CERN Document Server

Mandrekar, Vidyadhar

2015-01-01

Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integrati...

Nonlinear filtering and smoothing an introduction to martingales, stochastic integrals and estimation

CERN Document Server

Krishnan, Venkatarama

2005-01-01

Most useful for graduate students in engineering and finance who have a basic knowledge of probability theory, this volume is designed to give a concise understanding of martingales, stochastic integrals, and estimation. It emphasizes applications. Many theorems feature heuristic proofs; others include rigorous proofs to reinforce physical understanding. Numerous end-of-chapter problems enhance the book's practical value.After introducing the basic measure-theoretic concepts of probability and stochastic processes, the text examines martingales, square integrable martingales, and stopping time

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.

Understanding as Integration of Heterogeneous Representations

Science.gov (United States)

Martínez, Sergio F.

2014-03-01

The search for understanding is a major aim of science. Traditionally, understanding has been undervalued in the philosophy of science because of its psychological underpinnings; nowadays, however, it is widely recognized that epistemology cannot be divorced from psychology as sharp as traditional epistemology required. This eliminates the main obstacle to give scientific understanding due attention in philosophy of science. My aim in this paper is to describe an account of scientific understanding as an emergent feature of our mastering of different (causal) explanatory frameworks that takes place through the mastering of scientific practices. Different practices lead to different kinds of representations. Such representations are often heterogeneous. The integration of such representations constitute understanding.

Cuts of Feynman Integrals in Baikov representation

Energy Technology Data Exchange (ETDEWEB)

Frellesvig, Hjalte; Papadopoulos, Costas G. [Institute of Nuclear and Particle Physics, NCSR ‘Demokritos’,P.O. Box 60037, Agia Paraskevi, 15310 (Greece)

2017-04-13

Based on the Baikov representation, we present a systematic approach to compute cuts of Feynman Integrals, appropriately defined in d dimensions. The information provided by these computations may be used to determine the class of functions needed to analytically express the full integrals.

Cuts of Feynman Integrals in Baikov representation

International Nuclear Information System (INIS)

Frellesvig, Hjalte; Papadopoulos, Costas G.

2017-01-01

Based on the Baikov representation, we present a systematic approach to compute cuts of Feynman Integrals, appropriately defined in d dimensions. The information provided by these computations may be used to determine the class of functions needed to analytically express the full integrals.

Stochastic methods for the fermion determinant in lattice quantum chromodynamics

Energy Technology Data Exchange (ETDEWEB)

Finkenrath, Jacob Friedrich

2015-02-17

In this thesis, algorithms in lattice quantum chromodynamics are presented by developing and using stochastic methods for fermion determinant ratios. For that an integral representation is proved which can be used also for non hermitian matrices. The stochastic estimation or the Monte Carlo integration of this integral representation introduces stochastic fluctuations which are controlled by using Domain Decomposition of the Dirac operator and introducing interpolation techniques. Determinant ratios of the lattice fermion operator, here the Wilson Dirac operator, are needed for corrections of the Boltzmann weight. These corrections have interesting applications e.g. in the mass by using mass reweighting. It will be shown that mass reweighting can be used e.g. to improve extrapolation in the light quark mass towards the chiral or physical point or to introduce an isospin breaking by splitting up the mass of the light quark. Furthermore the extraction of the light quark masses will be shown by using dynamical 2 flavor CLS ensembles. Stochastic estimation of determinant ratios can be used in Monte Carlo algorithms, e.g. in the Partial Stochastic Multi Step algorithm which can sample two mass-degenerate quarks. The idea is to propose a new configuration weighted by the pure gauge weight and including afterwards the fermion weight by using Metropolis accept-reject steps. It is shown by using an adequate interpolation with relative gauge fixing and a hierarchical filter structure that it is possible to simulate moderate lattices up to (2.1 fm){sup 4}. Furthermore the iteration of the pure gauge update can be increased which can decouple long autocorrelation times from the weighting with the fermions. Moreover a novel Hybrid Monte Carlo algorithm based on Domain Decomposition and combined with mass reweighting is presented. By using Domain Decomposition it is possible to split up the mass term in the Schur complement and the block operators. By introducing a higher mass

Coarse-graining stochastic biochemical networks: adiabaticity and fast simulations

Energy Technology Data Exchange (ETDEWEB)

Nemenman, Ilya [Los Alamos National Laboratory; Sinitsyn, Nikolai [Los Alamos National Laboratory; Hengartner, Nick [Los Alamos National Laboratory

2008-01-01

We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscoplc, non-Poissonian fluctuations of the slow ones. Our approach, which is similar to the Born-Oppenhelmer approximation in quantum mechanics, follows from the stochastic path Integral representation of the cumulant generating function of reaction events. In applications with a small number of chemIcal reactions, It produces analytical expressions for cumulants of chemical fluxes between the slow variables. This allows for a low-dimensional, Interpretable representation and can be used for coarse-grained numerical simulation schemes with a small computational complexity and yet high accuracy. As an example, we derive the coarse-grained description for a chain of biochemical reactions, and show that the coarse-grained and the microscopic simulations are in an agreement, but the coarse-gralned simulations are three orders of magnitude faster.

Efficient stochastic thermostatting of path integral molecular dynamics.

Science.gov (United States)

Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E; Manolopoulos, David E

2010-09-28

The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.

Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition

Directory of Open Access Journals (Sweden)

Malinowski Marek T.

2015-01-01

Full Text Available We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors. The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect to data of the equation is also presented. We consider equations driven by semimartingale Z and equations driven by processes A;M from decomposition of Z, where A is a process of finite variation and M is a local martingale. These equations are not equivalent. Finally, we show that the analysis of the set-valued stochastic integral equations can be extended to a case of fuzzy stochastic integral equations driven by semimartingales under Osgood type condition. To obtain our results we use the set-valued and fuzzy Maruyama type approximations and Bihari’s inequality.

Representation and integration of sociological knowledge using knowledge graphs

NARCIS (Netherlands)

Popping, R; Strijker, [No Value

1997-01-01

The representation and integration of sociological knowledge using knowledge graphs, a specific kind of semantic network, is discussed. Knowledge it systematically searched this reveals. inconsistencies, reducing superfluous research and knowledge, and showing gaps in a theory. This representation

Quantum stochastic walks on networks for decision-making.

Science.gov (United States)

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-03-31

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Quantum stochastic walks on networks for decision-making

Science.gov (United States)

Martínez-Martínez, Ismael; Sánchez-Burillo, Eduardo

2016-03-01

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Unbounded representations of symmetry groups in gauge quantum field theory. II. Integration

International Nuclear Information System (INIS)

Voelkel, A.H.

1986-01-01

Within the gauge quantum field theory of the Wightman--Garding type, the integration of representations of Lie algebras is investigated. By means of the covariance condition (substitution rules) for the basic fields, it is shown that a form skew-symmetric representation of a Lie algebra can be integrated to a form isometric and in general unbounded representation of the universal covering group of a corresponding Lie group provided the conditions (Nelson, Sternheimer, etc.), which are well known for the case of Hilbert or Banach representations, hold. If a form isometric representation leaves the subspace from which the physical Hilbert space is obtained via factorization and completion invariant, then the same is proved to be true for its differential. Conversely, a necessary and sufficient condition is derived for the transmission of the invariance of this subspace under a form skew-symmetric representation of a Lie algebra to its integral

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 ...

A unified approach to stochastic integration on the real line

DEFF Research Database (Denmark)

Basse-O'Connor, Andreas; Graversen, Svend-Erik; Pedersen, Jan

Stochastic integration on the predictable σ-field with respect to σ-finite L0-valued measures, also known as formal semimartingales, is studied. In particular, the triplet of such measures is introduced and used to characterize the set of integrable processes. Special attention is given to Lévy...... processes indexed by the real line. Surprisingly, many of the basic properties break down in this situation compared to the usual R+ case....

Integral equations for four identical particles in angular momentum representation

International Nuclear Information System (INIS)

Kharchenko, V.F.; Shadchin, S.A.

1975-01-01

In integral equations of motion for a system of four identical spinless particles with central pair interactions, transition is realized from the representation of relative Jacobi momenta to the representation of their moduli and relative angular moments. As a result, the variables associated with the rotation of the system as a whole are separated in the equations. The integral equations of motion for four particles are reduced to the form of an infinite system of three-demensional integral equations. The four-particle kinematic factors contained in integral kernels are expressed in terms of three-particle type kinematic factors. In the case of separable two-particle interaction, the equations of motion for four particles have the form of an infinite system of two-dimensional integral equations

New integral representations of the Maslov canonical operator in singular charts

Science.gov (United States)

Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Shafarevich, A. I.

2017-04-01

We construct a new integral representation of the Maslov canonical operator convenient in numerical-analytical calculations, present an algorithm implementing this representation, and consider a number of examples.

A new path-integral representation of the T-matrix in potential scattering

International Nuclear Information System (INIS)

Carron, J.; Rosenfelder, R.

2011-01-01

We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the T-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious variables as was necessary before. The resulting expression serves as a starting point for a variational approximation applied to high-energy scattering from a Gaussian potential. Good agreement with exact partial-wave calculations is found even at large scattering angles. A novel path-integral representation of the scattering length is obtained in the low-energy limit. -- Highlights: → We derive a new path-integral representation for the T-matrix in quantum scattering from a potential. → The method is based on a technique used by Barbashov and collaborators in Quantum Field Theory. → Unlike previous approaches no unphysical degrees of freedom in the path integral are needed. → The new representation is used for a variational approximation of the T-matrix at high energies. → A new expression for the scattering length at low energy is derived.

Differential form representation of stochastic electromagnetic fields

Science.gov (United States)

Haider, Michael; Russer, Johannes A.

2017-09-01

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

An Exact Line Integral Representation of the Magnetic Physical Optics Scattered Field

DEFF Research Database (Denmark)

Meincke, Peter; Breinbjerg, Olav; Jørgensen, Erik

2003-01-01

An exact line integral representation is derived for the magnetic physical optics field scattered by a perfectly electrically conducting planar plate illuminated by electric or magnetic Hertzian dipoles. The positions of source and observation points can be almost arbitrary. Numerical examples...... are presented to illustrate the exactness of the line integral representation....

Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of

Directory of Open Access Journals (Sweden)

Arman Karapetyan

2010-01-01

Full Text Available We obtain weighted integral representations for spaces of functions holomorphic in the unit ball and belonging to area-integrable weighted -classes with “anisotropic” weight function of the type ∏=1(1−|1|2−|2|2−⋯−||2, =(1,2,…,∈. The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for =2.

Optimal Integration of Intermittent Renewables: A System LCOE Stochastic Approach

Directory of Open Access Journals (Sweden)

Carlo Lucheroni

2018-03-01

Full Text Available We propose a system level approach to value the impact on costs of the integration of intermittent renewable generation in a power system, based on expected breakeven cost and breakeven cost risk. To do this, we carefully reconsider the definition of Levelized Cost of Electricity (LCOE when extended to non-dispatchable generation, by examining extra costs and gains originated by the costly management of random power injections. We are thus lead to define a ‘system LCOE’ as a system dependent LCOE that takes properly into account intermittent generation. In order to include breakeven cost risk we further extend this deterministic approach to a stochastic setting, by introducing a ‘stochastic system LCOE’. This extension allows us to discuss the optimal integration of intermittent renewables from a broad, system level point of view. This paper thus aims to provide power producers and policy makers with a new methodological scheme, still based on the LCOE but which updates this valuation technique to current energy system configurations characterized by a large share of non-dispatchable production. Quantifying and optimizing the impact of intermittent renewables integration on power system costs, risk and CO 2 emissions, the proposed methodology can be used as powerful tool of analysis for assessing environmental and energy policies.

Assessing Exhaustiveness of Stochastic Sampling for Integrative Modeling of Macromolecular Structures.

Science.gov (United States)

Viswanath, Shruthi; Chemmama, Ilan E; Cimermancic, Peter; Sali, Andrej

2017-12-05

Modeling of macromolecular structures involves structural sampling guided by a scoring function, resulting in an ensemble of good-scoring models. By necessity, the sampling is often stochastic, and must be exhaustive at a precision sufficient for accurate modeling and assessment of model uncertainty. Therefore, the very first step in analyzing the ensemble is an estimation of the highest precision at which the sampling is exhaustive. Here, we present an objective and automated method for this task. As a proxy for sampling exhaustiveness, we evaluate whether two independently and stochastically generated sets of models are sufficiently similar. The protocol includes testing 1) convergence of the model score, 2) whether model scores for the two samples were drawn from the same parent distribution, 3) whether each structural cluster includes models from each sample proportionally to its size, and 4) whether there is sufficient structural similarity between the two model samples in each cluster. The evaluation also provides the sampling precision, defined as the smallest clustering threshold that satisfies the third, most stringent test. We validate the protocol with the aid of enumerated good-scoring models for five illustrative cases of binary protein complexes. Passing the proposed four tests is necessary, but not sufficient for thorough sampling. The protocol is general in nature and can be applied to the stochastic sampling of any set of models, not just structural models. In addition, the tests can be used to stop stochastic sampling as soon as exhaustiveness at desired precision is reached, thereby improving sampling efficiency; they may also help in selecting a model representation that is sufficiently detailed to be informative, yet also sufficiently coarse for sampling to be exhaustive. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Differential form representation of stochastic electromagnetic fields

Directory of Open Access Journals (Sweden)

M. Haider

2017-09-01

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

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

Science.gov (United States)

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

2016-01-01

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

A stochastic approach for quantifying immigrant integration: the Spanish test case

Science.gov (United States)

Agliari, Elena; Barra, Adriano; Contucci, Pierluigi; Sandell, Richard; Vernia, Cecilia

2014-10-01

We apply stochastic process theory to the analysis of immigrant integration. Using a unique and detailed data set from Spain, we study the relationship between local immigrant density and two social and two economic immigration quantifiers for the period 1999-2010. As opposed to the classic time-series approach, by letting immigrant density play the role of ‘time’ and the quantifier the role of ‘space,’ it becomes possible to analyse the behavior of the quantifiers by means of continuous time random walks. Two classes of results are then obtained. First, we show that social integration quantifiers evolve following diffusion law, while the evolution of economic quantifiers exhibits ballistic dynamics. Second, we make predictions of best- and worst-case scenarios taking into account large local fluctuations. Our stochastic process approach to integration lends itself to interesting forecasting scenarios which, in the hands of policy makers, have the potential to improve political responses to integration problems. For instance, estimating the standard first-passage time and maximum-span walk reveals local differences in integration performance for different immigration scenarios. Thus, by recognizing the importance of local fluctuations around national means, this research constitutes an important tool to assess the impact of immigration phenomena on municipal budgets and to set up solid multi-ethnic plans at the municipal level as immigration pressures build.

A stochastic approach for quantifying immigrant integration: the Spanish test case

International Nuclear Information System (INIS)

Agliari, Elena; Barra, Adriano; Contucci, Pierluigi; Sandell, Richard; Vernia, Cecilia

2014-01-01

We apply stochastic process theory to the analysis of immigrant integration. Using a unique and detailed data set from Spain, we study the relationship between local immigrant density and two social and two economic immigration quantifiers for the period 1999–2010. As opposed to the classic time-series approach, by letting immigrant density play the role of ‘time’ and the quantifier the role of ‘space,’ it becomes possible to analyse the behavior of the quantifiers by means of continuous time random walks. Two classes of results are then obtained. First, we show that social integration quantifiers evolve following diffusion law, while the evolution of economic quantifiers exhibits ballistic dynamics. Second, we make predictions of best- and worst-case scenarios taking into account large local fluctuations. Our stochastic process approach to integration lends itself to interesting forecasting scenarios which, in the hands of policy makers, have the potential to improve political responses to integration problems. For instance, estimating the standard first-passage time and maximum-span walk reveals local differences in integration performance for different immigration scenarios. Thus, by recognizing the importance of local fluctuations around national means, this research constitutes an important tool to assess the impact of immigration phenomena on municipal budgets and to set up solid multi-ethnic plans at the municipal level as immigration pressures build. (paper)

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...

Approximation of itô integrals arising in stochastic time-delayed systems

NARCIS (Netherlands)

Bagchi, Arunabha

1984-01-01

Likelihood functional for stochastic linear time-delayed systems involve Itô integrals with respect to the observed data. Since the Wiener process appearing in the standard observation process model for such systems is not realizable and the physically observed process is smooth, one needs to study

Path integral methods for the dynamics of stochastic and disordered systems

DEFF Research Database (Denmark)

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

2017-01-01

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

Stochastic processes and the non-perturbative structure of the QCD vacuum

International Nuclear Information System (INIS)

Vilela Mendes, R.

1992-01-01

Based on a local Gaussian evaluation of the functional integral representation, a method is developed to obtain ground state functionals. The method is applied to the gluon sector of QCD. For the leading term in the ground state functional, stochastic techniques are used to check consistency of the quantum theory, finiteness of the mass gap and the scaling relation in the continuum limit. The functional also implies strong chromomagnetic fluctuations which constrain the propagators in the fermion sector. (orig.)

Constant Jacobian Matrix-Based Stochastic Galerkin Method for Probabilistic Load Flow

Directory of Open Access Journals (Sweden)

Yingyun Sun

2016-03-01

Full Text Available An intrusive spectral method of probabilistic load flow (PLF is proposed in the paper, which can handle the uncertainties arising from renewable energy integration. Generalized polynomial chaos (gPC expansions of dependent random variables are utilized to build a spectral stochastic representation of PLF model. Instead of solving the coupled PLF model with a traditional, cumbersome method, a modified stochastic Galerkin (SG method is proposed based on the P-Q decoupling properties of load flow in power system. By introducing two pre-calculated constant sparse Jacobian matrices, the computational burden of the SG method is significantly reduced. Two cases, IEEE 14-bus and IEEE 118-bus systems, are used to verify the computation speed and efficiency of the proposed method.

On the use of stochastic approximation Monte Carlo for Monte Carlo integration

KAUST Repository

Liang, Faming

2009-01-01

The stochastic approximation Monte Carlo (SAMC) algorithm has recently been proposed as a dynamic optimization algorithm in the literature. In this paper, we show in theory that the samples generated by SAMC can be used for Monte Carlo integration

Integrating Globality and Locality for Robust Representation Based Classification

Directory of Open Access Journals (Sweden)

Zheng Zhang

2014-01-01

Full Text Available The representation based classification method (RBCM has shown huge potential for face recognition since it first emerged. Linear regression classification (LRC method and collaborative representation classification (CRC method are two well-known RBCMs. LRC and CRC exploit training samples of each class and all the training samples to represent the testing sample, respectively, and subsequently conduct classification on the basis of the representation residual. LRC method can be viewed as a “locality representation” method because it just uses the training samples of each class to represent the testing sample and it cannot embody the effectiveness of the “globality representation.” On the contrary, it seems that CRC method cannot own the benefit of locality of the general RBCM. Thus we propose to integrate CRC and LRC to perform more robust representation based classification. The experimental results on benchmark face databases substantially demonstrate that the proposed method achieves high classification accuracy.

Stochastic forward and inverse groundwater flow and solute transport modeling

NARCIS (Netherlands)

Janssen, G.M.C.M.

2008-01-01

Keywords: calibration, inverse modeling, stochastic modeling, nonlinear biodegradation, stochastic-convective, advective-dispersive, travel time, network design, non-Gaussian distribution, multimodal distribution, representers

This thesis offers three new approaches that contribute

Stochastic displacement group and its application in physics

International Nuclear Information System (INIS)

Namsraj, Kh.; Tsehrehn, D.; Sehrdamba, L.

1978-01-01

Within the stochastic displacement the equation of the brownian motion and the Dirac and Klein-Gordon equations are obtained. It is noted that the existance of a new equation describing four states with certain energy is possible. The notion of stochastic groups and its representations with illustrations in concrete examples and applications are given. The diffusion equation is obtained on the basis of the notion of stochastic rotation

Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes

International Nuclear Information System (INIS)

Wehner, M.F.

1983-01-01

A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is show t give accurate results. 35 refs., 5 figs

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

Science.gov (United States)

Zhang, Zhihua

2014-01-01

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842

A minimax stochastic optimal semi-active control strategy for uncertain quasi-integrable Hamiltonian systems using magneto-rheological dampers

DEFF Research Database (Denmark)

Feng, Ju; Ying, Zu-Guang; Zhu, Wei-Qiu

2012-01-01

A minimax stochastic optimal semi-active control strategy for stochastically excited quasi-integrable Hamiltonian systems with parametric uncertainty by using magneto-rheological (MR) dampers is proposed. Firstly, the control problem is formulated as an n-degree-of-freedom (DOF) controlled, uncer...

Finite-Dimensional Representations for Controlled Diffusions with Delay

Energy Technology Data Exchange (ETDEWEB)

Federico, Salvatore, E-mail: salvatore.federico@unimi.it [Università di Milano, Dipartimento di Economia, Management e Metodi Quantitativi (Italy); Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr [Université Paris Diderot, Laboratoire de Probabilités et Modèles Aléatoires (France)

2015-02-15

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

Differential equations for loop integrals in Baikov representation

Science.gov (United States)

Bosma, Jorrit; Larsen, Kasper J.; Zhang, Yang

2018-05-01

We present a proof that differential equations for Feynman loop integrals can always be derived in Baikov representation without involving dimension-shift identities. We moreover show that in a large class of two- and three-loop diagrams it is possible to avoid squared propagators in the intermediate steps of setting up the differential equations.

On integral representation, relaxation and homogenization for unbounded functionals

International Nuclear Information System (INIS)

Carbone, L.; De Arcangelis, R.

1997-01-01

A theory of integral representation, relaxation and homogenization for some types of variational functionals taking extended real values and possibly being not finite also on large classes of regular functions is presented. Some applications to gradient constrained relaxation and homogenization problems are given

Integration of renewable generation uncertainties into stochastic unit commitment considering reserve and risk: A comparative study

International Nuclear Information System (INIS)

Quan, Hao; Srinivasan, Dipti; Khosravi, Abbas

2016-01-01

The uncertainties of renewable energy have brought great challenges to power system commitment, dispatches and reserve requirement. This paper presents a comparative study on integration of renewable generation uncertainties into SCUC (stochastic security-constrained unit commitment) considering reserve and risk. Renewable forecast uncertainties are captured by a list of PIs (prediction intervals). A new scenario generation method is proposed to generate scenarios from these PIs. Different system uncertainties are considered as scenarios in the stochastic SCUC problem formulation. Two comparative simulations with single (E1: wind only) and multiple sources of uncertainty (E2: load, wind, solar and generation outages) are investigated. Five deterministic and four stochastic case studies are performed. Different generation costs, reserve strategies and associated risks are compared under various scenarios. Demonstrated results indicate the overall costs of E2 is lower than E1 due to penetration of solar power and the associated risk in deterministic cases of E2 is higher than E1. It implies the superimposed effect of uncertainties during uncertainty integration. The results also demonstrate that power systems run a higher level of risk during peak load hours, and that stochastic models are more robust than deterministic ones. - Highlights: • An extensive comparative study for renewable integration is presented. • A novel scenario generation method is proposed. • Wind and solar uncertainties are represented by a list of prediction intervals. • Unit commitment and dispatch costs are discussed considering reserve and risk.

The possible social representations of astronomy by students from integrated high school

Science.gov (United States)

Barbosa, J. I. L.; Voelzke, M. R.

2017-12-01

In this paper, we present the possible Social Representations, which students of the Integrated High School of the Federal Institute of Alagoas (IFAL) have on the term inductor Astronomy, as well as identifying how they were probably elaborated. Therefore, in agreement with Moscovici (2010) is used the Theory of Social Representations.

On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm

International Nuclear Information System (INIS)

Contreras-Astorga, Alonso; Schulze-Halberg, Axel

2015-01-01

We construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential representation are obtained using this relationship. Furthermore, it is used to find normalization constants of wave functions of quantum systems that feature energy-dependent potentials. Additionally, this relationship is used to express certain integrals involving functions that are solution of Schrödinger equations through derivatives. (paper)

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

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 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...

Path integrals for inertialess classical particles under-going rapid stochastic trembling. I

International Nuclear Information System (INIS)

Bezak, V.

1978-01-01

Feynman path integrals are studied in reference to the Fokker-Planck (Smoluchowski) equation. Examples are presented including the motion of an inertialess classical charged particle between electrodes in plate and cylindrical capacitors with charges fluctuating rapidly as Gaussian white-noise stochastic processes. Another example concerns magnetodiffusion of a charged particle in an non-polarized electromagnetic beam characterized by a white-noise spectrum. (author)

FERN - a Java framework for stochastic simulation and evaluation of reaction networks.

Science.gov (United States)

Erhard, Florian; Friedel, Caroline C; Zimmer, Ralf

2008-08-29

Stochastic simulation can be used to illustrate the development of biological systems over time and the stochastic nature of these processes. Currently available programs for stochastic simulation, however, are limited in that they either a) do not provide the most efficient simulation algorithms and are difficult to extend, b) cannot be easily integrated into other applications or c) do not allow to monitor and intervene during the simulation process in an easy and intuitive way. Thus, in order to use stochastic simulation in innovative high-level modeling and analysis approaches more flexible tools are necessary. In this article, we present FERN (Framework for Evaluation of Reaction Networks), a Java framework for the efficient simulation of chemical reaction networks. FERN is subdivided into three layers for network representation, simulation and visualization of the simulation results each of which can be easily extended. It provides efficient and accurate state-of-the-art stochastic simulation algorithms for well-mixed chemical systems and a powerful observer system, which makes it possible to track and control the simulation progress on every level. To illustrate how FERN can be easily integrated into other systems biology applications, plugins to Cytoscape and CellDesigner are included. These plugins make it possible to run simulations and to observe the simulation progress in a reaction network in real-time from within the Cytoscape or CellDesigner environment. FERN addresses shortcomings of currently available stochastic simulation programs in several ways. First, it provides a broad range of efficient and accurate algorithms both for exact and approximate stochastic simulation and a simple interface for extending to new algorithms. FERN's implementations are considerably faster than the C implementations of gillespie2 or the Java implementations of ISBJava. Second, it can be used in a straightforward way both as a stand-alone program and within new

A novel integral representation for the Adler function

International Nuclear Information System (INIS)

Nesterenko, A V; Papavassiliou, J

2006-01-01

New integral representations for the Adler D-function and the R-ratio of the electron-positron annihilation into hadrons are derived in the general framework of the analytic approach to QCD. These representations capture the nonperturbative information encoded in the dispersion relation for the D-function, the effects due to the interrelation between spacelike and timelike domains, and the effects due to the nonvanishing pion mass. The latter plays a crucial role in this analysis, forcing the Adler function to vanish in the infrared limit. Within the developed approach the D-function is calculated by employing its perturbative approximation as the only additional input. The obtained result is found to be in reasonable agreement with the experimental prediction for the Adler function in the entire range of momenta 0 ≤ Q 2 < ∞

Knowledge Representation and Management, It's Time to Integrate!

Science.gov (United States)

Dhombres, F; Charlet, J

2017-08-01

Objectives: To select, present, and summarize the best papers published in 2016 in the field of Knowledge Representation and Management (KRM). Methods: A comprehensive and standardized review of the medical informatics literature was performed based on a PubMed query. Results: Among the 1,421 retrieved papers, the review process resulted in the selection of four best papers focused on the integration of heterogeneous data via the development and the alignment of terminological resources. In the first article, the authors provide a curated and standardized version of the publicly available US FDA Adverse Event Reporting System. Such a resource will improve the quality of the underlying data, and enable standardized analyses using common vocabularies. The second article describes a project developed in order to facilitate heterogeneous data integration in the i2b2 framework. The originality is to allow users integrate the data described in different terminologies and to build a new repository, with a unique model able to support the representation of the various data. The third paper is dedicated to model the association between multiple phenotypic traits described within the Human Phenotype Ontology (HPO) and the corresponding genotype in the specific context of rare diseases (rare variants). Finally, the fourth paper presents solutions to annotation-ontology mapping in genome-scale data. Of particular interest in this work is the Experimental Factor Ontology (EFO) and its generic association model, the Ontology of Biomedical AssociatioN (OBAN). Conclusion: Ontologies have started to show their efficiency to integrate medical data for various tasks in medical informatics: electronic health records data management, clinical research, and knowledge-based systems development. Georg Thieme Verlag KG Stuttgart.

Social Representations of the Integrated High School Students about Astronomy

Science.gov (United States)

Barbosa, Jose Isnaldo de Lima; Voelzke, Marcos Rincon

2017-07-01

Astronomy issues are not always adequately handled in the formal education system, as well as, their dissemination in the media is often loaded with sensationalism. However, in this context the students are forming their explanations about it. Therefore, this work has the objective of identifying the possible social representations of students from the Integrated High School on the inductor term Astronomy. It is basically a descriptive research, therefore, a quali-qualitative approach was adopted. The procedures for obtaining the data occurred in the form of a survey, and they involved 653 subjects students from the Integrated High School. The results indicate that the surveyed students have social representations of the object Astronomy, which are based on elements from the formal education space, and also disclosed in the media. In addition, they demonstrate that the students have information about Astronomy, and a value judgment in relation to this science.

Integral-functional representation of mass operator of quasiparticles interacting with polarizational phonons at T = 0 K

International Nuclear Information System (INIS)

Tkach, M.V.

2002-01-01

The integral-functional representation of mass operator of spinless quasiparticles interacting with polarizational phonons at T = 0 K is obtained for the first time. This representation is equivalent to the infinite branched integral fraction. It does not depend on the binding force and effectively takes into account the many phonon processes

On integral representation of the Clebsh-Gordan coefficients of SU(3) group

International Nuclear Information System (INIS)

Mal'tsev, V.M.

1985-01-01

The projection of arbitrary quark-gluon state on a singlet representation of SU(3) group is considered. It is given by an integral on the group. In this case the square of a Clebsch-Gordan coefficient is evaluated as the eight-fold integral over corresponding Eulerian angles

Climate SPHINX: High-resolution present-day and future climate simulations with an improved representation of small-scale variability

Science.gov (United States)

Davini, Paolo; von Hardenberg, Jost; Corti, Susanna; Subramanian, Aneesh; Weisheimer, Antje; Christensen, Hannah; Juricke, Stephan; Palmer, Tim

2016-04-01

The PRACE Climate SPHINX project investigates the sensitivity of climate simulations to model resolution and stochastic parameterization. The EC-Earth Earth-System Model is used to explore the impact of stochastic physics in 30-years climate integrations as a function of model resolution (from 80km up to 16km for the atmosphere). The experiments include more than 70 simulations in both a historical scenario (1979-2008) and a climate change projection (2039-2068), using RCP8.5 CMIP5 forcing. A total amount of 20 million core hours will be used at end of the project (March 2016) and about 150 TBytes of post-processed data will be available to the climate community. Preliminary results show a clear improvement in the representation of climate variability over the Euro-Atlantic following resolution increase. More specifically, the well-known atmospheric blocking negative bias over Europe is definitely resolved. High resolution runs also show improved fidelity in representation of tropical variability - such as the MJO and its propagation - over the low resolution simulations. It is shown that including stochastic parameterization in the low resolution runs help to improve some of the aspects of the MJO propagation further. These findings show the importance of representing the impact of small scale processes on the large scale climate variability either explicitly (with high resolution simulations) or stochastically (in low resolution simulations).

A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions

Directory of Open Access Journals (Sweden)

Tomás Pérez Becerra

2018-01-01

Full Text Available Using a bounded bilinear operator, we define the Henstock-Stieltjes integral for vector-valued functions; we prove some integration by parts theorems for Henstock integral and a Riesz-type theorem which provides an alternative proof of the representation theorem for real functions proved by Alexiewicz.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

Science.gov (United States)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low

A non-linear dimension reduction methodology for generating data-driven stochastic input models

International Nuclear Information System (INIS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-01-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R n . An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R d (d<< n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology

Learning from graphically integrated 2D and 3D representations improves retention of neuroanatomy

Science.gov (United States)

Naaz, Farah

Visualizations in the form of computer-based learning environments are highly encouraged in science education, especially for teaching spatial material. Some spatial material, such as sectional neuroanatomy, is very challenging to learn. It involves learning the two dimensional (2D) representations that are sampled from the three dimensional (3D) object. In this study, a computer-based learning environment was used to explore the hypothesis that learning sectional neuroanatomy from a graphically integrated 2D and 3D representation will lead to better learning outcomes than learning from a sequential presentation. The integrated representation explicitly demonstrates the 2D-3D transformation and should lead to effective learning. This study was conducted using a computer graphical model of the human brain. There were two learning groups: Whole then Sections, and Integrated 2D3D. Both groups learned whole anatomy (3D neuroanatomy) before learning sectional anatomy (2D neuroanatomy). The Whole then Sections group then learned sectional anatomy using 2D representations only. The Integrated 2D3D group learned sectional anatomy from a graphically integrated 3D and 2D model. A set of tests for generalization of knowledge to interpreting biomedical images was conducted immediately after learning was completed. The order of presentation of the tests of generalization of knowledge was counterbalanced across participants to explore a secondary hypothesis of the study: preparation for future learning. If the computer-based instruction programs used in this study are effective tools for teaching anatomy, the participants should continue learning neuroanatomy with exposure to new representations. A test of long-term retention of sectional anatomy was conducted 4-8 weeks after learning was completed. The Integrated 2D3D group was better than the Whole then Sections group in retaining knowledge of difficult instances of sectional anatomy after the retention interval. The benefit

Unit commitment with wind power generation: integrating wind forecast uncertainty and stochastic programming.

Energy Technology Data Exchange (ETDEWEB)

Constantinescu, E. M.; Zavala, V. M.; Rocklin, M.; Lee, S.; Anitescu, M. (Mathematics and Computer Science); (Univ. of Chicago); (New York Univ.)

2009-10-09

We present a computational framework for integrating the state-of-the-art Weather Research and Forecasting (WRF) model in stochastic unit commitment/energy dispatch formulations that account for wind power uncertainty. We first enhance the WRF model with adjoint sensitivity analysis capabilities and a sampling technique implemented in a distributed-memory parallel computing architecture. We use these capabilities through an ensemble approach to model the uncertainty of the forecast errors. The wind power realizations are exploited through a closed-loop stochastic unit commitment/energy dispatch formulation. We discuss computational issues arising in the implementation of the framework. In addition, we validate the framework using real wind speed data obtained from a set of meteorological stations. We also build a simulated power system to demonstrate the developments.

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.)

Classical representation of wave functions for integrable systems

International Nuclear Information System (INIS)

Kay, Kenneth G.

2004-01-01

Classical exact (CE) wave functions are certain integral representations of energy eigenfunctions that are parameterized in terms of the motion of the corresponding classical system in a semiclassically relevant way. When applied to systems for which they are not exact, such expressions serve as semiclassical approximations. Previous work identified CE wave functions for a number of specific systems and established their semiclassical usefulness. This paper explores the degree to which such representations can be found for more general systems. It is shown that CE wave functions exist, in principle, for bound states of an arbitrary integrable system that are confined to a single classically allowed region. Evidence is presented that CE representations also exist for more general states of such a system that are unbound, or that extend over more than one allowed region. The CE expressions are not unique: an innumerable variety exists for each such system. The existence proof provides a formal method for constructing CE expressions by Fourier transforming certain superpositions of energy eigenstates. The parameterization in terms of the classical motion is achieved by identifying certain quantities in these superpositions as classical action and angle variables. The semiclassical relevance of this identification is ensured by imposing some mild conditions on the coefficients in the superposition. This procedure for parameterizing exact wave functions in terms of classical variables indicates a basic relationship between the quantum and classical descriptions of states. The method of constructing CE wave functions introduced in the proof is shown to be consistent with a number of previously obtained CE formulas and is used to derive two new, closed-form, CE expressions. A simple numerical example is presented to illustrate the semiclassical application of one of these expressions and to further verify the physical significance of the classical parameterization

AMBRE - a mathematica package for the construction of Mellin-Barnes representations for Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Gluza, J.; Kajda, K. [Silesia Univ, Katowice (Poland). Dept. of Field Theory and Particle Physics, Inst. of Phsyics; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2007-05-15

The Mathematica toolkit AMBRE derives Mellin-Barnes (MB) representations for Feynman integrals in d=4-2{epsilon} dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. AMBRE uses a loop-by-loop approach and aims at lowest dimensions of the final MB representations. The present version of AMBRE works fine for planar Feynman diagrams. The output may be further processed by the package MB for the determination of its singularity structure in {epsilon}. The AMBRE package contains various sample applications for Feynman integrals with up to six external particles and up to four loops. (orig.)

Path integral representation of Lorentzian spinfoam model, asymptotics and simplicial geometries

International Nuclear Information System (INIS)

Han, Muxin; Krajewski, Thomas

2014-01-01

A new path integral representation of Lorentzian Engle–Pereira–Rovelli–Livine spinfoam model is derived by employing the theory of unitary representation of SL(2,C). The path integral representation is taken as a starting point of semiclassical analysis. The relation between the spinfoam model and classical simplicial geometry is studied via the large-spin asymptotic expansion of the spinfoam amplitude with all spins uniformly large. More precisely, in the large-spin regime, there is an equivalence between the spinfoam critical configuration (with certain nondegeneracy assumption) and a classical Lorentzian simplicial geometry. Such an equivalence relation allows us to classify the spinfoam critical configurations by their geometrical interpretations, via two types of solution-generating maps. The equivalence between spinfoam critical configuration and simplical geometry also allows us to define the notion of globally oriented and time-oriented spinfoam critical configuration. It is shown that only at the globally oriented and time-oriented spinfoam critical configuration, the leading-order contribution of spinfoam large-spin asymptotics gives precisely an exponential of Lorentzian Regge action of General Relativity. At all other (unphysical) critical configurations, spinfoam large-spin asymptotics modifies the Regge action at the leading-order approximation. (paper)

Students' integration of multiple representations in a titration experiment

Science.gov (United States)

Kunze, Nicole M.

A complete understanding of a chemical concept is dependent upon a student's ability to understand the microscopic or particulate nature of the phenomenon and integrate the microscopic, symbolic, and macroscopic representations of the phenomenon. Acid-base chemistry is a general chemistry topic requiring students to understand the topics of chemical reactions, solutions, and equilibrium presented earlier in the course. In this study, twenty-five student volunteers from a second semester general chemistry course completed two interviews. The first interview was completed prior to any classroom instruction on acids and bases. The second interview took place after classroom instruction, a prelab activity consisting of a titration calculation worksheet, a titration computer simulation, or a microscopic level animation of a titration, and two microcomputer-based laboratory (MBL) titration experiments. During the interviews, participants were asked to define and describe acid-base concepts and in the second interview they also drew the microscopic representations of four stages in an acid-base titration. An analysis of the data showed that participants had integrated the three representations of an acid-base titration to varying degrees. While some participants showed complete understanding of acids, bases, titrations, and solution chemistry, other participants showed several alternative conceptions concerning strong acid and base dissociation, the formation of titration products, and the dissociation of soluble salts. Before instruction, participants' definitions of acid, base, and pH were brief and consisted of descriptive terms. After instruction, the definitions were more scientific and reflected the definitions presented during classroom instruction.

Crossmodal integration enhances neural representation of task-relevant features in audiovisual face perception.

Science.gov (United States)

Li, Yuanqing; Long, Jinyi; Huang, Biao; Yu, Tianyou; Wu, Wei; Liu, Yongjian; Liang, Changhong; Sun, Pei

2015-02-01

Previous studies have shown that audiovisual integration improves identification performance and enhances neural activity in heteromodal brain areas, for example, the posterior superior temporal sulcus/middle temporal gyrus (pSTS/MTG). Furthermore, it has also been demonstrated that attention plays an important role in crossmodal integration. In this study, we considered crossmodal integration in audiovisual facial perception and explored its effect on the neural representation of features. The audiovisual stimuli in the experiment consisted of facial movie clips that could be classified into 2 gender categories (male vs. female) or 2 emotion categories (crying vs. laughing). The visual/auditory-only stimuli were created from these movie clips by removing the auditory/visual contents. The subjects needed to make a judgment about the gender/emotion category for each movie clip in the audiovisual, visual-only, or auditory-only stimulus condition as functional magnetic resonance imaging (fMRI) signals were recorded. The neural representation of the gender/emotion feature was assessed using the decoding accuracy and the brain pattern-related reproducibility indices, obtained by a multivariate pattern analysis method from the fMRI data. In comparison to the visual-only and auditory-only stimulus conditions, we found that audiovisual integration enhanced the neural representation of task-relevant features and that feature-selective attention might play a role of modulation in the audiovisual integration. © The Author 2013. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Computing Optimal Stochastic Portfolio Execution Strategies: A Parametric Approach Using Simulations

Science.gov (United States)

Moazeni, Somayeh; Coleman, Thomas F.; Li, Yuying

2010-09-01

Computing optimal stochastic portfolio execution strategies under appropriate risk consideration presents great computational challenge. We investigate a parametric approach for computing optimal stochastic strategies using Monte Carlo simulations. This approach allows reduction in computational complexity by computing coefficients for a parametric representation of a stochastic dynamic strategy based on static optimization. Using this technique, constraints can be similarly handled using appropriate penalty functions. We illustrate the proposed approach to minimize the expected execution cost and Conditional Value-at-Risk (CVaR).

Uniform surface-to-line integral reduction of physical optics for curved surfaces by modified edge representation with higher-order correction

Science.gov (United States)

Lyu, Pengfei; Ando, Makoto

2017-09-01

The modified edge representation is one of the equivalent edge currents approximation methods for calculating the physical optics surface radiation integrals in diffraction analysis. The Stokes' theorem is used in the derivation of the modified edge representation from the physical optics for the planar scatterer case, which implies that the surface integral is rigorously reduced into the line integral of the modified edge representation equivalent edge currents, defined in terms of the local shape of the edge. On the contrary, for curved surfaces, the results of radiation integrals depend upon the global shape of the scatterer. The physical optics surface integral consists of two components, from the inner stationary phase point and the edge. The modified edge representation is defined independently from the orientation of the actual edge, and therefore, it could be available not only at the edge but also at the arbitrary points on the scatterer except the stationary phase point where the modified edge representation equivalent edge currents becomes infinite. If stationary phase point exists inside the illuminated region, the physical optics surface integration is reduced into two kinds of the modified edge representation line integrations, along the edge and infinitesimally small integration around the inner stationary phase point, the former and the latter give the diffraction and reflection components, respectively. The accuracy of the latter has been discussed for the curved surfaces and published. This paper focuses on the errors of the former and discusses its correction. It has been numerically observed that the modified edge representation works well for the physical optics diffraction in flat and concave surfaces; errors appear especially for the observer near the reflection shadow boundary if the frequency is low for the convex scatterer. This paper gives the explicit expression of the higher-order correction for the modified edge representation.

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.''

Theory of stochastic differential equations with jumps and applications mathematical and analytical techniques with applications to engineering

CERN Document Server

SITU, Rong

2005-01-01

Derivation of Ito's formulas, Girsanov's theorems and martingale representation theorem for stochastic DEs with jumpsApplications to population controlReflecting stochastic DE techniqueApplications to the stock market. (Backward stochastic DE approach)Derivation of Black-Scholes formula for market with and without jumpsNon-linear filtering problems with jumps.

Integrated multiperiod power generation and transmission expansion planning with sustainability aspects in a stochastic environment

International Nuclear Information System (INIS)

Seddighi, Amir Hossein; Ahmadi-Javid, Amir

2015-01-01

This paper presents a multistage stochastic programming model to address sustainable power generation and transmission expansion planning. The model incorporates uncertainties about future electricity demand, fuel prices, greenhouse gas emissions, as well as possible disruptions to which the power system is subject. A number of sustainability regulations and policies are considered to establish a framework for the social responsibility of the power system. The proposed model is applied to a real-world case, and several sensitivity analyses are carried out to provide managerial insights into different aspects of the model. The results emphasize the important role played by sustainability policies on the configuration of the power grid. - Highlights: • This paper considers integrated power generation and transmission expansion planning. • Sustainability aspects are incorporated into a multiperiod stochastic setting. • A stochastic mathematical programming model is developed to address the problem. • The model is applied to a real-world case and numerical studies are carried out

Matrix models and stochastic growth in Donaldson-Thomas theory

Energy Technology Data Exchange (ETDEWEB)

Szabo, Richard J. [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, United Kingdom and Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom); Tierz, Miguel [Grupo de Fisica Matematica, Complexo Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, PT-1649-003 Lisboa (Portugal); Departamento de Analisis Matematico, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain)

2012-10-15

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.

Matrix models and stochastic growth in Donaldson-Thomas theory

International Nuclear Information System (INIS)

Szabo, Richard J.; Tierz, Miguel

2012-01-01

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.

Path integral methods for the dynamics of stochastic and disordered systems

International Nuclear Information System (INIS)

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

2017-01-01

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

Diffusive processes in a stochastic magnetic field

International Nuclear Information System (INIS)

Wang, H.; Vlad, M.; Vanden Eijnden, E.; Spineanu, F.; Misguich, J.H.; Balescu, R.

1995-01-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing, in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle's trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works

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...

Green function of the double-fractional Fokker-Planck equation: Path integral and stochastic differential equations

Science.gov (United States)

Kleinert, H.; Zatloukal, V.

2013-11-01

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

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

Representation of the three-body Coulomb Green's function in parabolic coordinates: paths of integration

International Nuclear Information System (INIS)

Zaytsev, S A

2010-01-01

The possibility of using straight-line paths of integration in computing the integral representation of the three-body Coulomb Green's function is discussed. In our numerical examples two different kinds of integration contours in the complex energy planes are considered. It is demonstrated that straight-line paths, which cross the positive real axis, are suitable for numerical computation.

Integration of object-oriented knowledge representation with the CLIPS rule based system

Science.gov (United States)

Logie, David S.; Kamil, Hasan

1990-01-01

The paper describes a portion of the work aimed at developing an integrated, knowledge based environment for the development of engineering-oriented applications. An Object Representation Language (ORL) was implemented in C++ which is used to build and modify an object-oriented knowledge base. The ORL was designed in such a way so as to be easily integrated with other representation schemes that could effectively reason with the object base. Specifically, the integration of the ORL with the rule based system C Language Production Systems (CLIPS), developed at the NASA Johnson Space Center, will be discussed. The object-oriented knowledge representation provides a natural means of representing problem data as a collection of related objects. Objects are comprised of descriptive properties and interrelationships. The object-oriented model promotes efficient handling of the problem data by allowing knowledge to be encapsulated in objects. Data is inherited through an object network via the relationship links. Together, the two schemes complement each other in that the object-oriented approach efficiently handles problem data while the rule based knowledge is used to simulate the reasoning process. Alone, the object based knowledge is little more than an object-oriented data storage scheme; however, the CLIPS inference engine adds the mechanism to directly and automatically reason with that knowledge. In this hybrid scheme, the expert system dynamically queries for data and can modify the object base with complete access to all the functionality of the ORL from rules.

Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods

Directory of Open Access Journals (Sweden)

Tetsuya Misawa

2010-01-01

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

Object Representations in Human Visual Cortex Formed Through Temporal Integration of Dynamic Partial Shape Views.

Science.gov (United States)

Orlov, Tanya; Zohary, Ehud

2018-01-17

We typically recognize visual objects using the spatial layout of their parts, which are present simultaneously on the retina. Therefore, shape extraction is based on integration of the relevant retinal information over space. The lateral occipital complex (LOC) can represent shape faithfully in such conditions. However, integration over time is sometimes required to determine object shape. To study shape extraction through temporal integration of successive partial shape views, we presented human participants (both men and women) with artificial shapes that moved behind a narrow vertical or horizontal slit. Only a tiny fraction of the shape was visible at any instant at the same retinal location. However, observers perceived a coherent whole shape instead of a jumbled pattern. Using fMRI and multivoxel pattern analysis, we searched for brain regions that encode temporally integrated shape identity. We further required that the representation of shape should be invariant to changes in the slit orientation. We show that slit-invariant shape information is most accurate in the LOC. Importantly, the slit-invariant shape representations matched the conventional whole-shape representations assessed during full-image runs. Moreover, when the same slit-dependent shape slivers were shuffled, thereby preventing their spatiotemporal integration, slit-invariant shape information was reduced dramatically. The slit-invariant representation of the various shapes also mirrored the structure of shape perceptual space as assessed by perceptual similarity judgment tests. Therefore, the LOC is likely to mediate temporal integration of slit-dependent shape views, generating a slit-invariant whole-shape percept. These findings provide strong evidence for a global encoding of shape in the LOC regardless of integration processes required to generate the shape percept. SIGNIFICANCE STATEMENT Visual objects are recognized through spatial integration of features available simultaneously on

Chemical Entity Semantic Specification: Knowledge representation for efficient semantic cheminformatics and facile data integration

Science.gov (United States)

2011-01-01

Background Over the past several centuries, chemistry has permeated virtually every facet of human lifestyle, enriching fields as diverse as medicine, agriculture, manufacturing, warfare, and electronics, among numerous others. Unfortunately, application-specific, incompatible chemical information formats and representation strategies have emerged as a result of such diverse adoption of chemistry. Although a number of efforts have been dedicated to unifying the computational representation of chemical information, disparities between the various chemical databases still persist and stand in the way of cross-domain, interdisciplinary investigations. Through a common syntax and formal semantics, Semantic Web technology offers the ability to accurately represent, integrate, reason about and query across diverse chemical information. Results Here we specify and implement the Chemical Entity Semantic Specification (CHESS) for the representation of polyatomic chemical entities, their substructures, bonds, atoms, and reactions using Semantic Web technologies. CHESS provides means to capture aspects of their corresponding chemical descriptors, connectivity, functional composition, and geometric structure while specifying mechanisms for data provenance. We demonstrate that using our readily extensible specification, it is possible to efficiently integrate multiple disparate chemical data sources, while retaining appropriate correspondence of chemical descriptors, with very little additional effort. We demonstrate the impact of some of our representational decisions on the performance of chemically-aware knowledgebase searching and rudimentary reaction candidate selection. Finally, we provide access to the tools necessary to carry out chemical entity encoding in CHESS, along with a sample knowledgebase. Conclusions By harnessing the power of Semantic Web technologies with CHESS, it is possible to provide a means of facile cross-domain chemical knowledge integration with full

An Exact Line Integral Representation of the Physical Optics Far Field from Plane PEC Scatterers Illuminnated by Hertzian Dipoles

DEFF Research Database (Denmark)

Arslanagic, Samel; Meincke, Peter; Jørgensen, Erik

2003-01-01

We derive a line integral representation of the physical optics scattered far field that yields the exact same result as the conventional surface radiation integral. This representation applies to a perfectly electrically conducting plane scatterer illuminated by electric or magnetic Hertzian...... dipoles. The source and observation points can take on almost arbitrary positions. To illustrate the exactness and efficiency of the new line integral, numerical comparisons with the conventional surface radiation integral are carried out....

Representation and Integration: Combining Robot Control, High-Level Planning, and Action Learning

DEFF Research Database (Denmark)

Petrick, Ronald; Kraft, Dirk; Mourao, Kira

We describe an approach to integrated robot control, high-level planning, and action effect learning that attempts to overcome the representational difficulties that exist between these diverse areas. Our approach combines ideas from robot vision, knowledgelevel planning, and connectionist machine......-level action specifications, suitable for planning, from a robot’s interactions with the world. We present a detailed overview of our approach and show how it supports the learning of certain aspects of a high-level lepresentation from low-level world state information....... learning, and focuses on the representational needs of these components.We also make use of a simple representational unit called an instantiated state transition fragment (ISTF) and a related structure called an object-action complex (OAC). The goal of this work is a general approach for inducing high...

Stochastic simulation and robust design optimization of integrated photonic filters

Directory of Open Access Journals (Sweden)

Weng Tsui-Wei

2016-07-01

Full Text Available Manufacturing variations are becoming an unavoidable issue in modern fabrication processes; therefore, it is crucial to be able to include stochastic uncertainties in the design phase. In this paper, integrated photonic coupled ring resonator filters are considered as an example of significant interest. The sparsity structure in photonic circuits is exploited to construct a sparse combined generalized polynomial chaos model, which is then used to analyze related statistics and perform robust design optimization. Simulation results show that the optimized circuits are more robust to fabrication process variations and achieve a reduction of 11%–35% in the mean square errors of the 3 dB bandwidth compared to unoptimized nominal designs.

Mellin-Barnes meets Method of Brackets: a novel approach to Mellin-Barnes representations of Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Prausa, Mario [RWTH Aachen University, Institute for Theoretical Particle Physics and Cosmology, Aachen (Germany)

2017-09-15

In this paper, we present a new approach to the construction of Mellin-Barnes representations for Feynman integrals inspired by the Method of Brackets. The novel technique is helpful to lower the dimensionality of Mellin-Barnes representations in complicated cases, some examples are given. (orig.)

Stochastic stability of four-wheel-steering system

International Nuclear Information System (INIS)

Huang Dongwei; Wang Hongli; Zhu Zhiwen; Feng Zhang

2007-01-01

A four-wheel-steering system subjected to white noise excitations was reduced to a two-degree-of-freedom quasi-non-integrable-Hamiltonian system. Subsequently we obtained an one-dimensional Ito stochastic differential equation for the averaged Hamiltonian of the system by using the stochastic averaging method for quasi-non-integrable-Hamiltonian systems. Thus, the stochastic stability of four-wheel-steering system was analyzed by analyzing the sample behaviors of the averaged Hamiltonian at the boundary H = 0 and calculating its Lyapunov exponent. An example given at the end demonstrated that the conclusion obtained is of considerable significance

A stochastic model for the financial market with discontinuous prices

Directory of Open Access Journals (Sweden)

Leda D. Minkova

1996-01-01

Full Text Available This paper models some situations occurring in the financial market. The asset prices evolve according to a stochastic integral equation driven by a Gaussian martingale. A portfolio process is constrained in such a way that the wealth process covers some obligation. A solution to a linear stochastic integral equation is obtained in a class of cadlag stochastic processes.

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

KAUST Repository

Navarro, Marí a; Le Maitre, Olivier; Knio, Omar

2016-01-01

sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity

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.

On the use of stochastic approximation Monte Carlo for Monte Carlo integration

KAUST Repository

Liang, Faming

2009-03-01

The stochastic approximation Monte Carlo (SAMC) algorithm has recently been proposed as a dynamic optimization algorithm in the literature. In this paper, we show in theory that the samples generated by SAMC can be used for Monte Carlo integration via a dynamically weighted estimator by calling some results from the literature of nonhomogeneous Markov chains. Our numerical results indicate that SAMC can yield significant savings over conventional Monte Carlo algorithms, such as the Metropolis-Hastings algorithm, for the problems for which the energy landscape is rugged. © 2008 Elsevier B.V. All rights reserved.

Stochastic and epistemic uncertainty propagation in LCA

DEFF Research Database (Denmark)

Clavreul, Julie; Guyonnet, Dominique; Tonini, Davide

2013-01-01

of epistemic uncertainty representation using fuzzy intervals. The propagation methods used are the Monte Carlo analysis for probability distribution and an optimisation on alpha-cuts for fuzzy intervals. The proposed method (noted as Independent Random Set, IRS) generalizes the process of random sampling...... to probability distributions as well as fuzzy intervals, thus making the simultaneous use of both representations possible.The results highlight the fundamental difference between the probabilistic and possibilistic representations: while the Monte Carlo analysis generates a single probability distribution...... or expert judgement (epistemic uncertainty). The possibility theory has been developed over the last decades to address this problem. The objective of this study is to present a methodology that combines probability and possibility theories to represent stochastic and epistemic uncertainties in a consistent...

On Parameter Differentiation for Integral Representations of Associated Legendre Functions

Directory of Open Access Journals (Sweden)

Howard S. Cohl

2011-05-01

Full Text Available For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-half-integer degrees, for general complex-orders, and derivatives with respect to the order are evaluated at integer-orders, for general complex-degrees. We also discuss the properties of the complex function f: C{−1,1}→C given by f(z=z/((z+1^{1/2}(z−1^{1/2}.

Heterogeneous recurrence monitoring and control of nonlinear stochastic processes

Energy Technology Data Exchange (ETDEWEB)

Yang, Hui, E-mail: huiyang@usf.edu; Chen, Yun [Complex Systems Monitoring, Modeling and Analysis Laboratory, University of South Florida, Tampa, Florida 33620 (United States)

2014-03-15

Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.

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.

Perception of stochastically undersampled sound waveforms: A model of auditory deafferentation

Directory of Open Access Journals (Sweden)

Enrique A Lopez-Poveda

2013-07-01

Full Text Available Auditory deafferentation, or permanent loss of auditory nerve afferent terminals, occurs after noise overexposure and aging and may accompany many forms of hearing loss. It could cause significant auditory impairment but is undetected by regular clinical tests and so its effects on perception are poorly understood. Here, we hypothesize and test a neural mechanism by which deafferentation could deteriorate perception. The basic idea is that the spike train produced by each auditory afferent resembles a stochastically digitized version of the sound waveform and that the quality of the waveform representation in the whole nerve depends on the number of aggregated spike trains or auditory afferents. We reason that because spikes occur stochastically in time with a higher probability for high- than for low-intensity sounds, more afferents would be required for the nerve to faithfully encode high-frequency or low-intensity waveform features than low-frequency or high-intensity features. Deafferentation would thus degrade the encoding of these features. We further reason that due to the stochastic nature of nerve firing, the degradation would be greater in noise than in quiet. This hypothesis is tested using a vocoder. Sounds were filtered through ten adjacent frequency bands. For the signal in each band, multiple stochastically subsampled copies were obtained to roughly mimic different stochastic representations of that signal conveyed by different auditory afferents innervating a given cochlear region. These copies were then aggregated to obtain an acoustic stimulus. Tone detection and speech identification tests were performed by young, normal-hearing listeners using different numbers of stochastic samplers per frequency band in the vocoder. Results support the hypothesis that stochastic undersampling of the sound waveform, inspired by deafferentation, impairs speech perception in noise more than in quiet, consistent with auditory aging effects.

Perception of stochastically undersampled sound waveforms: a model of auditory deafferentation

Science.gov (United States)

Lopez-Poveda, Enrique A.; Barrios, Pablo

2013-01-01

Auditory deafferentation, or permanent loss of auditory nerve afferent terminals, occurs after noise overexposure and aging and may accompany many forms of hearing loss. It could cause significant auditory impairment but is undetected by regular clinical tests and so its effects on perception are poorly understood. Here, we hypothesize and test a neural mechanism by which deafferentation could deteriorate perception. The basic idea is that the spike train produced by each auditory afferent resembles a stochastically digitized version of the sound waveform and that the quality of the waveform representation in the whole nerve depends on the number of aggregated spike trains or auditory afferents. We reason that because spikes occur stochastically in time with a higher probability for high- than for low-intensity sounds, more afferents would be required for the nerve to faithfully encode high-frequency or low-intensity waveform features than low-frequency or high-intensity features. Deafferentation would thus degrade the encoding of these features. We further reason that due to the stochastic nature of nerve firing, the degradation would be greater in noise than in quiet. This hypothesis is tested using a vocoder. Sounds were filtered through ten adjacent frequency bands. For the signal in each band, multiple stochastically subsampled copies were obtained to roughly mimic different stochastic representations of that signal conveyed by different auditory afferents innervating a given cochlear region. These copies were then aggregated to obtain an acoustic stimulus. Tone detection and speech identification tests were performed by young, normal-hearing listeners using different numbers of stochastic samplers per frequency band in the vocoder. Results support the hypothesis that stochastic undersampling of the sound waveform, inspired by deafferentation, impairs speech perception in noise more than in quiet, consistent with auditory aging effects. PMID:23882176

An Integral Representation of Standard Automorphic L Functions for Unitary Groups

Directory of Open Access Journals (Sweden)

Yujun Qin

2007-01-01

Full Text Available Let F be a number field, G a quasi-split unitary group of rank n. We show that given an irreducible cuspidal automorphic representation π of G(A, its (partial L function LS(s,π,σ can be represented by a Rankin-Selberg-type integral involving cusp forms of π, Eisenstein series, and theta series.

A stochastic framework for the grid integration of wind power using flexible load approach

International Nuclear Information System (INIS)

Heydarian-Forushani, E.; Moghaddam, M.P.; Sheikh-El-Eslami, M.K.; Shafie-khah, M.; Catalão, J.P.S.

2014-01-01

Highlights: • This paper focuses on the potential of Demand Response Programs (DRPs) to contribute to flexibility. • A stochastic network constrained unit commitment associated with DR is presented. • DR participation levels and electricity tariffs are evaluated on providing a flexible load profile. • Novel quantitative indices for evaluating flexibility are defined to assess the success of DRPs. • DR types and customer participation levels are the main factors to modify the system load profile. - Abstract: Wind power integration has always been a key research area due to the green future power system target. However, the intermittent nature of wind power may impose some technical and economic challenges to Independent System Operators (ISOs) and increase the need for additional flexibility. Motivated by this need, this paper focuses on the potential of Demand Response Programs (DRPs) as an option to contribute to the flexible operation of power systems. On this basis, in order to consider the uncertain nature of wind power and the reality of electricity market, a Stochastic Network Constrained Unit Commitment associated with DR (SNCUCDR) is presented to schedule both generation units and responsive loads in power systems with high penetration of wind power. Afterwards, the effects of both price-based and incentive-based DRPs are evaluated, as well as DR participation levels and electricity tariffs on providing a flexible load profile and facilitating grid integration of wind power. For this reason, novel quantitative indices for evaluating flexibility are defined to assess the success of DRPs in terms of wind integration. Sensitivity studies indicate that DR types and customer participation levels are the main factors to modify the system load profile to support wind power integration

Multidimensional integral representations problems of analytic continuation

CERN Document Server

Kytmanov, Alexander M

2015-01-01

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem.   This book is a valuable resource for specialists in complex analysis, theoretical physics, as well as graduate and postgraduate students with an understanding of standard university courses in complex, real and functional analysis, as well as algebra and geometry.

An efficient forward-reverse expectation-maximization algorithm for statistical inference in stochastic reaction networks

KAUST Repository

Vilanova, Pedro

2016-01-07

In this work, we present an extension of the forward-reverse representation introduced in Simulation of forward-reverse stochastic representations for conditional diffusions , a 2014 paper by Bayer and Schoenmakers to the context of stochastic reaction networks (SRNs). We apply this stochastic representation to the computation of efficient approximations of expected values of functionals of SRN bridges, i.e., SRNs conditional on their values in the extremes of given time-intervals. We then employ this SRN bridge-generation technique to the statistical inference problem of approximating reaction propensities based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during phase I, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate ordinary differential equations approximation; then, during phase II, we apply the Monte Carlo version of the Expectation-Maximization algorithm to the phase I output. By selecting a set of over-dispersed seeds as initial points in phase I, the output of parallel runs from our two-phase method is a cluster of approximate maximum likelihood estimates. Our results are supported by numerical examples.

Markovian approach: From Ising model to stochastic radiative transfer

International Nuclear Information System (INIS)

Kassianov, E.; Veron, D.

2009-01-01

The origin of the Markovian approach can be traced back to 1906; however, it gained explicit recognition in the last few decades. This overview outlines some important applications of the Markovian approach, which illustrate its immense prestige, respect, and success. These applications include examples in the statistical physics, astronomy, mathematics, computational science and the stochastic transport problem. In particular, the overview highlights important contributions made by Pomraning and Titov to the neutron and radiation transport theory in a stochastic medium with homogeneous statistics. Using simple probabilistic assumptions (Markovian approximation), they have introduced a simplified, but quite realistic, representation of the neutron/radiation transfer through a two-component discrete stochastic mixture. New concepts and methodologies introduced by these two distinguished scientists allow us to generalize the Markovian treatment to the stochastic medium with inhomogeneous statistics and demonstrate its improved predictive performance for the down-welling shortwave fluxes. (authors)

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.

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.

High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

KAUST Repository

Abdulle, Assyr

2012-01-01

© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.

Measurement of definite integral of sinusoidal signal absolute value third power using digital stochastic method

Directory of Open Access Journals (Sweden)

Beljić Željko

2017-01-01

Full Text Available In this paper a special case of digital stochastic measurement of the third power of definite integral of sinusoidal signal’s absolute value, using 2-bit AD converters is presented. This case of digital stochastic method had emerged from the need to measure power and energy of the wind. Power and energy are proportional to the third power of wind speed. Anemometer output signal is sinusoidal. Therefore an integral of the third power of sinusoidal signal is zero. Two approaches are proposed for the third power calculation of the wind speed signal. One approach is to use absolute value of sinusoidal signal (before AD conversion for which there is no need of multiplier hardware change. The second approach requires small multiplier hardware change, but input signal remains unchanged. For the second approach proposed minimal hardware change was made to calculate absolute value of the result after AD conversion. Simulations have confirmed theoretical analysis. Expected precision of wind energy measurement of proposed device is better than 0,00051% of full scale. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. TR32019

Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation

International Nuclear Information System (INIS)

Kalmykov, Mikhail Yu.; Kniehl, Bernd A.

2017-06-01

A number of irreducible master integrals for L-loop sunrise and bubble Feynman diagrams with generic values of masses and external momenta are explicitly evaluated via the Mellin-Barnes representation.

Stochastic theory of relaxation and collisional broadening of spectral line shapes

International Nuclear Information System (INIS)

Faid, K.

1986-01-01

A complete stochastic theory of relaxation is developed in terms of a homogeneous equation for the averaged density matrix of a system immersed in a thermal bath. This theory is then used as the basis of a new stochastic approach to the phenomenon of collisional broadening of spectral line shapes. Single-photon and multiphoton processes are studied. The features of a line shape are linked by simple expressions to the statistical properties of a stochastic hermitian Hamiltonian. The ordinary line shape predicted by Kubo's approach is generalized. The present approach predicts broadening as well as asymmetry and shift. A representation of line shapes in multiphoton processes by diagrams is also developed

On the continuous selections of solution sets of Lipschitzian quantum stochastic differential inclusions

International Nuclear Information System (INIS)

Ayoola, E.O.

2004-05-01

We prove that a multifunction associated with the set of solutions of Lipschitzian quantum stochastic differential inclusion (QSDI) admits a selection continuous from some subsets of complex numbers to the space of the matrix elements of adapted weakly absolutely continuous quantum stochastic processes. In particular, we show that the solution set map as well as the reachable set of the QSDI admit some continuous representations. (author)

Stochastic calculus in physics

International Nuclear Information System (INIS)

Fox, R.F.

1987-01-01

The relationship of Ito-Stratonovich stochastic calculus to studies of weakly colored noise is explained. A functional calculus approach is used to obtain an effective Fokker-Planck equation for the weakly colored noise regime. In a smooth limit, this representation produces the Stratonovich version of the Ito-Stratonovich calculus for white noise. It also provides an approach to steady state behavior for strongly colored noise. Numerical simulation algorithms are explored, and a novel suggestion is made for efficient and accurate simulation of white noise equations

Quantum Stochastic Trajectories: The Fokker-Planck-Bohm Equation Driven by the Reduced Density Matrix.

Science.gov (United States)

Avanzini, Francesco; Moro, Giorgio J

2018-03-15

The quantum molecular trajectory is the deterministic trajectory, arising from the Bohm theory, that describes the instantaneous positions of the nuclei of molecules by assuring the agreement with the predictions of quantum mechanics. Therefore, it provides the suitable framework for representing the geometry and the motions of molecules without neglecting their quantum nature. However, the quantum molecular trajectory is extremely demanding from the computational point of view, and this strongly limits its applications. To overcome such a drawback, we derive a stochastic representation of the quantum molecular trajectory, through projection operator techniques, for the degrees of freedom of an open quantum system. The resulting Fokker-Planck operator is parametrically dependent upon the reduced density matrix of the open system. Because of the pilot role played by the reduced density matrix, this stochastic approach is able to represent accurately the main features of the open system motions both at equilibrium and out of equilibrium with the environment. To verify this procedure, the predictions of the stochastic and deterministic representation are compared for a model system of six interacting harmonic oscillators, where one oscillator is taken as the open quantum system of interest. The undeniable advantage of the stochastic approach is that of providing a simplified and self-contained representation of the dynamics of the open system coordinates. Furthermore, it can be employed to study the out of equilibrium dynamics and the relaxation of quantum molecular motions during photoinduced processes, like photoinduced conformational changes and proton transfers.

Bound states of quarks calculated with stochastic integration of the Bethe-Salpeter equation

International Nuclear Information System (INIS)

Salomon, M.

1992-07-01

We have computed the masses, wave functions and sea quark content of mesons in their ground state by integrating the Bethe-Salpeter equation with a stochastic algorithm. This method allows the inclusion of a large set of diagrams. Inspection of the kernel of the equation shows that q-q-bar pairs with similar constituent masses in a singlet spin state exhibit a high bound state which is not present in other pairs. The pion, kaon and eta belongs to this category. 19 refs., 2 figs., 2 tabs

A Line Integral Representation of the Physical Optics Far Field from Plane PEC Scatterers Illuminated by Electric or Magnetic Hertzian Dipoles

DEFF Research Database (Denmark)

Arslanagic, S.; Meincke, Peter; Jørgensen, E.

2002-01-01

We derive a line integral representation of the physical optics (PO) scattered far field that yields the exact same result as the conventional surface radiation integral. This representation applies to a perfectly electrically conducting plane scatterer illuminated by electric or magnetic Hertzian...... dipoles....

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)

Automatic frame-centered object representation and integration revealed by iconic memory, visual priming, and backward masking.

Science.gov (United States)

Lin, Zhicheng; He, Sheng

2012-10-25

Object identities ("what") and their spatial locations ("where") are processed in distinct pathways in the visual system, raising the question of how the what and where information is integrated. Because of object motions and eye movements, the retina-based representations are unstable, necessitating nonretinotopic representation and integration. A potential mechanism is to code and update objects according to their reference frames (i.e., frame-centered representation and integration). To isolate frame-centered processes, in a frame-to-frame apparent motion configuration, we (a) presented two preceding or trailing objects on the same frame, equidistant from the target on the other frame, to control for object-based (frame-based) effect and space-based effect, and (b) manipulated the target's relative location within its frame to probe frame-centered effect. We show that iconic memory, visual priming, and backward masking depend on objects' relative frame locations, orthogonal of the retinotopic coordinate. These findings not only reveal that iconic memory, visual priming, and backward masking can be nonretinotopic but also demonstrate that these processes are automatically constrained by contextual frames through a frame-centered mechanism. Thus, object representation is robustly and automatically coupled to its reference frame and continuously being updated through a frame-centered, location-specific mechanism. These findings lead to an object cabinet framework, in which objects ("files") within the reference frame ("cabinet") are orderly coded relative to the frame.

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 quantization of instantons

International Nuclear Information System (INIS)

Grandati, Y.; Berard, A.; Grange, P.

1996-01-01

The method of Parisi and Wu to quantize classical fields is applied to instanton solutions var-phi I of euclidian non-linear theory in one dimension. The solution var-phi var-epsilon of the corresponding Langevin equation is built through a singular perturbative expansion in var-epsilon=h 1/2 in the frame of the center of the mass of the instanton, where the difference var-phi var-epsilon -var-phi I carries only fluctuations of the instanton form. The relevance of the method is shown for the stochastic K dV equation with uniform noise in space: the exact solution usually obtained by the inverse scattering method is retrieved easily by the singular expansion. A general diagrammatic representation of the solution is then established which makes a thorough use of regrouping properties of stochastic diagrams derived in scalar field theory. Averaging over the noise and in the limit of infinite stochastic time, the authors obtain explicit expressions for the first two orders in var-epsilon of the pertrubed instanton of its Green function. Specializing to the Sine-Gordon and var-phi 4 models, the first anaharmonic correction is obtained analytically. The calculation is carried to second order for the var-phi 4 model, showing good convergence. 21 refs., 5 fig

Integral representations of solutions of the wave equation based on relativistic wavelets

International Nuclear Information System (INIS)

Perel, Maria; Gorodnitskiy, Evgeny

2012-01-01

A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed. (paper)

Stochastic Geometry and Quantum Gravity: Some Rigorous Results

Science.gov (United States)

Zessin, H.

The aim of these lectures is a short introduction into some recent developments in stochastic geometry which have one of its origins in simplicial gravity theory (see Regge Nuovo Cimento 19: 558-571, 1961). The aim is to define and construct rigorously point processes on spaces of Euclidean simplices in such a way that the configurations of these simplices are simplicial complexes. The main interest then is concentrated on their curvature properties. We illustrate certain basic ideas from a mathematical point of view. An excellent representation of this area can be found in Schneider and Weil (Stochastic and Integral Geometry, Springer, Berlin, 2008. German edition: Stochastische Geometrie, Teubner, 2000). In Ambjørn et al. (Quantum Geometry Cambridge University Press, Cambridge, 1997) you find a beautiful account from the physical point of view. More recent developments in this direction can be found in Ambjørn et al. ("Quantum gravity as sum over spacetimes", Lect. Notes Phys. 807. Springer, Heidelberg, 2010). After an informal axiomatic introduction into the conceptual foundations of Regge's approach the first lecture recalls the concepts and notations used. It presents the fundamental zero-infinity law of stochastic geometry and the construction of cluster processes based on it. The second lecture presents the main mathematical object, i.e. Poisson-Delaunay surfaces possessing an intrinsic random metric structure. The third and fourth lectures discuss their ergodic behaviour and present the two-dimensional Regge model of pure simplicial quantum gravity. We terminate with the formulation of basic open problems. Proofs are given in detail only in a few cases. In general the main ideas are developed. Sufficiently complete references are given.

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 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.

Multiscale Hy3S: Hybrid stochastic simulation for supercomputers

Directory of Open Access Journals (Sweden)

Kaznessis Yiannis N

2006-02-01

Full Text Available Abstract Background Stochastic simulation has become a useful tool to both study natural biological systems and design new synthetic ones. By capturing the intrinsic molecular fluctuations of "small" systems, these simulations produce a more accurate picture of single cell dynamics, including interesting phenomena missed by deterministic methods, such as noise-induced oscillations and transitions between stable states. However, the computational cost of the original stochastic simulation algorithm can be high, motivating the use of hybrid stochastic methods. Hybrid stochastic methods partition the system into multiple subsets and describe each subset as a different representation, such as a jump Markov, Poisson, continuous Markov, or deterministic process. By applying valid approximations and self-consistently merging disparate descriptions, a method can be considerably faster, while retaining accuracy. In this paper, we describe Hy3S, a collection of multiscale simulation programs. Results Building on our previous work on developing novel hybrid stochastic algorithms, we have created the Hy3S software package to enable scientists and engineers to both study and design extremely large well-mixed biological systems with many thousands of reactions and chemical species. We have added adaptive stochastic numerical integrators to permit the robust simulation of dynamically stiff biological systems. In addition, Hy3S has many useful features, including embarrassingly parallelized simulations with MPI; special discrete events, such as transcriptional and translation elongation and cell division; mid-simulation perturbations in both the number of molecules of species and reaction kinetic parameters; combinatorial variation of both initial conditions and kinetic parameters to enable sensitivity analysis; use of NetCDF optimized binary format to quickly read and write large datasets; and a simple graphical user interface, written in Matlab, to help users

Integral-based event triggering controller design for stochastic LTI systems via convex optimisation

Science.gov (United States)

Mousavi, S. H.; Marquez, H. J.

2016-07-01

The presence of measurement noise in the event-based systems can lower system efficiency both in terms of data exchange rate and performance. In this paper, an integral-based event triggering control system is proposed for LTI systems with stochastic measurement noise. We show that the new mechanism is robust against noise and effectively reduces the flow of communication between plant and controller, and also improves output performance. Using a Lyapunov approach, stability in the mean square sense is proved. A simulated example illustrates the properties of our approach.

Stochastic simulation of ecohydrological interactions between vegetation and groundwater

Science.gov (United States)

Dwelle, M. C.; Ivanov, V. Y.; Sargsyan, K.

2017-12-01

The complex interactions between groundwater and vegetation in the Amazon rainforest may yield vital ecophysiological interactions in specific landscape niches such as buffering plant water stress during dry season or suppression of water uptake due to anoxic conditions. Representation of such processes is greatly impacted by both external and internal sources of uncertainty: inaccurate data and subjective choice of model representation. The models that can simulate these processes are complex and computationally expensive, and therefore make it difficult to address uncertainty using traditional methods. We use the ecohydrologic model tRIBS+VEGGIE and a novel uncertainty quantification framework applied to the ZF2 watershed near Manaus, Brazil. We showcase the capability of this framework for stochastic simulation of vegetation-hydrology dynamics. This framework is useful for simulation with internal and external stochasticity, but this work will focus on internal variability of groundwater depth distribution and model parameterizations. We demonstrate the capability of this framework to make inferences on uncertain states of groundwater depth from limited in situ data, and how the realizations of these inferences affect the ecohydrological interactions between groundwater dynamics and vegetation function. We place an emphasis on the probabilistic representation of quantities of interest and how this impacts the understanding and interpretation of the dynamics at the groundwater-vegetation interface.

A Posteriori Error Analysis of Stochastic Differential Equations Using Polynomial Chaos Expansions

KAUST Repository

Butler, T.; Dawson, C.; Wildey, T.

2011-01-01

We develop computable a posteriori error estimates for linear functionals of a solution to a general nonlinear stochastic differential equation with random model/source parameters. These error estimates are based on a variational analysis applied to stochastic Galerkin methods for forward and adjoint problems. The result is a representation for the error estimate as a polynomial in the random model/source parameter. The advantage of this method is that we use polynomial chaos representations for the forward and adjoint systems to cheaply produce error estimates by simple evaluation of a polynomial. By comparison, the typical method of producing such estimates requires repeated forward/adjoint solves for each new choice of random parameter. We present numerical examples showing that there is excellent agreement between these methods. © 2011 Society for Industrial and Applied Mathematics.

A novel integrated condition-based maintenance and stochastic flexible job shop scheduling problem

DEFF Research Database (Denmark)

Rahmati, Seyed Habib A.; Ahmadi, Abbas; Govindan, Kannan

2018-01-01

the level of the system optimization. By means of this equipment, managers can benefit from a condition-based maintenance (CBM) for monitoring and managing their system. The chief aim of the paper is to develop a stochastic maintenance problem based on CBM activities engaged with a complex applied......Integrated consideration of production planning and maintenance processes is a real world assumption. Specifically, by improving the monitoring equipment such as various sensors or product-embedded information devices in recent years, joint assessment of these processes is inevitable for enhancing...... production problem called flexible job shop scheduling problem (FJSP). This integrated problem considers two maintenance scenarios in terms of corrective maintenance (CM) and preventive maintenance (PM). The activation of scenario is done by monitoring the degradation condition of the system and comparing...

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

Energy Technology Data Exchange (ETDEWEB)

Gitman, D.M. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Kupriyanov, V.G. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Tomsk State University, Physics Department, Tomsk (Russian Federation)

2008-03-15

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them {theta}-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing {theta}-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract {theta}-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as {theta}-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The {theta}-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case. (orig.)

Stochastic Analysis and Related Topics

CERN Document Server

Ustunel, Ali

1988-01-01

The Silvri Workshop was divided into a short summer school and a working conference, producing lectures and research papers on recent developments in stochastic analysis on Wiener space. The topics treated in the lectures relate to the Malliavin calculus, the Skorohod integral and nonlinear functionals of white noise. Most of the research papers are applications of these subjects. This volume addresses researchers and graduate students in stochastic processes and theoretical physics.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

Energy Technology Data Exchange (ETDEWEB)

Opanchuk, B.; Drummond, P. D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Hawthorn VIC 3122 (Australia)

2013-04-15

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

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.

Integrated logistic support studies using behavioral Monte Carlo simulation, supported by Generalized Stochastic Petri Nets

International Nuclear Information System (INIS)

Garnier, Robert; Chevalier, Marcel

2000-01-01

Studying large and complex industrial sites, requires more and more accuracy in modeling. In particular, when considering Spares, Maintenance and Repair / Replacement processes, determining optimal Integrated Logistic Support policies requires a high level modeling formalism, in order to make the model as close as possible to the real considered processes. Generally, numerical methods are used to process this kind of study. In this paper, we propose an alternate way to process optimal Integrated Logistic Support policy determination when dealing with large, complex and distributed multi-policies industrial sites. This method is based on the use of behavioral Monte Carlo simulation, supported by Generalized Stochastic Petri Nets. (author)

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

Recent Advances in Registration, Integration and Fusion of Remotely Sensed Data: Redundant Representations and Frames

Science.gov (United States)

Czaja, Wojciech; Le Moigne-Stewart, Jacqueline

2014-01-01

In recent years, sophisticated mathematical techniques have been successfully applied to the field of remote sensing to produce significant advances in applications such as registration, integration and fusion of remotely sensed data. Registration, integration and fusion of multiple source imagery are the most important issues when dealing with Earth Science remote sensing data where information from multiple sensors, exhibiting various resolutions, must be integrated. Issues ranging from different sensor geometries, different spectral responses, differing illumination conditions, different seasons, and various amounts of noise need to be dealt with when designing an image registration, integration or fusion method. This tutorial will first define the problems and challenges associated with these applications and then will review some mathematical techniques that have been successfully utilized to solve them. In particular, we will cover topics on geometric multiscale representations, redundant representations and fusion frames, graph operators, diffusion wavelets, as well as spatial-spectral and operator-based data fusion. All the algorithms will be illustrated using remotely sensed data, with an emphasis on current and operational instruments.

Ambit processes and stochastic partial differential equations

DEFF Research Database (Denmark)

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

Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection betwe...... ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis....

Integration of stochastic generation in power systems

NARCIS (Netherlands)

Papaefthymiou, G.; Schavemaker, P.H.; Sluis, van der L.; Kling, W.L.; Kurowicka, D.; Cooke, R.M.

2006-01-01

Stochastic generation, i.e., electrical power production by an uncontrolled primary energy source, is expected to play an important role in future power systems. A new power system structure is created due to the large-scale implementation of this small-scale, distributed, non-dispatchable

Decomposing Gratitude: Representation and Integration of Cognitive Antecedents of Gratitude in the Brain.

Science.gov (United States)

Yu, Hongbo; Gao, Xiaoxue; Zhou, Yuanyuan; Zhou, Xiaolin

2018-05-23

Gratitude is a typical social-moral emotion that plays a crucial role in maintaining human cooperative interpersonal relationship. Although neural correlates of gratitude have been investigated, the neurocognitive processes that lead to gratitude, namely, the representation and integration of its cognitive antecedents, remain largely unknown. Here, we combined fMRI and a human social interactive task to investigate how benefactor's cost and beneficiary's benefit, two critical antecedents of gratitude, are encoded and integrated in beneficiary's brain, and how the neural processing of gratitude is converted to reciprocity. A coplayer decided whether to help a human participant (either male or female) avoid pain at his/her own monetary cost; the participants could transfer monetary points to the benefactor with the knowledge that the benefactor was unaware of this transfer. By independently manipulating monetary cost and the degree of pain reduction, we could identify the neural signatures of benefactor's cost and recipient's benefit and examine how they were integrated. Recipient's self-benefit was encoded in reward-sensitive regions (e.g., ventral striatum), whereas benefactor-cost was encoded in regions associated with mentalizing (e.g., temporoparietal junction). Gratitude was represented in perigenual anterior cingulate cortex (pgACC), the strength of which correlated with trait gratitude. Dynamic causal modeling showed that the neural signals representing benefactor-cost and self-benefit passed to pgACC via effective connectivities, suggesting an integrative role of pgACC in generating gratitude. Moreover, gyral ACC plays an intermediary role in converting gratitude representation into reciprocal behaviors. Our findings provide a neural mechanistic account of gratitude and its role in social-moral life. SIGNIFICANCE STATEMENT Gratitude plays an integral role in subjective well-being and harmonious interpersonal relationships. However, the neurocognitive

A concise course on stochastic partial differential equations

CERN Document Server

Prévôt, Claudia

2007-01-01

These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.

Stochastic Sizing of Energy Storage Systems for Wind Integration

Directory of Open Access Journals (Sweden)

D. D. Le

2018-06-01

Full Text Available In this paper, we present an optimal capacity decision model for energy storage systems (ESSs in combined operation with wind energy in power systems. We use a two-stage stochastic programming approach to take into account both wind and load uncertainties. The planning problem is formulated as an AC optimal power flow (OPF model with the objective of minimizing ESS installation cost and system operation cost. Stochastic wind and load inputs for the model are generated from historical data using clustering technique. The model is tested on the IEEE 39-bus system.

Wigner representation in scattering problems

International Nuclear Information System (INIS)

Remler, E.A.

1975-01-01

The basic equations of quantum scattering are translated into the Wigner representation. This puts quantum mechanics in the form of a stochastic process in phase space. Instead of complex valued wavefunctions and transition matrices, one now works with real-valued probability distributions and source functions, objects more responsive to physical intuition. Aside from writing out certain necessary basic expressions, the main purpose is to develop and stress the interpretive picture associated with this representation and to derive results used in applications published elsewhere. The quasiclassical guise assumed by the formalism lends itself particularly to approximations of complex multiparticle scattering problems is laid. The foundation for a systematic application of statistical approximations to such problems. The form of the integral equation for scattering as well as its mulitple scattering expansion in this representation are derived. Since this formalism remains unchanged upon taking the classical limit, these results also constitute a general treatment of classical multiparticle collision theory. Quantum corrections to classical propogators are discussed briefly. The basic approximation used in the Monte Carlo method is derived in a fashion that allows for future refinement and includes bound state production. The close connection that must exist between inclusive production of a bound state and of its constituents is brought out in an especially graphic way by this formalism. In particular one can see how comparisons between such cross sections yield direct physical insight into relevant production mechanisms. A simple illustration of scattering by a bound two-body system is treated. Simple expressions for single- and double-scattering contributions to total and differential cross sections, as well as for all necessary shadow corrections thereto, are obtained and compared to previous results of Glauber and Goldberger

A New Methodology for Open Pit Slope Design in Karst-Prone Ground Conditions Based on Integrated Stochastic-Limit Equilibrium Analysis

Science.gov (United States)

Zhang, Ke; Cao, Ping; Ma, Guowei; Fan, Wenchen; Meng, Jingjing; Li, Kaihui

2016-07-01

Using the Chengmenshan Copper Mine as a case study, a new methodology for open pit slope design in karst-prone ground conditions is presented based on integrated stochastic-limit equilibrium analysis. The numerical modeling and optimization design procedure contain a collection of drill core data, karst cave stochastic model generation, SLIDE simulation and bisection method optimization. Borehole investigations are performed, and the statistical result shows that the length of the karst cave fits a negative exponential distribution model, but the length of carbonatite does not exactly follow any standard distribution. The inverse transform method and acceptance-rejection method are used to reproduce the length of the karst cave and carbonatite, respectively. A code for karst cave stochastic model generation, named KCSMG, is developed. The stability of the rock slope with the karst cave stochastic model is analyzed by combining the KCSMG code and the SLIDE program. This approach is then applied to study the effect of the karst cave on the stability of the open pit slope, and a procedure to optimize the open pit slope angle is presented.

Path integration quantization

International Nuclear Information System (INIS)

DeWitt-Morette, C.

1983-01-01

Much is expected of path integration as a quantization procedure. Much more is possible if one recognizes that path integration is at the crossroad of stochastic and differential calculus and uses the full power of both stochastic and differential calculus in setting up and computing path integrals. In contrast to differential calculus, stochastic calculus has only comparatively recently become an instrument of thought. It has nevertheless already been used in a variety of challenging problems, for instance in the quantization problem. The author presents some applications of the stochastic scheme. (Auth.)

Stochastic calculus for uncoupled continuous-time random walks.

Science.gov (United States)

Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L

2009-06-01

The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingale transform theorem, if the CTRW is a martingale, the Itō integral is a martingale too. It is shown how the definition of the stochastic integrals can be used to easily compute them by Monte Carlo simulation. The relations between a CTRW, its quadratic variation, its Stratonovich integral, and its Itō integral are highlighted by numerical calculations when the jumps in space of the CTRW have a symmetric Lévy alpha -stable distribution and its waiting times have a one-parameter Mittag-Leffler distribution. Remarkably, these distributions have fat tails and an unbounded quadratic variation. In the diffusive limit of vanishing scale parameters, the probability density of this kind of CTRW satisfies the space-time fractional diffusion equation (FDE) or more in general the fractional Fokker-Planck equation, which generalizes the standard diffusion equation, solved by the probability density of the Wiener process, and thus provides a phenomenologic model of anomalous diffusion. We also provide an analytic expression for the quadratic variation of the stochastic process described by the FDE and check it by Monte Carlo.

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 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

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

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

International Nuclear Information System (INIS)

Sutrisno; Widowati; Solikhin

2016-01-01

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

Embedded data representations

DEFF Research Database (Denmark)

Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre

2017-01-01

We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles...

An h-adaptive stochastic collocation method for stochastic EMC/EMI analysis

KAUST Repository

Yücel, Abdulkadir C.

2010-07-01

The analysis of electromagnetic compatibility and interference (EMC/EMI) phenomena is often fraught by randomness in a system\\'s excitation (e.g., the amplitude, phase, and location of internal noise sources) or configuration (e.g., the routing of cables, the placement of electronic systems, component specifications, etc.). To bound the probability of system malfunction, fast and accurate techniques to quantify the uncertainty in system observables (e.g., voltages across mission-critical circuit elements) are called for. Recently proposed stochastic frameworks [1-2] combine deterministic electromagnetic (EM) simulators with stochastic collocation (SC) methods that approximate system observables using generalized polynomial chaos expansion (gPC) [3] (viz. orthogonal polynomials spanning the entire random domain) to estimate their statistical moments and probability density functions (pdfs). When constructing gPC expansions, the EM simulator is used solely to evaluate system observables at collocation points prescribed by the SC-gPC scheme. The frameworks in [1-2] therefore are non-intrusive and straightforward to implement. That said, they become inefficient and inaccurate for system observables that vary rapidly or are discontinuous in the random variables (as their representations may require very high-order polynomials). © 2010 IEEE.

Renormalization in the stochastic quantization of field theories

International Nuclear Information System (INIS)

Brunelli, J.C.

1991-01-01

In the stochastic quantization scheme of Parisi and Wu the renormalization of the stochastic theory of some models in field theory is studied. Following the path integral approach for stochastic process the 1/N expansion of the non linear sigma model is performed and, using a Ward identity obtained, from a BRS symmetry of the effective action of this formulation. It is shown the renormalizability of the model. Using the Langevin approach for stochastic process the renormalizability of the massive Thirring model is studied showing perturbatively the vanishing of the renormalization group's beta functions at finite fictitious time. (author)

Stochastic bias-correction of daily rainfall scenarios for hydrological applications

Directory of Open Access Journals (Sweden)

I. Portoghese

2011-09-01

Full Text Available The accuracy of rainfall predictions provided by climate models is crucial for the assessment of climate change impacts on hydrological processes. In fact, the presence of bias in downscaled precipitation may produce large bias in the assessment of soil moisture dynamics, river flows and groundwater recharge.

In this study, a comparison between statistical properties of rainfall observations and model control simulations from a Regional Climate Model (RCM was performed through a robust and meaningful representation of the precipitation process. The output of the adopted RCM was analysed and re-scaled exploiting the structure of a stochastic model of the point rainfall process. In particular, the stochastic model is able to adequately reproduce the rainfall intermittency at the synoptic scale, which is one of the crucial aspects for the Mediterranean environments. Possible alteration in the local rainfall regime was investigated by means of the historical daily time-series from a dense rain-gauge network, which were also used for the analysis of the RCM bias in terms of dry and wet periods and storm intensity. The result is a stochastic scheme for bias-correction at the RCM-cell scale, which produces a realistic representation of the daily rainfall intermittency and precipitation depths, though a residual bias in the storm intensity of longer storm events persists.

Experimental verification of displacement control on integrated ionic polymer-metal composite actuators with stochastic on/off controller

Science.gov (United States)

Kimura, Keishiro; Kamamichi, Norihiro

2017-04-01

An ionic polymer-metal composite (IPMC) actuator is one of polymer-based soft actuators. It is produced by chemically plating gold or platinum on both surface of a perfluorosulfonic acid membrane which is known as an ion-exchange membrane. It is able to be activated by a simple driving circuit and generate a large deformation under a low applied voltage (0.5-3 V). However, individual difference and characteristics changes from environmental conditions should be considered for realizing a stable or precise control. To solve these problems, we applied a stochastic ON/OFF controller to an integrated IPMC actuator with parallel connections. The controller consists of a central controller and distributed controllers. The central controller broadcasts a control signal such as an error signal to distributed controllers uniformly. The distributed controllers switch the ON/OFF states based on the broadcasted signal stochastically. The central controller dose not measure the states of each IPMC actuator, and the control signals is calculated by using the output signal of the integrated actuator and reference signal. The validity of the applied method was investigated through numerical simulations and experiments.

Minimal representation of matrix valued white stochastic processes and U–D factorisation of algorithms for optimal control

NARCIS (Netherlands)

Willigenburg, van L.G.; Koning, de W.L.

2013-01-01

Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic

Contour integral representations for the characters of rational conformal field theories

International Nuclear Information System (INIS)

Mukhi, S.; Panda, S.; Sen, A.

1989-01-01

We propose simple Feigin-Fuchs contour integral representations for the characters of a large class of rational conformal field theories. These include the A, D and E series SU(2) WZW theories, the A and D series c<1 minimal theories, and the k=1 SU(N) WZW theories. All these theories are characterized by the absence of the zeroes in the wronskian determinant of the characters in the interior of moduli space. This proposal is verified by several calculations. (orig.)

Computational singular perturbation analysis of stochastic chemical systems with stiffness

Science.gov (United States)

Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; Najm, Habib N.

2017-04-01

Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.

Ontology-based data integration from heterogeneous urban systems : A knowledge representation framework for smart cities

NARCIS (Netherlands)

Psyllidis, A.

2015-01-01

This paper presents a novel knowledge representation framework for smart city planning and management that enables the semantic integration of heterogeneous urban data from diverse sources. Currently, the combination of information across city agencies is cumbersome, as the increasingly available

Stochastic differential equations and a biological system

DEFF Research Database (Denmark)

Wang, Chunyan

1994-01-01

The purpose of this Ph.D. study is to explore the property of a growth process. The study includes solving and simulating of the growth process which is described in terms of stochastic differential equations. The identification of the growth and variability parameters of the process based...... on experimental data is considered. As an example, the growth of bacteria Pseudomonas fluorescens is taken. Due to the specific features of stochastic differential equations, namely that their solutions do not exist in the general sense, two new integrals - the Ito integral and the Stratonovich integral - have...... description. In order to identify the parameters, a Maximum likelihood estimation method is used together with a simplified truncated second order filter. Because of the continuity feature of the predictor equation, two numerical integration methods, called the Odeint and the Discretization method...

New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series

Directory of Open Access Journals (Sweden)

Snezhana Georgieva Gocheva-Ilieva

2013-01-01

Full Text Available There are obtained integral form and recurrence representations for some Fourier series and connected with them Favard constants. The method is based on preliminary integration of Fourier series which permits to establish general recursion formulas for Favard constants. This gives the opportunity for effective summation of infinite series and calculation of some classes of multiple singular integrals by the Favard constants.

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.

? filtering for stochastic systems driven by Poisson processes

Science.gov (United States)

Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya

2015-01-01

This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

Diagrammatical methods within the path integral representation for quantum systems

International Nuclear Information System (INIS)

Alastuey, A

2014-01-01

The path integral representation has been successfully applied to the study of equilibrium properties of quantum systems for a long time. In particular, such a representation allowed Ginibre to prove the convergence of the low-fugacity expansions for systems with short-range interactions. First, I will show that the crucial trick underlying Ginibre's proof is the introduction of an equivalent classical system made with loops. Within the Feynman-Kac formula for the density matrix, such loops naturally emerge by collecting together the paths followed by particles exchanged in a given cyclic permutation. Two loops interact via an average of two- body genuine interactions between particles belonging to different loops, while the interactions between particles inside a given loop are accounted for in a loop fugacity. It turns out that the grand-partition function of the genuine quantum system exactly reduces to its classical counterpart for the gas of loops. The corresponding so-called magic formula can be combined with standard Mayer diagrammatics for the classical gas of loops. This provides low-density representations for the quantum correlations or thermodynamical functions, which are quite useful when collective effects must be taken into account properly. Indeed, resummations and or reorganizations of Mayer graphs can be performed by exploiting their remarkable topological and combinatorial properties, while statistical weights and bonds are purely c-numbers. The interest of that method will be illustrated through a brief description of its application to two long-standing problems, namely recombination in Coulomb systems and condensation in the interacting Bose gas.

Stochastic interaction between TAE and alpha particles

International Nuclear Information System (INIS)

Krlin, L.; Pavlo, P.; Malijevsky, I.

1996-01-01

The interaction of toroidicity-induced Alfven eigenmodes with thermonuclear alpha particles in the intrinsic stochasticity regime was investigated based on the numerical integration of the equation of motion of alpha particles in the tokamak. The first results obtained for the ITER parameters and moderate wave amplitudes indicate that the stochasticity is highest in the trapped/passing boundary region, where the alpha particles jump stochastically between the two regimes with an appreciable radial excursion (about 0.5 m amplitudes). A similar chaotic behavior was also found for substantially lower energies (about 350 keV). 7 figs., 15 refs

Stochastic process variation in deep-submicron CMOS circuits and algorithms

CERN Document Server

Zjajo, Amir

2014-01-01

One of the most notable features of nanometer scale CMOS technology is the increasing magnitude of variability of the key device parameters affecting performance of integrated circuits. The growth of variability can be attributed to multiple factors, including the difficulty of manufacturing control, the emergence of new systematic variation-generating mechanisms, and most importantly, the increase in atomic-scale randomness, where device operation must be described as a stochastic process. In addition to wide-sense stationary stochastic device variability and temperature variation, existence of non-stationary stochastic electrical noise associated with fundamental processes in integrated-circuit devices represents an elementary limit on the performance of electronic circuits. In an attempt to address these issues, Stochastic Process Variation in Deep-Submicron CMOS: Circuits and Algorithms offers unique combination of mathematical treatment of random process variation, electrical noise and temperature and ne...

Binary Stochastic Representations for Large Multi-class Classification

KAUST Repository

Gerald, Thomas

2017-10-23

Classification with a large number of classes is a key problem in machine learning and corresponds to many real-world applications like tagging of images or textual documents in social networks. If one-vs-all methods usually reach top performance in this context, these approaches suffer of a high inference complexity, linear w.r.t. the number of categories. Different models based on the notion of binary codes have been proposed to overcome this limitation, achieving in a sublinear inference complexity. But they a priori need to decide which binary code to associate to which category before learning using more or less complex heuristics. We propose a new end-to-end model which aims at simultaneously learning to associate binary codes with categories, but also learning to map inputs to binary codes. This approach called Deep Stochastic Neural Codes (DSNC) keeps the sublinear inference complexity but do not need any a priori tuning. Experimental results on different datasets show the effectiveness of the approach w.r.t. baseline methods.

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...

An efficient forward-reverse expectation-maximization algorithm for statistical inference in stochastic reaction networks

KAUST Repository

Vilanova, Pedro

2016-01-01

reaction networks (SRNs). We apply this stochastic representation to the computation of efficient approximations of expected values of functionals of SRN bridges, i.e., SRNs conditional on their values in the extremes of given time-intervals. We then employ

Improving basic math skills through integrated dynamic representation strategies.

Science.gov (United States)

González-Castro, Paloma; Cueli, Marisol; Cabeza, Lourdes; Álvarez-García, David; Rodríguez, Celestino

2014-01-01

In this paper, we analyze the effectiveness of the Integrated Dynamic Representation strategy (IDR) to develop basic math skills. The study involved 72 students, aged between 6 and 8 years. We compared the development of informal basic skills (numbers, comparison, informal calculation, and informal concepts) and formal (conventionalisms, number facts, formal calculus, and formal concepts) in an experimental group (n = 35) where we applied the IDR strategy and in a Control group (n = 37) in order to identify the impact of the procedure. The experimental group improved significantly in all variables except for number facts and formal calculus. It can therefore be concluded that IDR favors the development of the skills more closely related to applied mathematics than those related to automatic mathematics and mental arithmetic.

Promoting a Shared Representation of Workers' Activities to Improve Integrated Prevention of Work-Related Musculoskeletal Disorders

Directory of Open Access Journals (Sweden)

Yves Roquelaure

2016-06-01

Full Text Available Effective and sustainable prevention of work-related musculoskeletal disorders (WR-MSDs remains a challenge for preventers and policy makers. Coordination of stakeholders involved in the prevention of WR-MSDs is a key factor that requires greater reflection on common knowledge and shared representation of workers' activities among stakeholders. Information on workers' strategies and operational leeway should be the core of common representations, because it places workers at the center of the “work situation system” considered by the intervention models. Participatory ergonomics permitting debates among stakeholders about workers' activity and strategies to cope with the work constraints in practice could help them to share representations of the “work situation system” and cooperate. Sharing representation therefore represents a useful tool for prevention, and preventers should provide sufficient space and time for dialogue and discussion of workers' activities among stakeholders during the conception, implementation, and management of integrated prevention programs.

A combined stochastic programming and optimal control approach to personal finance and pensions

DEFF Research Database (Denmark)

Konicz, Agnieszka Karolina; Pisinger, David; Rasmussen, Kourosh Marjani

2015-01-01

The paper presents a model that combines a dynamic programming (stochastic optimal control) approach and a multi-stage stochastic linear programming approach (SLP), integrated into one SLP formulation. Stochastic optimal control produces an optimal policy that is easy to understand and implement....

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.

An integrable Hamiltonian hierarchy and its constrained flows with generalized Hamiltonian regular representations, as well as its expanding integrable system

International Nuclear Information System (INIS)

Zhang Yufeng

2003-01-01

A new subalgebra of loop algebra A-tilde 2 is first constructed. It follows that an isospectral problem is established. Using Tu-pattern gives rise to a new integrable hierarchy, which possesses bi-Hamiltonian structure. As its reduction cases, the well-known standard Schrodinger equation and MKdV equation are presented, respectively. Furthermore, by making use of bi-symmetry constraints, generalized Hamiltonian regular representations for the hierarchy are obtained. At last, we obtain an expanding integrable system of this hierarchy by applying a scalar transformation between two isospectral problems and constructing a five-dimensional loop algebra G-tilde. In particular, the expanding integrable models of Schrodinger equation and MKdV equation are presented, respectively

Stochastic Parametrisations and Regime Behaviour of Atmospheric Models

Science.gov (United States)

Arnold, Hannah; Moroz, Irene; Palmer, Tim

2013-04-01

The presence of regimes is a characteristic of non-linear, chaotic systems (Lorenz, 2006). In the atmosphere, regimes emerge as familiar circulation patterns such as the El-Nino Southern Oscillation (ENSO), the North Atlantic Oscillation (NAO) and Scandinavian Blocking events. In recent years there has been much interest in the problem of identifying and studying atmospheric regimes (Solomon et al, 2007). In particular, how do these regimes respond to an external forcing such as anthropogenic greenhouse gas emissions? The importance of regimes in observed trends over the past 50-100 years indicates that in order to predict anthropogenic climate change, our climate models must be able to represent accurately natural circulation regimes, their statistics and variability. It is well established that representing model uncertainty as well as initial condition uncertainty is important for reliable weather forecasts (Palmer, 2001). In particular, stochastic parametrisation schemes have been shown to improve the skill of weather forecast models (e.g. Berner et al., 2009; Frenkel et al., 2012; Palmer et al., 2009). It is possible that including stochastic physics as a representation of model uncertainty could also be beneficial in climate modelling, enabling the simulator to explore larger regions of the climate attractor including other flow regimes. An alternative representation of model uncertainty is a perturbed parameter scheme, whereby physical parameters in subgrid parametrisation schemes are perturbed about their optimal value. Perturbing parameters gives a greater control over the ensemble than multi-model or multiparametrisation ensembles, and has been used as a representation of model uncertainty in climate prediction (Stainforth et al., 2005; Rougier et al., 2009). We investigate the effect of including representations of model uncertainty on the regime behaviour of a simulator. A simple chaotic model of the atmosphere, the Lorenz '96 system, is used to study

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

International Nuclear Information System (INIS)

Qian, Hong

2011-01-01

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

Sparse Representation Based Range-Doppler Processing for Integrated OFDM Radar-Communication Networks

Directory of Open Access Journals (Sweden)

Bo Kong

2017-01-01

Full Text Available In an integrated radar-communication network, multiuser access techniques with minimal performance degradation and without range-Doppler ambiguities are required, especially in a dense user environment. In this paper, a multiuser access scheme with random subcarrier allocation mechanism is proposed for orthogonal frequency division multiplexing (OFDM based integrated radar-communication networks. The expression of modulation Symbol-Domain method combined with sparse representation (SR for range-Doppler estimation is introduced and a parallel reconstruction algorithm is employed. The radar target detection performance is improved with less spectrum occupation. Additionally, a Doppler frequency detector is exploited to decrease the computational complexity. Numerical simulations show that the proposed method outperforms the traditional modulation Symbol-Domain method under ideal and realistic nonideal scenarios.

A modern theory of random variation with applications in stochastic calculus, financial mathematics, and Feynman integration

CERN Document Server

Muldowney, Patrick

2012-01-01

A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. I...

Numerical Analysis for Stochastic Partial Differential Delay Equations with Jumps

OpenAIRE

Li, Yan; Hu, Junhao

2013-01-01

We investigate the convergence rate of Euler-Maruyama method for a class of stochastic partial differential delay equations driven by both Brownian motion and Poisson point processes. We discretize in space by a Galerkin method and in time by using a stochastic exponential integrator. We generalize some results of Bao et al. (2011) and Jacob et al. (2009) in finite dimensions to a class of stochastic partial differential delay equations with jumps in infinite dimensions.

Design Of Combined Stochastic Feedforward/Feedback Control

Science.gov (United States)

Halyo, Nesim

1989-01-01

Methodology accommodates variety of control structures and design techniques. In methodology for combined stochastic feedforward/feedback control, main objectives of feedforward and feedback control laws seen clearly. Inclusion of error-integral feedback, dynamic compensation, rate-command control structure, and like integral element of methodology. Another advantage of methodology flexibility to develop variety of techniques for design of feedback control with arbitrary structures to obtain feedback controller: includes stochastic output feedback, multiconfiguration control, decentralized control, or frequency and classical control methods. Control modes of system include capture and tracking of localizer and glideslope, crab, decrab, and flare. By use of recommended incremental implementation, control laws simulated on digital computer and connected with nonlinear digital simulation of aircraft and its systems.

Dynamic and stochastic multi-project planning

CERN Document Server

Melchiors, Philipp

2015-01-01

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

Scheduling of Power System Cells Integrating Stochastic Power Generation

International Nuclear Information System (INIS)

Costa, L.M.

2008-12-01

Energy supply and climate change are nowadays two of the most outstanding problems which societies have to cope with under a context of increasing energy needs. Public awareness of these problems is driving political willingness to take actions for tackling them in a swift and efficient manner. Such actions mainly focus in increasing energy efficiency, in decreasing dependence on fossil fuels, and in reducing greenhouse gas emissions. In this context, power systems are undergoing important changes in the way they are planned and managed. On the one hand, vertically integrated structures are being replaced by market structures in which power systems are un-bundled. On the other, power systems that once relied on large power generation facilities are witnessing the end of these facilities' life-cycle and, consequently, their decommissioning. The role of distributed energy resources such as wind and solar power generators is becoming increasingly important in this context. However, the large-scale integration of such type of generation presents many challenges due, for instance, to the uncertainty associated to the variability of their production. Nevertheless, advanced forecasting tools may be combined with more controllable elements such as energy storage devices, gas turbines, and controllable loads to form systems that aim to reduce the impacts that may be caused by these uncertainties. This thesis addresses the management under market conditions of these types of systems that act like independent societies and which are herewith named power system cells. From the available literature, a unified view of power system scheduling problems is also proposed as a first step for managing sets of power system cells in a multi-cell management framework. Then, methodologies for performing the optimal day-ahead scheduling of single power system cells are proposed, discussed and evaluated under both a deterministic and a stochastic framework that directly integrates the

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

The Schrödinger–Robinson inequality from stochastic analysis on a complex Hilbert space

International Nuclear Information System (INIS)

Khrennikov, Andrei

2013-01-01

We explored the stochastic analysis on a complex Hilbert space to show that one of the cornerstones of quantum mechanics (QM), namely Heisenberg's uncertainty relation, can be derived in the classical probabilistic framework. We created a new mathematical representation of quantum averages: as averages with respect to classical random fields. The existence of a classical stochastic model matching with Heisenberg's uncertainty relation makes the connection between classical and quantum probabilistic models essentially closer. In real physical situations, random fields are valued in the L 2 -space. Hence, although we model QM and not QFT, the classical systems under consideration have an infinite number of degrees of freedom. And in our modeling, infinite-dimensional stochastic analysis is the basic mathematical tool. (comment)

Inadequacy representation of flamelet-based RANS model for turbulent non-premixed flame

Science.gov (United States)

Lee, Myoungkyu; Oliver, Todd; Moser, Robert

2017-11-01

Stochastic representations for model inadequacy in RANS-based models of non-premixed jet flames are developed and explored. Flamelet-based RANS models are attractive for engineering applications relative to higher-fidelity methods because of their low computational costs. However, the various assumptions inherent in such models introduce errors that can significantly affect the accuracy of computed quantities of interest. In this work, we develop an approach to represent the model inadequacy of the flamelet-based RANS model. In particular, we pose a physics-based, stochastic PDE for the triple correlation of the mixture fraction. This additional uncertain state variable is then used to construct perturbations of the PDF for the instantaneous mixture fraction, which is used to obtain an uncertain perturbation of the flame temperature. A hydrogen-air non-premixed jet flame is used to demonstrate the representation of the inadequacy of the flamelet-based RANS model. This work was supported by DARPA-EQUiPS(Enabling Quantification of Uncertainty in Physical Systems) program.

Stochastic thermodynamics

Science.gov (United States)

Eichhorn, Ralf; Aurell, Erik

2014-04-01

theory for small deviations from equilibrium, in which a general framework is constructed from the analysis of non-equilibrium states close to equilibrium. In a next step, Prigogine and others developed linear irreversible thermodynamics, which establishes relations between transport coefficients and entropy production on a phenomenological level in terms of thermodynamic forces and fluxes. However, beyond the realm of linear response no general theoretical results were available for quite a long time. This situation has changed drastically over the last 20 years with the development of stochastic thermodynamics, revealing that the range of validity of thermodynamic statements can indeed be extended deep into the non-equilibrium regime. Early developments in that direction trace back to the observations of symmetry relations between the probabilities for entropy production and entropy annihilation in non-equilibrium steady states [5-8] (nowadays categorized in the class of so-called detailed fluctuation theorems), and the derivations of the Bochkov-Kuzovlev [9, 10] and Jarzynski relations [11] (which are now classified as so-called integral fluctuation theorems). Apart from its fundamental theoretical interest, the developments in stochastic thermodynamics have experienced an additional boost from the recent experimental progress in fabricating, manipulating, controlling and observing systems on the micro- and nano-scale. These advances are not only of formidable use for probing and monitoring biological processes on the cellular, sub-cellular and molecular level, but even include the realization of a microscopic thermodynamic heat engine [12] or the experimental verification of Landauer's principle in a colloidal system [13]. The scientific program Stochastic Thermodynamics held between 4 and 15 March 2013, and hosted by The Nordic Institute for Theoretical Physics (Nordita), was attended by more than 50 scientists from the Nordic countries and elsewhere, amongst them

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.

Neuro-Inspired Computing with Stochastic Electronics

KAUST Repository

Naous, Rawan

2016-01-06

The extensive scaling and integration within electronic systems have set the standards for what is addressed to as stochastic electronics. The individual components are increasingly diverting away from their reliable behavior and producing un-deterministic outputs. This stochastic operation highly mimics the biological medium within the brain. Hence, building on the inherent variability, particularly within novel non-volatile memory technologies, paves the way for unconventional neuromorphic designs. Neuro-inspired networks with brain-like structures of neurons and synapses allow for computations and levels of learning for diverse recognition tasks and applications.

Day-ahead stochastic economic dispatch of wind integrated power system considering demand response of residential hybrid energy system

International Nuclear Information System (INIS)

Jiang, Yibo; Xu, Jian; Sun, Yuanzhang; Wei, Congying; Wang, Jing; Ke, Deping; Li, Xiong; Yang, Jun; Peng, Xiaotao; Tang, Bowen

2017-01-01

Highlights: • Improving the utilization of wind power by the demand response of residential hybrid energy system. • An optimal scheduling of home energy management system integrating micro-CHP. • The scattered response capability of consumers is aggregated by demand bidding curve. • A stochastic day-ahead economic dispatch model considering demand response and wind power. - Abstract: As the installed capacity of wind power is growing, the stochastic variability of wind power leads to the mismatch of demand and generated power. Employing the regulating capability of demand to improve the utilization of wind power has become a new research direction. Meanwhile, the micro combined heat and power (micro-CHP) allows residential consumers to choose whether generating electricity by themselves or purchasing from the utility company, which forms a residential hybrid energy system. However, the impact of the demand response with hybrid energy system contained micro-CHP on the large-scale wind power utilization has not been analyzed quantitatively. This paper proposes an operation optimization model of the residential hybrid energy system based on price response, integrating micro-CHP and smart appliances intelligently. Moreover, a novel load aggregation method is adopted to centralize scattered response capability of residential load. At the power grid level, a day-ahead stochastic economic dispatch model considering demand response and wind power is constructed. Furthermore, simulation is conducted respectively on the modified 6-bus system and IEEE 118-bus system. The results show that with the method proposed, the wind power curtailment of the system decreases by 78% in 6-bus system. In the meantime, the energy costs of residential consumers and the operating costs of the power system reduced by 10.7% and 11.7% in 118-bus system, respectively.

Astronomy: Social Representations of the Integrated High School Students and Graduates in Physics

Science.gov (United States)

Barbosa, J. I. L.

The topics related to Astronomy are spread through almost all levels of basic education in Brazil and are also disseminated through the mass media, activities that do not always occur in the proper way. However, their students form their explanations about the phenomena studied by Astronomy, that is, they begin to construct their opinions, their beliefs and their attitudes regarding this object or this situation. In this sense, this work was divided in two fronts, which have the following objectives: (1) To identify the social representations of Astronomy elaborated by students of Integrated secondary education and undergraduate students in Physics; (2) To verify to what extent the social representations developed by the investigated students are equivalent; (3) To Investigate if the social representations designed per undergraduate students in Physics about Astronomy undergo changes after these participate in a course on basic subjects of Astronomy, in comparison with those exposed before the mentioned event. On the first front there is a research of a basic nature, where the data were obtained through of survey, and analysed in accordance with the methodologies pertinent to Central Nucleus Theory, the second front deals with an investigation of an applied nature, and the data obtained were explored through statistical analyses. The results indicate that the researchers have been involved in social representations of the object Astronomy, which are based on elements of the formal education space, and also disclosed in the media, in addition, demonstrate that the students have information about Astronomy and a valuation position in relation to this Science. On the second front, the results indicate that there were changes in the social representations of the undergraduate students in Physics about the term inductor Astronomy, after the course, that is, several elements evoked before the course were replaced by others, which were worked during the event.

Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

Science.gov (United States)

Marrero-Ponce, Yovani; Martínez-Albelo, Eugenio R; Casañola-Martín, Gerardo M; Castillo-Garit, Juan A; Echevería-Díaz, Yunaimy; Zaldivar, Vicente Romero; Tygat, Jan; Borges, José E Rodriguez; García-Domenech, Ramón; Torrens, Francisco; Pérez-Giménez, Facundo

2010-11-01

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity

Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models

Energy Technology Data Exchange (ETDEWEB)

Niccoli, G.

2009-12-15

In an earlier paper (G. Niccoli and J. Teschner, 2009), the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This characterization for cyclic representations has been derived by the use of the Separation of Variables (SOV) method of Sklyanin and by the direct construction of the Baxter Q-operator family. Here, we reconstruct the Baxter Q-operator and the same characterization of the spectrum by only using the SOV method. This analysis allows us to deduce the main features required for the extension to cyclic representations of other integrable quantum models of this kind of spectrum characterization. (orig.)

Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models

International Nuclear Information System (INIS)

Niccoli, G.

2009-12-01

In an earlier paper (G. Niccoli and J. Teschner, 2009), the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This characterization for cyclic representations has been derived by the use of the Separation of Variables (SOV) method of Sklyanin and by the direct construction of the Baxter Q-operator family. Here, we reconstruct the Baxter Q-operator and the same characterization of the spectrum by only using the SOV method. This analysis allows us to deduce the main features required for the extension to cyclic representations of other integrable quantum models of this kind of spectrum characterization. (orig.)

On the path integral representation of the Wigner function and the Barker–Murray ansatz

International Nuclear Information System (INIS)

Sels, Dries; Brosens, Fons; Magnus, Wim

2012-01-01

The propagator of the Wigner function is constructed from the Wigner–Liouville equation as a phase space path integral over a new effective Lagrangian. In contrast to a paper by Barker and Murray (1983) , we show that the path integral can in general not be written as a linear superposition of classical phase space trajectories over a family of non-local forces. Instead, we adopt a saddle point expansion to show that the semiclassical Wigner function is a linear superposition of classical solutions for a different set of non-local time dependent forces. As shown by a simple example the specific form of the path integral makes the formulation ideal for Monte Carlo simulation. -- Highlights: ► We derive the quantum mechanical propagator of the Wigner function in the path integral representation. ► We show that the Barker–Murray ansatz is incomplete, explain the error and provide an alternative. ► An example of a Monte Carlo simulation of the semiclassical path integral is included.

Stochastic flows in the Brownian web and net

Czech Academy of Sciences Publication Activity Database

Schertzer, E.; Sun, R.; Swart, Jan M.

2014-01-01

Roč. 227, č. 1065 (2014), s. 1-160 ISSN 0065-9266 R&D Projects: GA ČR GA201/07/0237; GA ČR GA201/09/1931 Institutional support: RVO:67985556 Keywords : Brownian web * Brownian net * stochastic flow of kernels * measure-valued process * Howitt-Warren flow * linear system * random walk in random environment * finite graph representation Subject RIV: BA - General Mathematics Impact factor: 1.727, year: 2014 http://library.utia.cas.cz/separaty/2013/SI/swart-0396636.pdf

Stochastic and infinite dimensional analysis

CERN Document Server

Carpio-Bernido, Maria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria; Silva, José

2016-01-01

This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.

Aspects of a representation of quantum theory in terms of classical probability theory by means of integration in Hilbert space

International Nuclear Information System (INIS)

Bach, A.

1981-01-01

A representation of quantum mechanics in terms of classical probability theory by means of integration in Hilbert space is discussed. This formal hidden-variables representation is analysed in the context of impossibility proofs concerning hidden-variables theories. The structural analogy of this formulation of quantum theory with classical statistical mechanics is used to elucidate the difference between classical mechanics and quantum mechanics. (author)

Stochastic synchronization in finite size spiking networks

Science.gov (United States)

Doiron, Brent; Rinzel, John; Reyes, Alex

2006-09-01

We study a stochastic synchronization of spiking activity in feedforward networks of integrate-and-fire model neurons. A stochastic mean field analysis shows that synchronization occurs only when the network size is sufficiently small. This gives evidence that the dynamics, and hence processing, of finite size populations can be drastically different from that observed in the infinite size limit. Our results agree with experimentally observed synchrony in cortical networks, and further strengthen the link between synchrony and propagation in cortical systems.

A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach for contaminated sites management

Energy Technology Data Exchange (ETDEWEB)

Hu, Yan; Wen, Jing-ya; Li, Xiao-li; Wang, Da-zhou; Li, Yu, E-mail: liyuxx8@hotmail.com

2013-10-15

Highlights: • Using interval mathematics to describe spatial and temporal variability and parameter uncertainty. • Using fuzzy theory to quantify variability of environmental guideline values. • Using probabilistic approach to integrate interval concentrations and fuzzy environmental guideline. • Establishment of dynamic multimedia environmental integrated risk assessment framework. -- Abstract: A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach was developed for contaminated sites management. The contaminant concentrations were simulated by a validated interval dynamic multimedia fugacity model, and different guideline values for the same contaminant were represented as a fuzzy environmental guideline. Then, the probability of violating environmental guideline (Pv) can be determined by comparison between the modeled concentrations and the fuzzy environmental guideline, and the constructed relationship between the Pvs and environmental risk levels was used to assess the environmental risk level. The developed approach was applied to assess the integrated environmental risk at a case study site in China, simulated from 1985 to 2020. Four scenarios were analyzed, including “residential land” and “industrial land” environmental guidelines under “strict” and “loose” strictness. It was found that PAH concentrations will increase steadily over time, with soil found to be the dominant sink. Source emission in soil was the leading input and atmospheric sedimentation was the dominant transfer process. The integrated environmental risks primarily resulted from petroleum spills and coke ovens, while the soil environmental risks came from coal combustion. The developed approach offers an effective tool for quantifying variability and uncertainty in the dynamic multimedia integrated environmental risk assessment and the contaminated site management.

A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach for contaminated sites management

International Nuclear Information System (INIS)

Hu, Yan; Wen, Jing-ya; Li, Xiao-li; Wang, Da-zhou; Li, Yu

2013-01-01

Highlights: • Using interval mathematics to describe spatial and temporal variability and parameter uncertainty. • Using fuzzy theory to quantify variability of environmental guideline values. • Using probabilistic approach to integrate interval concentrations and fuzzy environmental guideline. • Establishment of dynamic multimedia environmental integrated risk assessment framework. -- Abstract: A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach was developed for contaminated sites management. The contaminant concentrations were simulated by a validated interval dynamic multimedia fugacity model, and different guideline values for the same contaminant were represented as a fuzzy environmental guideline. Then, the probability of violating environmental guideline (Pv) can be determined by comparison between the modeled concentrations and the fuzzy environmental guideline, and the constructed relationship between the Pvs and environmental risk levels was used to assess the environmental risk level. The developed approach was applied to assess the integrated environmental risk at a case study site in China, simulated from 1985 to 2020. Four scenarios were analyzed, including “residential land” and “industrial land” environmental guidelines under “strict” and “loose” strictness. It was found that PAH concentrations will increase steadily over time, with soil found to be the dominant sink. Source emission in soil was the leading input and atmospheric sedimentation was the dominant transfer process. The integrated environmental risks primarily resulted from petroleum spills and coke ovens, while the soil environmental risks came from coal combustion. The developed approach offers an effective tool for quantifying variability and uncertainty in the dynamic multimedia integrated environmental risk assessment and the contaminated site management

Geometro-stochastic quantization of gauge fields in curved space-time

International Nuclear Information System (INIS)

Prugovecki, E.

1988-01-01

It is shown that the geometro-stochastic method of quantization of massive fields in curved space-time can be extended to the massless cases of electromagnetic fields and general Yang-Mills fields. The Fock fibres of the massive case are replaced in the present context by fibres with indefinite inner products, such as Gupta-Bleuler fibres in the electromagnetic case. The quantum space-time form factor used in the massive case gives rise in the present case to quantum gauge frames whose elements are generalized coherent states corresponding to pseudounitary spin-one representations of direct products of the Poincare group with the U(1), SU(N) or other internal gauge groups. Quantum connections are introduced on bundles of second-quantized frames, and the corresponding parallel transport is expressed in terms of path integrals for quantum frame propagators. In the Yang-Mills case, these path integral make use of Faddeev-Popov quantum frames. It is shown, however, that in the present framework the ghost fields that give rise to these frames possess a geometric interpretation related to the presence of a super-gauge group that, in addition to the external Poincare and Yang-Mills gauge degrees of freedom, involves also the internal ones related to choices of gauge bases within the quantum fibres

Differential and integral comparisons of three representations of the prompt neutron spectrum for the spontaneous fission of 252Cf

International Nuclear Information System (INIS)

Madland, D.G.; LaBauve, R.J.; Nix, J.R.

1984-01-01

Because of their importance as neutron standards, we present comparisons of measured and calculated prompt fission neutron spectra N(E) and average prompt neutron multiplicities anti nu/sub p/ for the spontaneous fission of 252 Cf. In particular, we test three representations of N(E) against recent experimental measurements of the differential spectrum and threshold integral cross sections. These representations are the Maxwellian spectrum, the NBS spectrum, and the Los Alamos spectrum of Madland and Nix. For the Maxwellian spectrum, we obtain the value of the Maxwellian temperature T/sub M/ by a least-squares adjustment to the experimental differential spectrum of Poenitz and Tamura. For the Los Alamos spectrum, a similar least-squares adjustment determines the nuclear level-density parameter a, which is the single unknown parameter that appears. The NBS spectrum has been previously constructed by adjustments to eight differential spectra measured during the period 1965 to 1974. Among these three representations, we find that the Los Alamos spectrum best reproduces both the differential and integral measurements, assuming ENDF/B-V cross sections in the calculation of the latter. Although the NBS spectrum reproduces the integral measurements fairly well, it fails to satisfactorily reproduce the new differential measurement, and the Maxwellian spectrum fails to satisfactorily reproduce the integral measurements. Additionally, we calculate a value of anti nu/sub p/ from the Los Alamos theory that is within approximately 1% of experiment. 25 references

Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. III. Exact stochastic path integral evaluation.

Science.gov (United States)

Moix, Jeremy M; Ma, Jian; Cao, Jianshu

2015-03-07

A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators, one can also immediately compute energy transfer rates using the multi-chromophoric Förster resonant energy transfer formalism. Benchmark calculations on the emission spectra of two level systems are presented demonstrating the efficacy of the stochastic approach. This is followed by calculations of the energy transfer rates between two weakly coupled dimer systems as a function of temperature and system-bath coupling strength. It is shown that the recently developed hybrid cumulant expansion (see Paper II) is the only perturbative method capable of generating uniformly reliable energy transfer rates and emission spectra across a broad range of system parameters.

Optimal control of stochastic difference Volterra equations an introduction

CERN Document Server

Shaikhet, Leonid

2015-01-01

This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equation...

An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

Science.gov (United States)

Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

2005-12-01

We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs.

An exact line integral representation of the physical optics scattered field: the case of a perfectly conducting polyhedral structure illuminated by electric Hertzian dipoles

DEFF Research Database (Denmark)

Johansen, Peter M.; Breinbjerg, Olav

1995-01-01

An exact line integral representation of the electric physical optics scattered field is presented. This representation applies to scattering configurations with perfectly electrically conducting polyhedral structures illuminated by a finite number of electric Hertzian dipoles. The positions...

Compensating Level-Dependent Frequency Representation in Auditory Cortex by Synaptic Integration of Corticocortical Input.

Directory of Open Access Journals (Sweden)

Max F K Happel

Full Text Available Robust perception of auditory objects over a large range of sound intensities is a fundamental feature of the auditory system. However, firing characteristics of single neurons across the entire auditory system, like the frequency tuning, can change significantly with stimulus intensity. Physiological correlates of level-constancy of auditory representations hence should be manifested on the level of larger neuronal assemblies or population patterns. In this study we have investigated how information of frequency and sound level is integrated on the circuit-level in the primary auditory cortex (AI of the Mongolian gerbil. We used a combination of pharmacological silencing of corticocortically relayed activity and laminar current source density (CSD analysis. Our data demonstrate that with increasing stimulus intensities progressively lower frequencies lead to the maximal impulse response within cortical input layers at a given cortical site inherited from thalamocortical synaptic inputs. We further identified a temporally precise intercolumnar synaptic convergence of early thalamocortical and horizontal corticocortical inputs. Later tone-evoked activity in upper layers showed a preservation of broad tonotopic tuning across sound levels without shifts towards lower frequencies. Synaptic integration within corticocortical circuits may hence contribute to a level-robust representation of auditory information on a neuronal population level in the auditory cortex.

An integrated stochastic environmental risk assessment method and its application to a petroleum-contaminated site

International Nuclear Information System (INIS)

Liu, L.; Fuller, G.A.; Huang, G.H.

1999-01-01

Contamination of soil and water and the resulting threat to public health and the environment are the frequent results of oil spills, leaks and other releases of gasoline, diesel fuel, heating oil and other petroleum products. Integrating an analytical groundwater solute transport model within its general framework, this paper proposes an integrated stochastic risk assessment method and ways to apply it to petroleum-contaminated sites. Both the analytical solute transport model and the general risk assessment framework are solved by the Monte Carlo simulation technique for approaching the theoretical output distribution. Results of this study show that the total cancer risk has approximately log-normal distribution, irrespective of the fact that a variety of distributions were used to define the related parameters. It is claimed that the method can improve the effectiveness of the risk assessment for subsurface, and provide useful result for site remediation decisions. 23 refs., 3 tabs., 4 figs

Integral Representation of the Pictorial Proof of Sum of [superscript n][subscript k=1]k[superscript 2] = 1/6n(n+1)(2n+1)

Science.gov (United States)

Kobayashi, Yukio

2011-01-01

The pictorial proof of the sum of [superscript n][subscript k=1] k[superscript 2] = 1/6n(n+1)(2n+1) is represented in the form of an integral. The integral representations are also applicable to the sum of [superscript n][subscript k-1] k[superscript m] (m greater than or equal to 3). These representations reveal that the sum of [superscript…

Analytical Assessment for Transient Stability Under Stochastic Continuous Disturbances

Energy Technology Data Exchange (ETDEWEB)

Ju, Ping [Hohai Univ., Nanjing (China); Li, Hongyu [Hohai Univ., Nanjing (China); Gan, Chun [The Univ. of Tennessee, Knoxville, TN (United States); Liu, Yong [The Univ. of Tennessee, Knoxville, TN (United States); Yu, Yiping [Hohai Univ., Nanjing (China); Liu, Yilu [Univ. of Tennessee, Knoxville, TN (United States)

2017-06-28

Here, with the growing integration of renewable power generation, plug-in electric vehicles, and other sources of uncertainty, increasing stochastic continuous disturbances are brought to power systems. The impact of stochastic continuous disturbances on power system transient stability attracts significant attention. To address this problem, this paper proposes an analytical assessment method for transient stability of multi-machine power systems under stochastic continuous disturbances. In the proposed method, a probability measure of transient stability is presented and analytically solved by stochastic averaging. Compared with the conventional method (Monte Carlo simulation), the proposed method is many orders of magnitude faster, which makes it very attractive in practice when many plans for transient stability must be compared or when transient stability must be analyzed quickly. Also, it is found that the evolution of system energy over time is almost a simple diffusion process by the proposed method, which explains the impact mechanism of stochastic continuous disturbances on transient stability in theory.

A Stochastic Flows Approach for Asset Allocation with Hidden Economic Environment

Directory of Open Access Journals (Sweden)

Tak Kuen Siu

2015-01-01

Full Text Available An optimal asset allocation problem for a quite general class of utility functions is discussed in a simple two-state Markovian regime-switching model, where the appreciation rate of a risky share changes over time according to the state of a hidden economy. As usual, standard filtering theory is used to transform a financial model with hidden information into one with complete information, where a martingale approach is applied to discuss the optimal asset allocation problem. Using a martingale representation coupled with stochastic flows of diffeomorphisms for the filtering equation, the integrand in the martingale representation is identified which gives rise to an optimal portfolio strategy under some differentiability conditions.

Assessment of the Impact of Stochastic Day-Ahead SCUC on Economic and Reliability Metrics at Multiple Timescales: Preprint

Energy Technology Data Exchange (ETDEWEB)

Wu, H.; Ela, E.; Krad, I.; Florita, A.; Zhang, J.; Hodge, B. M.; Ibanez, E.; Gao, W.

2015-03-01

This paper incorporates the stochastic day-ahead security-constrained unit commitment (DASCUC) within a multi-timescale, multi-scheduling application with commitment, dispatch, and automatic generation control. The stochastic DASCUC is solved using a progressive hedging algorithm with constrained ordinal optimization to accelerate the individual scenario solution. Sensitivity studies are performed in the RTS-96 system, and the results show how this new scheduling application would impact costs and reliability with a closer representation of timescales of system operations in practice.

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 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

Fuzzy Itand#244; Integral Driven by a Fuzzy Brownian Motion

Directory of Open Access Journals (Sweden)

Didier Kumwimba Seya

2015-11-01

Full Text Available In this paper we take into account the fuzzy stochastic integral driven by fuzzy Brownian motion. To define the metric between two fuzzy numbers and to take into account the limit of a sequence of fuzzy numbers, we invoke the Hausdorff metric. First this fuzzy stochastic integral is constructed for fuzzy simple stochastic functions, then the construction is done for fuzzy stochastic integrable functions.

Some continual integrals from gaussian forms

International Nuclear Information System (INIS)

Mazmanishvili, A.S.

1985-01-01

The result summary of continual integration of gaussian functional type is given. The summary contains 124 continual integrals which are the mathematical expectation of the corresponding gaussian form by the continuum of random trajectories of four types: real-valued Ornstein-Uhlenbeck process, Wiener process, complex-valued Ornstein-Uhlenbeck process and the stochastic harmonic one. The summary includes both the known continual integrals and the unpublished before integrals. Mathematical results of the continual integration carried in the work may be applied in the problem of the theory of stochastic process, approaching to the finding of mean from gaussian forms by measures generated by the pointed stochastic processes

A General Representation Theorem for Integrated Vector Autoregressive Processes

DEFF Research Database (Denmark)

Franchi, Massimo

We study the algebraic structure of an I(d) vector autoregressive process, where d is restricted to be an integer. This is useful to characterize its polynomial cointegrating relations and its moving average representation, that is to prove a version of the Granger representation theorem valid...

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

Science.gov (United States)

Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M

2016-12-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

Stochastic representation of fire behavior in a wildland fire protection planning model for California.

Science.gov (United States)

J. Keith Gilless; Jeremy S. Fried

1998-01-01

A fire behavior module was developed for the California Fire Economics Simulator version 2 (CFES2), a stochastic simulation model of initial attack on wildland fire used by the California Department of Forestry and Fire Protection. Fire rate of spread (ROS) and fire dispatch level (FDL) for simulated fires "occurring" on the same day are determined by making...

The fermion stochastic calculus I

International Nuclear Information System (INIS)

Streater, R.F.

1984-01-01

The author describes the stochastic calculus of quantum processes with fermions. After a description of the Clifford algebra as the csup(*)-algebra generated by spinor fields the damped harmonic oscillator with quantum noise is considered as example. Then the Clifford process is described. Finally the Ito-Clifford integral and the Ito-Clifford isometry are presented. (HSI)

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

International Nuclear Information System (INIS)

Zhu, Zhiwen; Zhang, Qingxin; Xu, Jia

2014-01-01

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

Efficient stochastic EMC/EMI analysis using HDMR-generated surrogate models

KAUST Repository

Yücel, Abdulkadir C.

2011-08-01

Stochastic methods have been used extensively to quantify effects due to uncertainty in system parameters (e.g. material, geometrical, and electrical constants) and/or excitation on observables pertinent to electromagnetic compatibility and interference (EMC/EMI) analysis (e.g. voltages across mission-critical circuit elements) [1]. In recent years, stochastic collocation (SC) methods, especially those leveraging generalized polynomial chaos (gPC) expansions, have received significant attention [2, 3]. SC-gPC methods probe surrogate models (i.e. compact polynomial input-output representations) to statistically characterize observables. They are nonintrusive, that is they use existing deterministic simulators, and often cost only a fraction of direct Monte-Carlo (MC) methods. Unfortunately, SC-gPC-generated surrogate models often lack accuracy (i) when the number of uncertain/random system variables is large and/or (ii) when the observables exhibit rapid variations. © 2011 IEEE.

A representation independent propagator. Pt. 1. Compact Lie groups

International Nuclear Information System (INIS)

Tome, W.A.

1995-01-01

Conventional path integral expressions for propagators are representation dependent. Rather than having to adapt each propagator to the representation in question, it is shown that for compact Lie groups it is possible to introduce a propagator that is representation independent. For a given set of kinematical variables this propagator is a single function independent of any particular choice of fiducial vector, which monetheless, correctly propagates each element of the coherent state representation associated with these kinematical variables. Although the configuration space is in general curved, nevertheless the lattice phase-space path integral for the representation independent propagator has the form appropriate to flat space. To illustrate the general theory a representation independent propagator is explicitly constructed for the Lie group SU(2). (orig.)

Capacity expansion of stochastic power generation under two-stage electricity markets

DEFF Research Database (Denmark)

Pineda, Salvador; Morales González, Juan Miguel

2016-01-01

are first formulated from the standpoint of a social planner to characterize a perfectly competitive market. We investigate the effect of two paradigmatic market designs on generation expansion planning: a day-ahead market that is cleared following a conventional cost merit-order principle, and an ideal...... of stochastic power generating units. This framework includes the explicit representation of a day-ahead and a balancing market-clearing mechanisms to properly capture the impact of forecast errors of power production on the short-term operation of a power system. The proposed generation expansion problems...... market-clearing procedure that determines day-ahead dispatch decisions accounting for their impact on balancing operation costs. Furthermore, we reformulate the proposed models to determine the optimal expansion decisions that maximize the profit of a collusion of stochastic power producers in order...

Uncertainty Representation and Interpretation in Model-Based Prognostics Algorithms Based on Kalman Filter Estimation

Science.gov (United States)

Galvan, Jose Ramon; Saxena, Abhinav; Goebel, Kai Frank

2012-01-01

This article discusses several aspects of uncertainty representation and management for model-based prognostics methodologies based on our experience with Kalman Filters when applied to prognostics for electronics components. In particular, it explores the implications of modeling remaining useful life prediction as a stochastic process, and how it relates to uncertainty representation, management and the role of prognostics in decision-making. A distinction between the interpretations of estimated remaining useful life probability density function is explained and a cautionary argument is provided against mixing interpretations for two while considering prognostics in making critical decisions.

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.

Stochastic chemical kinetics theory and (mostly) systems biological applications

CERN Document Server

Érdi, Péter; Lente, Gabor

2014-01-01

This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory. In recent years, due to the development in experimental techniques, such as optical imaging, single cell analysis, and fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly been available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods.

Distributed parallel computing in stochastic modeling of groundwater systems.

Science.gov (United States)

Dong, Yanhui; Li, Guomin; Xu, Haizhen

2013-03-01

Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.

Stochastic structure of annual discharges of large European rivers

Directory of Open Access Journals (Sweden)

Stojković Milan

2015-03-01

Full Text Available Water resource has become a guarantee for sustainable development on both local and global scales. Exploiting water resources involves development of hydrological models for water management planning. In this paper we present a new stochastic model for generation of mean annul flows. The model is based on historical characteristics of time series of annual flows and consists of the trend component, long-term periodic component and stochastic component. The rest of specified components are model errors which are represented as a random time series. The random time series is generated by the single bootstrap model (SBM. Stochastic ensemble of error terms at the single hydrological station is formed using the SBM method. The ultimate stochastic model gives solutions of annual flows and presents a useful tool for integrated river basin planning and water management studies. The model is applied for ten large European rivers with long observed period. Validation of model results suggests that the stochastic flows simulated by the model can be used for hydrological simulations in river basins.

ARIMA-Based Time Series Model of Stochastic Wind Power Generation

DEFF Research Database (Denmark)

Chen, Peiyuan; Pedersen, Troels; Bak-Jensen, Birgitte

2010-01-01

This paper proposes a stochastic wind power model based on an autoregressive integrated moving average (ARIMA) process. The model takes into account the nonstationarity and physical limits of stochastic wind power generation. The model is constructed based on wind power measurement of one year from...... the Nysted offshore wind farm in Denmark. The proposed limited-ARIMA (LARIMA) model introduces a limiter and characterizes the stochastic wind power generation by mean level, temporal correlation and driving noise. The model is validated against the measurement in terms of temporal correlation...... and probability distribution. The LARIMA model outperforms a first-order transition matrix based discrete Markov model in terms of temporal correlation, probability distribution and model parameter number. The proposed LARIMA model is further extended to include the monthly variation of the stochastic wind power...

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)

A time use survey derived integrative human-physical household system energy performance model

Energy Technology Data Exchange (ETDEWEB)

Chiou, Y.S. [Carnegie Mellon Univ., Pittsburgh, PA (United States). School of Architecture

2009-07-01

This paper reported on a virtual experiment that extrapolated the stochastic yet patterned behaviour of the integrative model of a 4-bedroom house in Chicago with 4 different household compositions. The integrative household system theory considers the household as a combination of 2 sub-systems, notably the physical system and the human system. The physical system is the materials and devices of a dwelling, and the human system is the occupants that live within the dwelling. A third element is the environment that influences the operation of the 2 sub-systems. The human-physical integrative household energy model provided a platform to simulate the effect of sub-house energy conservation measures. The virtual experiment showed that the use of the bootstrap sampling approach on American Time Use Survey (ATUS) data to determine the occupant's stochastic energy consumption behaviour has resulted in a robust complex system model. Bell-shaped distributions were presented for annual appliance, heating and cooling load demands. The virtual experiment also pointed to the development of advanced multi-zone residential HVAC system as a suitable strategy for major residential energy efficiency improvement. The load profiles generated from the integrative model simulation were found to be in good agreement with those from field studies. It was concluded that the behaviour of the integrative model is a good representation of the energy consumption behaviour of real households. 10 refs., 4 tabs., 12 figs.

Lattice design of the integrable optics test accelerator and optical stochastic cooling experiment at Fermilab

Energy Technology Data Exchange (ETDEWEB)

Kafka, Gene [Illinois Inst. of Technology, Chicago, IL (United States)

2015-05-01

The Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab will serve as the backbone for a broad spectrum of Advanced Accelerator R&D (AARD) experiments, and as such, must be designed with signi cant exibility in mind, but without compromising cost e ciency. The nonlinear experiments at IOTA will include: achievement of a large nonlinear tune shift/spread without degradation of dynamic aperture; suppression of strong lattice resonances; study of stability of nonlinear systems to perturbations; and studies of di erent variants of nonlinear magnet design. The ring optics control has challenging requirements that reach or exceed the present state of the art. The development of a complete self-consistent design of the IOTA ring optics, meeting the demands of all planned AARD experiments, is presented. Of particular interest are the precise control for nonlinear integrable optics experiments and the transverse-to-longitudinal coupling and phase stability for the Optical Stochastic Cooling Experiment (OSC). Since the beam time-of- ight must be tightly controlled in the OSC section, studies of second order corrections in this section are presented.

Stochastic representation of a class of non-Markovian completely positive evolutions

International Nuclear Information System (INIS)

Budini, Adrian A.

2004-01-01

By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose solution is a completely positive map. The structure of these master equations is associated with a random renewal process where each event consist in the application of a superoperator over a density matrix. Strong nonexponential decay arise by choosing different statistics of the renewal process. As examples we analyze the stochastic and averaged dynamics of simple systems that admit an analytical solution. The problem of positivity in quantum master equations induced by memory effects [S. M. Barnett and S. Stenholm, Phys. Rev. A 64, 033808 (2001)] is clarified in this context

Modeling and Simulation of High Dimensional Stochastic Multiscale PDE Systems at the Exascale

Energy Technology Data Exchange (ETDEWEB)

Kevrekidis, Ioannis [Princeton Univ., NJ (United States)

2017-03-22

The thrust of the proposal was to exploit modern data-mining tools in a way that will create a systematic, computer-assisted approach to the representation of random media -- and also to the representation of the solutions of an array of important physicochemical processes that take place in/on such media. A parsimonious representation/parametrization of the random media links directly (via uncertainty quantification tools) to good sampling of the distribution of random media realizations. It also links directly to modern multiscale computational algorithms (like the equation-free approach that has been developed in our group) and plays a crucial role in accelerating the scientific computation of solutions of nonlinear PDE models (deterministic or stochastic) in such media – both solutions in particular realizations of the random media, and estimation of the statistics of the solutions over multiple realizations (e.g. expectations).

Linear stochastic differential equations with anticipating initial conditions

DEFF Research Database (Denmark)

Khalifa, Narjess; Kuo, Hui-Hsiung; Ouerdiane, Habib

In this paper we use the new stochastic integral introduced by Ayed and Kuo (2008) and the results obtained by Kuo et al. (2012b) to find a solution to a drift-free linear stochastic differential equation with anticipating initial condition. Our solution is based on well-known results from...... classical Itô theory and anticipative Itô formula results from Kue et al. (2012b). We also show that the solution obtained by our method is consistent with the solution obtained by the methods of Malliavin calculus, e.g. Buckdahn and Nualart (1994)....

Qualitative and Quantitative Integrated Modeling for Stochastic Simulation and Optimization

Directory of Open Access Journals (Sweden)

Xuefeng Yan

2013-01-01

Full Text Available The simulation and optimization of an actual physics system are usually constructed based on the stochastic models, which have both qualitative and quantitative characteristics inherently. Most modeling specifications and frameworks find it difficult to describe the qualitative model directly. In order to deal with the expert knowledge, uncertain reasoning, and other qualitative information, a qualitative and quantitative combined modeling specification was proposed based on a hierarchical model structure framework. The new modeling approach is based on a hierarchical model structure which includes the meta-meta model, the meta-model and the high-level model. A description logic system is defined for formal definition and verification of the new modeling specification. A stochastic defense simulation was developed to illustrate how to model the system and optimize the result. The result shows that the proposed method can describe the complex system more comprehensively, and the survival probability of the target is higher by introducing qualitative models into quantitative simulation.

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

Science.gov (United States)

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

Semantic Representation and Scale-Up of Integrated Air Traffic Management Data

Science.gov (United States)

Keller, Richard M.; Ranjan, Shubha; Wei, Mie; Eshow, Michelle

2016-01-01

Each day, the global air transportation industry generates a vast amount of heterogeneous data from air carriers, air traffic control providers, and secondary aviation entities handling baggage, ticketing, catering, fuel delivery, and other services. Generally, these data are stored in isolated data systems, separated from each other by significant political, regulatory, economic, and technological divides. These realities aside, integrating aviation data into a single, queryable, big data store could enable insights leading to major efficiency, safety, and cost advantages. In this paper, we describe an implemented system for combining heterogeneous air traffic management data using semantic integration techniques. The system transforms data from its original disparate source formats into a unified semantic representation within an ontology-based triple store. Our initial prototype stores only a small sliver of air traffic data covering one day of operations at a major airport. The paper also describes our analysis of difficulties ahead as we prepare to scale up data storage to accommodate successively larger quantities of data -- eventually covering all US commercial domestic flights over an extended multi-year timeframe. We review several approaches to mitigating scale-up related query performance concerns.

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.

Stochastic fuzzy environmental risk characterization of uncertainty and variability in risk assessments: A case study of polycyclic aromatic hydrocarbons in soil at a petroleum-contaminated site in China

International Nuclear Information System (INIS)

Hu, Yan; Wang, Zesen; Wen, Jingya; Li, Yu

2016-01-01

Highlights: • Deal with environmental quality guidelines absence in risk characterization. • Quantitative represention of uncertainty from environmental quality guidelines. • Quantitative represention of variability from contaminant exposure concentrations. • Establishment of stochastic-fuzzy environmental risk characterization approach framework. - Abstract: Better decisions are made using risk assessment models when uncertainty and variability are explicitly acknowledged. Uncertainty caused by a lack of uniform and scientifically supported environmental quality guidelines and variability in the degree of exposure of environmental systems to contaminants are here incorporated in a stochastic fuzzy environmental risk characterization (SFERC) approach. The approach is based on quotient probability distribution and environmental risk level fuzzy membership function methods. The SFERC framework was used to characterize the environmental risks posed by 16 priority polycyclic aromatic hydrocarbons (PAHs) in soil at a typical petroleum-contaminated site in China. This relied on integrating data from the literature and field and laboratory experiments. The environmental risk levels posed by the PAHs under four risk scenarios were determined using the SFERC approach, using “residential land” and “industrial land” environmental quality guidelines under “loose” and “strict” strictness parameters. The results showed that environmental risks posed by PAHs in soil are primarily caused by oil exploitation, traffic emissions, and coal combustion. The SFERC approach is an effective tool for characterizing uncertainty and variability in environmental risk assessments and for managing contaminated sites.

Stochastic fuzzy environmental risk characterization of uncertainty and variability in risk assessments: A case study of polycyclic aromatic hydrocarbons in soil at a petroleum-contaminated site in China

Energy Technology Data Exchange (ETDEWEB)

Hu, Yan [MOE Key Laboratory of Regional Energy Systems Optimization, Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206 (China); State Key Laboratory of Environmental Criteria and Risk Assessment, Chinese Research Academy of Environment Sciences, Beijing 100012 (China); Wang, Zesen [MOE Key Laboratory of Regional Energy Systems Optimization, Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206 (China); Wen, Jingya [MOE Key Laboratory of Regional Energy Systems Optimization, Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206 (China); Institute of Hydropower and Environment Research, Beijing 100012 (China); Li, Yu, E-mail: liyuxx8@hotmail.com [MOE Key Laboratory of Regional Energy Systems Optimization, Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206 (China)

2016-10-05

Highlights: • Deal with environmental quality guidelines absence in risk characterization. • Quantitative represention of uncertainty from environmental quality guidelines. • Quantitative represention of variability from contaminant exposure concentrations. • Establishment of stochastic-fuzzy environmental risk characterization approach framework. - Abstract: Better decisions are made using risk assessment models when uncertainty and variability are explicitly acknowledged. Uncertainty caused by a lack of uniform and scientifically supported environmental quality guidelines and variability in the degree of exposure of environmental systems to contaminants are here incorporated in a stochastic fuzzy environmental risk characterization (SFERC) approach. The approach is based on quotient probability distribution and environmental risk level fuzzy membership function methods. The SFERC framework was used to characterize the environmental risks posed by 16 priority polycyclic aromatic hydrocarbons (PAHs) in soil at a typical petroleum-contaminated site in China. This relied on integrating data from the literature and field and laboratory experiments. The environmental risk levels posed by the PAHs under four risk scenarios were determined using the SFERC approach, using “residential land” and “industrial land” environmental quality guidelines under “loose” and “strict” strictness parameters. The results showed that environmental risks posed by PAHs in soil are primarily caused by oil exploitation, traffic emissions, and coal combustion. The SFERC approach is an effective tool for characterizing uncertainty and variability in environmental risk assessments and for managing contaminated sites.

Copula-based modeling of stochastic wind power in Europe and implications for the Swiss power grid

International Nuclear Information System (INIS)

Hagspiel, Simeon; Papaemannouil, Antonis; Schmid, Matthias; Andersson, Göran

2012-01-01

Highlights: ► We model stochastic wind power using copula theory. ► Stochastic wind power is integrated in a European system adequacy evaluation. ► The Swiss power grid is put at risk by further integrating wind power in Europe. ► System elements located at or close to Swiss borders are affected the most. ► A criticality indicator allows prioritizing expansion plans on a probabilistic basis. -- Abstract: Large scale integration of wind energy poses new challenges to the European power system due to its stochastic nature and often remote location. In this paper a multivariate uncertainty analysis problem is formulated for the integration of stochastic wind energy in the European grid. By applying copula theory a synthetic set of data is generated from scarce wind speed reanalysis data in order to achieve the increased sample size for the subsequent Monte Carlo simulation. In the presented case study, European wind power samples are generated from the modeled stochastic process. Under the precondition of a modeled perfect market environment, wind power impacts dispatch decisions and therefore leads to alterations in power balances. Stochastic power balances are implemented in a detailed model of the European electricity network, based on the generated samples. Finally, a Monte Carlo method is used to determine power flows and contingencies in the system. An indicator is elaborated in order to analyze risk of overloading and to prioritize necessary grid reinforcements. Implications for the Swiss power grid are investigated in detail, revealing that the current system is significantly put at risk in certain areas by the further integration of wind power in Europe. It is the first time that the results of a probabilistic model for wind energy are further deployed within a power system analysis of the interconnected European grid. The method presented in this paper allows to account for stochastic wind energy in a load flow analysis and to evaluate

Representations of the Magnitudes of Fractions

Science.gov (United States)

Schneider, Michael; Siegler, Robert S.

2010-01-01

We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However,…

Renormalization in the complete Mellin representation of Feynman amplitudes

International Nuclear Information System (INIS)

Calan, C. de; David, F.; Rivasseau, V.

1981-01-01

The Feynmann amplitudes are renormalized in the formalism of the CM representation. This Mellin-Barnes type integral representation, previously introduced for the study of asymptotic behaviours, is shown to have the following interesting property: in contrast with the usual subtraction procedures, the renormalization leaves the CM intergrand unchanged, and only results into translations of the integration path. The explicit CM representation of the renormalized amplitudes is given. In addition, the dimensional regularization and the extension to spinor amplitudes are sketched. (orig.)

Foundations of infinitesimal stochastic analysis

CERN Document Server

Stroyan, KD

2011-01-01

This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.

Image accuracy and representational enhancement through low-level, multi-sensor integration techniques

International Nuclear Information System (INIS)

Baker, J.E.

1993-05-01

Multi-Sensor Integration (MSI) is the combining of data and information from more than one source in order to generate a more reliable and consistent representation of the environment. The need for MSI derives largely from basic ambiguities inherent in our current sensor imaging technologies. These ambiguities exist as long as the mapping from reality to image is not 1-to-1. That is, if different 44 realities'' lead to identical images, a single image cannot reveal the particular reality which was the truth. MSI techniques can be divided into three categories based on the relative information content of the original images with that of the desired representation: (1) ''detail enhancement,'' wherein the relative information content of the original images is less rich than the desired representation; (2) ''data enhancement,'' wherein the MSI techniques axe concerned with improving the accuracy of the data rather than either increasing or decreasing the level of detail; and (3) ''conceptual enhancement,'' wherein the image contains more detail than is desired, making it difficult to easily recognize objects of interest. In conceptual enhancement one must group pixels corresponding to the same conceptual object and thereby reduce the level of extraneous detail. This research focuses on data and conceptual enhancement algorithms. To be useful in many real-world applications, e.g., autonomous or teleoperated robotics, real-time feedback is critical. But, many MSI/image processing algorithms require significant processing time. This is especially true of feature extraction, object isolation, and object recognition algorithms due to their typical reliance on global or large neighborhood information. This research attempts to exploit the speed currently available in state-of-the-art digitizers and highly parallel processing systems by developing MSI algorithms based on pixel rather than global-level features

An efficient forward–reverse expectation-maximization algorithm for statistical inference in stochastic reaction networks

KAUST Repository

Bayer, Christian

2016-02-20

© 2016 Taylor & Francis Group, LLC. ABSTRACT: In this work, we present an extension of the forward–reverse representation introduced by Bayer and Schoenmakers (Annals of Applied Probability, 24(5):1994–2032, 2014) to the context of stochastic reaction networks (SRNs). We apply this stochastic representation to the computation of efficient approximations of expected values of functionals of SRN bridges, that is, SRNs conditional on their values in the extremes of given time intervals. We then employ this SRN bridge-generation technique to the statistical inference problem of approximating reaction propensities based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during phase I, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate ordinary differential equations approximation; then, during phase II, we apply the Monte Carlo version of the expectation-maximization algorithm to the phase I output. By selecting a set of overdispersed seeds as initial points in phase I, the output of parallel runs from our two-phase method is a cluster of approximate maximum likelihood estimates. Our results are supported by numerical examples.

Stochastic formulation of quantum field at finite temperature

International Nuclear Information System (INIS)

Lim, S.C.

1989-01-01

This paper reports that, based on an extension of the stochastic quantization method of Nelson, it is possible to obtain finite temperature fields in both the imaginary and real time formalisms which are usually quantized by using the functional integral technique

Stochastic kinetics

International Nuclear Information System (INIS)

Colombino, A.; Mosiello, R.; Norelli, F.; Jorio, V.M.; Pacilio, N.

1975-01-01

A nuclear system kinetics is formulated according to a stochastic approach. The detailed probability balance equations are written for the probability of finding the mixed population of neutrons and detected neutrons, i.e. detectrons, at a given level for a given instant of time. Equations are integrated in search of a probability profile: a series of cases is analyzed through a progressive criterium. It tends to take into account an increasing number of physical processes within the chosen model. The most important contribution is that solutions interpret analytically experimental conditions of equilibrium (moise analysis) and non equilibrium (pulsed neutron measurements, source drop technique, start up procedures)

Stochastic calculus and applications

CERN Document Server

Cohen, Samuel N

2015-01-01

Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to wo...

Fuzzy production planning models for an unreliable production system with fuzzy production rate and stochastic/fuzzy demand rate

Directory of Open Access Journals (Sweden)

K. A. Halim

2011-01-01

Full Text Available In this article, we consider a single-unit unreliable production system which produces a single item. During a production run, the production process may shift from the in-control state to the out-of-control state at any random time when it produces some defective items. The defective item production rate is assumed to be imprecise and is characterized by a trapezoidal fuzzy number. The production rate is proportional to the demand rate where the proportionality constant is taken to be a fuzzy number. Two production planning models are developed on the basis of fuzzy and stochastic demand patterns. The expected cost per unit time in the fuzzy sense is derived in each model and defuzzified by using the graded mean integration representation method. Numerical examples are provided to illustrate the optimal results of the proposed fuzzy models.

Karhunen-Loève-Based Reduced-Complexity Representation of the Mixed-Density Messages in SPA on Factor Graph and Its Impact on BER

Directory of Open Access Journals (Sweden)

Prochazka Pavel

2010-01-01

Full Text Available The sum product algorithm on factor graphs (FG/SPA is a widely used tool to solve various problems in a wide area of fields. A representation of generally-shaped continuously valued messages in the FG/SPA is commonly solved by a proper parameterization of the messages. Obtaining such a proper parameterization is, however, a crucial problem in general. The paper introduces a systematic procedure for obtaining a scalar message representation with well-defined fidelity criterion in a general FG/SPA. The procedure utilizes a stochastic nature of the messages as they evolve during the FG/SPA processing. A Karhunen-Loève Transform (KLT is used to find a generic canonical message representation which exploits the message stochastic behavior with mean square error (MSE fidelity criterion. We demonstrate the procedure on a range of scenarios including mixture-messages (a digital modulation in phase parametric channel. The proposed systematic procedure achieves equal results as the Fourier parameterization developed especially for this particular class of scenarios.

An integration of minimum local feature representation methods to recognize large variation of foods

Science.gov (United States)

Razali, Mohd Norhisham bin; Manshor, Noridayu; Halin, Alfian Abdul; Mustapha, Norwati; Yaakob, Razali

2017-10-01

Local invariant features have shown to be successful in describing object appearances for image classification tasks. Such features are robust towards occlusion and clutter and are also invariant against scale and orientation changes. This makes them suitable for classification tasks with little inter-class similarity and large intra-class difference. In this paper, we propose an integrated representation of the Speeded-Up Robust Feature (SURF) and Scale Invariant Feature Transform (SIFT) descriptors, using late fusion strategy. The proposed representation is used for food recognition from a dataset of food images with complex appearance variations. The Bag of Features (BOF) approach is employed to enhance the discriminative ability of the local features. Firstly, the individual local features are extracted to construct two kinds of visual vocabularies, representing SURF and SIFT. The visual vocabularies are then concatenated and fed into a Linear Support Vector Machine (SVM) to classify the respective food categories. Experimental results demonstrate impressive overall recognition at 82.38% classification accuracy based on the challenging UEC-Food100 dataset.

MarkoLAB: A simulator to study ionic channel's stochastic behavior.

Science.gov (United States)

da Silva, Robson Rodrigues; Goroso, Daniel Gustavo; Bers, Donald M; Puglisi, José Luis

2017-08-01

Mathematical models of the cardiac cell have started to include markovian representations of the ionic channels instead of the traditional Hodgkin & Huxley formulations. There are many reasons for this: Markov models are not restricted to the idea of independent gates defining the channel, they allow more complex description with specific transitions between open, closed or inactivated states, and more importantly those states can be closely related to the underlying channel structure and conformational changes. We used the LabVIEW ® and MATLAB ® programs to implement the simulator MarkoLAB that allow a dynamical 3D representation of the markovian model of the channel. The Monte Carlo simulation was used to implement the stochastic transitions among states. The user can specify the voltage protocol by setting the holding potential, the step-to voltage and the duration of the stimuli. The most studied feature of a channel is the current flowing through it. This happens when the channel stays in the open state, but most of the time, as revealed by the low open probability values, the channel remains on the inactive or closed states. By focusing only when the channel enters or leaves the open state we are missing most of its activity. MarkoLAB proved to be quite useful to visualize the whole behavior of the channel and not only when the channel produces a current. Such dynamic representation provides more complete information about channel kinetics and will be a powerful tool to demonstrate the effect of gene mutations or drugs on the channel function. MarkoLAB provides an original way of visualizing the stochastic behavior of a channel. It clarifies concepts, such as recovery from inactivation, calcium- versus voltage-dependent inactivation, and tail currents. It is not restricted to ionic channels only but it can be extended to other transporters, such as exchangers and pumps. This program is intended as a didactical tool to illustrate the dynamical behavior of a

Probability density function evolution of power systems subject to stochastic variation of renewable energy

Science.gov (United States)

Wei, J. Q.; Cong, Y. C.; Xiao, M. Q.

2018-05-01

As renewable energies are increasingly integrated into power systems, there is increasing interest in stochastic analysis of power systems.Better techniques should be developed to account for the uncertainty caused by penetration of renewables and consequently analyse its impacts on stochastic stability of power systems. In this paper, the Stochastic Differential Equations (SDEs) are used to represent the evolutionary behaviour of the power systems. The stationary Probability Density Function (PDF) solution to SDEs modelling power systems excited by Gaussian white noise is analysed. Subjected to such random excitation, the Joint Probability Density Function (JPDF) solution to the phase angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the numerical method is adopted. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. Both weak and strong intensities of the stochastic excitations are considered in a single machine infinite bus power system. The numerical analysis has the same result as the one given by the Monte Carlo simulation. Potential studies on stochastic behaviour of multi-machine power systems with random excitations are discussed at the end.

Global sensitivity analysis in stochastic simulators of uncertain reaction networks.

Science.gov (United States)

Navarro Jimenez, M; Le Maître, O P; Knio, O M

2016-12-28

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol's decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

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.

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

KAUST Repository

Navarro, María

2016-12-26

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition

KAUST Repository

Bessaih, Hakima

2015-04-01

The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries 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 obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.

Topological superposition of abstractions of stochastic processes

NARCIS (Netherlands)

Bujorianu, L.M.; Bujorianu, M.C.

2008-01-01

In this paper, we present a sound integration mechanism for Markov processes that are abstractions of stochastic hybrid systems (SHS). In a previous work, we have defined a very general model of SHS and we proved that the realization of an SHS is a Markov process. Moreover, we have developed a

Conspiracy theories as quasi-religious mentality: an integrated account from cognitive science, social representations theory, and frame theory.

Science.gov (United States)

Franks, Bradley; Bangerter, Adrian; Bauer, Martin W

2013-01-01

Conspiracy theories (CTs) can take many forms and vary widely in popularity, the intensity with which they are believed and their effects on individual and collective behavior. An integrated account of CTs thus needs to explain how they come to appeal to potential believers, how they spread from one person to the next via communication, and how they motivate collective action. We summarize these aspects under the labels of stick, spread, and action. We propose the quasi-religious hypothesis for CTs: drawing on cognitive science of religion, social representations theory, and frame theory. We use cognitive science of religion to describe the main features of the content of CTs that explain how they come to stick: CTs are quasi-religious representations in that their contents, forms and functions parallel those found in beliefs of institutionalized religions. However, CTs are quasi-religious in that CTs and the communities that support them, lack many of the institutional features of organized religions. We use social representations theory to explain how CTs spread as devices for making sense of sudden events that threaten existing worldviews. CTs allow laypersons to interpret such events by relating them to common sense, thereby defusing some of the anxiety that those events generate. We use frame theory to explain how some, but not all CTs mobilize collective counter-conspiratorial action by identifying a target and by proposing credible and concrete rationales for action. We specify our integrated account in 13 propositions.

An Improved Asymptotic Sampling Approach For Stochastic Finite Element Stiffness of a Laterally Loaded Monopile

DEFF Research Database (Denmark)

Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard

2012-01-01

In this study a stochastic approach is conducted to obtain the horizontal and rotational stiffness of an offshore monopile foundation. A nonlinear stochastic p-y curve is integrated into a finite element scheme for calculation of the monopile response in over-consolidated clay having spatial...

Characterization of stochastic uncertainty in the 1996 performance assessment for the Waste Isolation Pilot Plant

International Nuclear Information System (INIS)

Helton, Jon Craig; Davis, Freddie J.; Johnson, J.D.

2000-01-01

The 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) maintains a separation between stochastic (i.e., aleatory) and subjective (i.e., epistemic) uncertainty, with stochastic uncertainty arising from the possible disruptions that could occur at the WIPP over the 10,000 yr regulatory period specified by the US Environmental Protection Agency (40 CFR 191, 40 CFR 194) and subjective uncertainty arising from an inability to uniquely characterize many of the inputs required in the 1996 WIPP PA. The characterization of stochastic uncertainty is discussed including drilling intrusion time, drilling location penetration of excavated/nonexcavated areas of the repository, penetration of pressurized brine beneath the repository, borehole plugging patterns, activity level of waste, and occurrence of potash mining. Additional topics discussed include sampling procedures, generation of individual 10,000 yr futures for the WIPP, construction of complementary cumulative distribution functions (CCDFs), mechanistic calculations carried out to support CCDF construction the Kaplan/Garrick ordered triple representation for risk and determination of scenarios and scenario probabilities

Stochastic field theory and finite-temperature supersymmetry

International Nuclear Information System (INIS)

Ghosh, P.; Bandyopadhyay, P.

1988-01-01

The finite-temperature behavior of supersymmetry is considered from the viewpoint of stochastic field theory. To this end, it is considered that Nelson's stochastic mechanics may be generalized to the quantization of a Fermi field when the classical analog of such a field is taken to be a scalar nonlocal field where the internal space is anisotropic in nature such that when quantized this gives rise to two internal helicities corresponding to fermion and antifermion. Stochastic field theory at finite temperature is then formulated from stochastic mechanics which incorporates Brownian motion in the external space as well as in the internal space of a particle. It is shown that when the anisotropy of the internal space is suppressed so that the internal time ξ 0 vanishes and the internal space variables are integrated out one has supersymmetry at finite temperature. This result is true for T = 0, also. However, at this phase equilibrium will be destroyed. Thus for a random process van Hove's result involving quantum mechanical operators, i.e., that when supersymmetry remains unbroken at T = 0 it will also remain unbroken at Tnot =0, occurs. However, this formalism indicates that when at T = 0 broken supersymmetry results, supersymmetry may be restored at a critical temperature T/sub c/

GillesPy: A Python Package for Stochastic Model Building and Simulation

OpenAIRE

Abel, John H.; Drawert, Brian; Hellander, Andreas; Petzold, Linda R.

2016-01-01

GillesPy is an open-source Python package for model construction and simulation of stochastic biochemical systems. GillesPy consists of a Python framework for model building and an interface to the StochKit2 suite of efficient simulation algorithms based on the Gillespie stochastic simulation algorithms (SSA). To enable intuitive model construction and seamless integration into the scientific Python stack, we present an easy to understand, action-oriented programming interface. Here, we descr...

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

CERN Document Server

Capasso, Vincenzo

2015-01-01

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

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

Science.gov (United States)

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

2015-04-01

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

Stochastic Learning of Multi-Instance Dictionary for Earth Mover's Distance based Histogram Comparison

OpenAIRE

Fan, Jihong; Liang, Ru-Ze

2016-01-01

Dictionary plays an important role in multi-instance data representation. It maps bags of instances to histograms. Earth mover's distance (EMD) is the most effective histogram distance metric for the application of multi-instance retrieval. However, up to now, there is no existing multi-instance dictionary learning methods designed for EMD based histogram comparison. To fill this gap, we develop the first EMD-optimal dictionary learning method using stochastic optimization method. In the stoc...

Stability analysis for neutral stochastic differential equation of second order driven by Poisson jumps

Science.gov (United States)

Chadha, Alka; Bora, Swaroop Nandan

2017-11-01

This paper studies the existence, uniqueness, and exponential stability in mean square for the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. By utilizing the Banach fixed point theorem, first the existence and uniqueness of the mild solution of neutral second order stochastic differential equations is established. Then, the mean square exponential stability for the mild solution of the stochastic system with Poisson jumps is obtained with the help of an established integral inequality.

Stochastic integrated vendor–buyer model with unstable lead time and setup cost

Directory of Open Access Journals (Sweden)

Chandra K. Jaggi

2011-01-01

Full Text Available This paper presents a new vendor-buyer system where there are different objectives for both sides. The proposed method of this paper is different from the other previously published works since it considers different objectives for both sides. In this paper, the vendor’s emphasis is on the crashing of the setup cost, which not only helps him compete in the market but also provides better services to his customers; and the buyer’s aim is to reduce the lead time, which not only facilitates the buyer to fulfill the customers’ demand on time but also enables him to earn a good reputation in the market or vice versa. In the light of the above stated facts, an integrated vendor-buyer stochastic inventory model is also developed. The propsed model considers two cases for demand during lead time: Case (i Complete demand information, Case (ii Partial demand information. The proposed model jointly optimizes the buyer’s ordered quantity and lead time along with vendor’s setup cost and the number of shipments. The results are demonstrated with the help of numerical examples.

Stochastic Models for Laser Propagation in Atmospheric Turbulence.

Science.gov (United States)

Leland, Robert Patton

In this dissertation, stochastic models for laser propagation in atmospheric turbulence are considered. A review of the existing literature on laser propagation in the atmosphere and white noise theory is presented, with a view toward relating the white noise integral and Ito integral approaches. The laser beam intensity is considered as the solution to a random Schroedinger equation, or forward scattering equation. This model is formulated in a Hilbert space context as an abstract bilinear system with a multiplicative white noise input, as in the literature. The model is also modeled in the Banach space of Fresnel class functions to allow the plane wave case and the application of path integrals. Approximate solutions to the Schroedinger equation of the Trotter-Kato product form are shown to converge for each white noise sample path. The product forms are shown to be physical random variables, allowing an Ito integral representation. The corresponding Ito integrals are shown to converge in mean square, providing a white noise basis for the Stratonovich correction term associated with this equation. Product form solutions for Ornstein -Uhlenbeck process inputs were shown to converge in mean square as the input bandwidth was expanded. A digital simulation of laser propagation in strong turbulence was used to study properties of the beam. Empirical distributions for the irradiance function were estimated from simulated data, and the log-normal and Rice-Nakagami distributions predicted by the classical perturbation methods were seen to be inadequate. A gamma distribution fit the simulated irradiance distribution well in the vicinity of the boresight. Statistics of the beam were seen to converge rapidly as the bandwidth of an Ornstein-Uhlenbeck process was expanded to its white noise limit. Individual trajectories of the beam were presented to illustrate the distortion and bending of the beam due to turbulence. Feynman path integrals were used to calculate an

Stochastic numerical methods an introduction for students and scientists

CERN Document Server

Toral, Raul

2014-01-01

Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability ConceptsMonte Carlo IntegrationGeneration of Uniform and Non-uniformRandom Numbers: Non-correlated ValuesDynamical MethodsApplications to Statistical MechanicsIn...

On Space-Time Resolution of Inflow Representations for Wind Turbine Loads Analysis

Directory of Open Access Journals (Sweden)

Lance Manuel

2012-06-01

Full Text Available Efficient spatial and temporal resolution of simulated inflow wind fields is important in order to represent wind turbine dynamics and derive load statistics for design. Using Fourier-based stochastic simulation of inflow turbulence, we first investigate loads for a utility-scale turbine in the neutral atmospheric boundary layer. Load statistics, spectra, and wavelet analysis representations for different space and time resolutions are compared. Next, large-eddy simulation (LES is employed with space-time resolutions, justified on the basis of the earlier stochastic simulations, to again derive turbine loads. Extreme and fatigue loads from the two approaches used in inflow field generation are compared. On the basis of simulation studies carried out for three different wind speeds in the turbine’s operating range, it is shown that inflow turbulence described using 10-meter spatial resolution and 1 Hz temporal resolution is adequate for assessing turbine loads. Such studies on the investigation of adequate filtering or resolution of inflow wind fields help to establish efficient strategies for LES and other physical or stochastic simulation needed in turbine loads studies.

Fourier analysis and stochastic processes

CERN Document Server

Brémaud, Pierre

2014-01-01

This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...

Evolved Representation and Computational Creativity

Directory of Open Access Journals (Sweden)

Ashraf Fouad Hafez Ismail

2001-01-01

or design methods, but each individual computational design system has only one or very few different representations available.Whatever the choice of the representation, it is likely to influence the outcome of the design process. In any representation, some designs may be more difficult to represent than others, and some designs may not be representable at all.The same applies if the design process is implemented in a computer program. If a design cannot be represented with a given representation, it cannot be the outcome of a design process using this representation. As is the case for human designers, it is also possible that the representation influences a computational design process such that it is easier for the program to find some designs than others. Depending on the design process used, this might make those designs a more likely outcome of the design process. This is for example the case with stochastic optimization processes, like evolutionary systems and simulated annealing. In these cases, the representation is likely to introduce a bias into the design process.The selection of the representation is therefore of high importance in the development of a computational design system. Obviously, while choosing the representation the programmer has to ensure that all or as many as possible potentially ‘interesting’ designs can be represented. But it is also generally desirable to minimize the bias introduced by the representation. In contrast to the user-provided design criteria, the bias caused by the representation influences the outcome of the design process in an implicit way which is not obvious to the user, and is difficult to predict and control.The idea developed in this research is that it is possible to turn the bias caused by the representation into a virtue, by deliberately choosing or modifying the representation to influence the design process in a certain desired way. The resulting ‘focusing’ of the search process is connected to the

COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.

ABJM Wilson loops in arbitrary representations

Energy Technology Data Exchange (ETDEWEB)

Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Honda, Masazumi [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan); Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst. and Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics

2013-06-15

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

ABJM Wilson loops in arbitrary representations

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki; Moriyama, Sanefumi; Okuyama, Kazumi

2013-06-01

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement.

Science.gov (United States)

Roldán, Édgar; Gupta, Shamik

2017-08-01

We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.

The Effects of the Concrete-Representational-Abstract Integration Strategy on the Ability of Students with Learning Disabilities to Multiply Linear Expressions within Area Problems

Science.gov (United States)

Strickland, Tricia K.; Maccini, Paula

2013-01-01

We examined the effects of the Concrete-Representational-Abstract Integration strategy on the ability of secondary students with learning disabilities to multiply linear algebraic expressions embedded within contextualized area problems. A multiple-probe design across three participants was used. Results indicated that the integration of the…

Distinguishing Representations as Origin and Representations as Input: Roles for Individual Cells

Directory of Open Access Journals (Sweden)

Jonathan C.W. Edwards

2016-09-01

Full Text Available It is widely perceived that there is a problem in giving a naturalistic account of mental representation that deals adequately with meaning, interpretation or significance (semantic content. It is suggested here that this problem may arise partly from the conflation of two vernacular senses of representation: representation-as-origin and representation-as-input. The flash of a neon sign may in one sense represent a popular drink, but to function as representation it must provide an input to a ‘consumer’ in the street. The arguments presented draw on two principles – the neuron doctrine and the need for a venue for ‘presentation’ or ‘reception’ of a representation at a specified site, consistent with the locality principle. It is also argued that domains of representation cannot be defined by signal traffic, since they can be expected to include ‘null’ elements based on non-firing cells. In this analysis, mental representations-as-origin are distributed patterns of cell firing. Each firing cell is given semantic value in its own right - some form of atomic propositional significance – since different axonal branches may contribute to integration with different populations of signals at different downstream sites. Representations-as-input are patterns of local co-arrival of signals in the form of synaptic potentials in dendrites. Meaning then draws on the relationships between active and null inputs, forming ‘scenarios’ comprising a molecular combination of ‘premises’ from which a new output with atomic propositional significance is generated. In both types of representation, meaning, interpretation or significance pivots on events in an individual cell. (This analysis only applies to ‘occurrent’ representations based on current neural activity. The concept of representations-as-input emphasises the need for a ‘consumer’ of a representation and the dependence of meaning on the co-relationships involved in an

STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB

KAUST Repository

Klingbeil, G.

2011-02-25

Motivation: The importance of stochasticity in biological systems is becoming increasingly recognized and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new software tool STOCHSIMGPU that exploits graphics processing units (GPUs) for parallel stochastic simulations of biological/chemical reaction systems and show that significant gains in efficiency can be made. It is integrated into MATLAB and works with the Systems Biology Toolbox 2 (SBTOOLBOX2) for MATLAB. Results: The GPU-based parallel implementation of the Gillespie stochastic simulation algorithm (SSA), the logarithmic direct method (LDM) and the next reaction method (NRM) is approximately 85 times faster than the sequential implementation of the NRM on a central processing unit (CPU). Using our software does not require any changes to the user\\'s models, since it acts as a direct replacement of the stochastic simulation software of the SBTOOLBOX2. © The Author 2011. Published by Oxford University Press. All rights reserved.

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

Energy Technology Data Exchange (ETDEWEB)

El Hachem, S

1995-11-01

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

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.

Approximate models for broken clouds in stochastic radiative transfer theory

International Nuclear Information System (INIS)

Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas

2014-01-01

This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models

Application of commutator theorems to the integration of representations of Lie algebras and commutation relations

International Nuclear Information System (INIS)

Froehlich, J.

1977-01-01

Sufficient conditions on unbounded, symmetric operators A and B which imply that exp(itA)exp(isB)exp(-itA) satisfies the well known 'multiple commutator' formula are derived. This formula is then applied to prove new necessary and sufficient conditions for the integrability of representations of Lie algebras and canonical commutation relations and the commutativity of the spectral projections of two commuting, unbounded, self-adjoint operators. A classic theorem of Nelson's is obtained as a corollary. Our results are useful in relativistic quantum field theory. (orig.) [de

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

Science.gov (United States)

Li, Pu; Chen, Bing

2011-04-01

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

STOCHASTIC 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.

Integration of sparse multi-modality representation and geometrical constraint for isointense infant brain segmentation.

Science.gov (United States)

Wang, Li; Shi, Feng; Li, Gang; Lin, Weili; Gilmore, John H; Shen, Dinggang

2013-01-01

Segmentation of infant brain MR images is challenging due to insufficient image quality, severe partial volume effect, and ongoing maturation and myelination process. During the first year of life, the signal contrast between white matter (WM) and gray matter (GM) in MR images undergoes inverse changes. In particular, the inversion of WM/GM signal contrast appears around 6-8 months of age, where brain tissues appear isointense and hence exhibit extremely low tissue contrast, posing significant challenges for automated segmentation. In this paper, we propose a novel segmentation method to address the above-mentioned challenge based on the sparse representation of the complementary tissue distribution information from T1, T2 and diffusion-weighted images. Specifically, we first derive an initial segmentation from a library of aligned multi-modality images with ground-truth segmentations by using sparse representation in a patch-based fashion. The segmentation is further refined by the integration of the geometrical constraint information. The proposed method was evaluated on 22 6-month-old training subjects using leave-one-out cross-validation, as well as 10 additional infant testing subjects, showing superior results in comparison to other state-of-the-art methods.

A stochastic model for immunological feedback in carcinogenesis analysis and approximations

CERN Document Server

Dubin, Neil

1976-01-01

Stochastic processes often pose the difficulty that, as soon as a model devi­ ates from the simplest kinds of assumptions, the differential equations obtained for the density and the generating functions become mathematically formidable. Worse still, one is very often led to equations which have no known solution and don't yield to standard analytical methods for differential equations. In the model considered here, one for tumor growth with an immunological re­ sponse from the normal tissue, a nonlinear term in the transition probability for the death of a tumor cell leads to the above-mentioned complications. Despite the mathematical disadvantages of this nonlinearity, we are able to consider a more sophisticated model biologically. Ultimately, in order to achieve a more realistic representation of a complicated phenomenon, it is necessary to examine mechanisms which allow the model to deviate from the more mathematically tractable linear format. Thus far, stochastic models for tumor growth have almost ex...

Stochastic beam dynamics in storage rings

International Nuclear Information System (INIS)

Pauluhn, A.

1993-12-01

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

A Connection between Singular Stochastic Control and Optimal Stopping

International Nuclear Information System (INIS)

Espen Benth, Fred; Reikvam, Kristin

2003-01-01

We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions

L-functions and the oscillator representation

CERN Document Server

Rallis, Stephen

1987-01-01

These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an L-function (associated to the standard representation of the L-group of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard L-functions, (ii) see-saw dual reductive pairs and (iii) Siegel-Weil formula. The book addresses readers who specialize in the theory of automorphic forms and L-functions and the representation theory of Lie groups. N

Stochastic dynamic modeling of regular and slow earthquakes

Science.gov (United States)

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

2017-12-01

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

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

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

Directory of Open Access Journals (Sweden)

Hong Zhang

2017-01-01

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

On a stochastic process associated to non-abelian gauge fields

International Nuclear Information System (INIS)

Vilela Mendes, R.

1989-01-01

A stochastic process is constructed from a ground state measure that generalizes to non-abelian fields the ground state of abelian (free) gauge fields without fermions. Using a latticized version one shows how the process leads to a well-defined quantum theory in the Schroedinger representation. An analysis of the qualitative behaviour of the theory seems to imply a quasi-free behaviour at short distances and a maximally disordered field strength configuration for the low-momentum component of the ground state. Scaling relations for the mass gap are inferred from the theory of small random perturbations of dynamical systems. (orig.)

Stochastic differential equations for quantum dynamics of spin-boson networks

International Nuclear Information System (INIS)

Mandt, Stephan; Sadri, Darius; Houck, Andrew A; Türeci, Hakan E

2015-01-01

A popular approach in quantum optics is to map a master equation to a stochastic differential equation, where quantum effects manifest themselves through noise terms. We generalize this approach based on the positive-P representation to systems involving spin, in particular networks or lattices of interacting spins and bosons. We test our approach on a driven dimer of spins and photons, compare it to the master equation, and predict a novel dynamic phase transition in this system. Our numerical approach has scaling advantages over existing methods, but typically requires regularization in terms of drive and dissipation. (paper)

Design of problem-specific evolutionary algorithm/mixed-integer programming hybrids: two-stage stochastic integer programming applied to chemical batch scheduling

Science.gov (United States)

Urselmann, Maren; Emmerich, Michael T. M.; Till, Jochen; Sand, Guido; Engell, Sebastian

2007-07-01

Engineering optimization often deals with large, mixed-integer search spaces with a rigid structure due to the presence of a large number of constraints. Metaheuristics, such as evolutionary algorithms (EAs), are frequently suggested as solution algorithms in such cases. In order to exploit the full potential of these algorithms, it is important to choose an adequate representation of the search space and to integrate expert-knowledge into the stochastic search operators, without adding unnecessary bias to the search. Moreover, hybridisation with mathematical programming techniques such as mixed-integer programming (MIP) based on a problem decomposition can be considered for improving algorithmic performance. In order to design problem-specific EAs it is desirable to have a set of design guidelines that specify properties of search operators and representations. Recently, a set of guidelines has been proposed that gives rise to so-called Metric-based EAs (MBEAs). Extended by the minimal moves mutation they allow for a generalization of EA with self-adaptive mutation strength in discrete search spaces. In this article, a problem-specific EA for process engineering task is designed, following the MBEA guidelines and minimal moves mutation. On the background of the application, the usefulness of the design framework is discussed, and further extensions and corrections proposed. As a case-study, a two-stage stochastic programming problem in chemical batch process scheduling is considered. The algorithm design problem can be viewed as the choice of a hierarchical decision structure, where on different layers of the decision process symmetries and similarities can be exploited for the design of minimal moves. After a discussion of the design approach and its instantiation for the case-study, the resulting problem-specific EA/MIP is compared to a straightforward application of a canonical EA/MIP and to a monolithic mathematical programming algorithm. In view of the

Generalization of stochastic visuomotor rotations.

Directory of Open Access Journals (Sweden)

Hugo L Fernandes

Full Text Available Generalization studies examine the influence of perturbations imposed on one movement onto other movements. The strength of generalization is traditionally interpreted as a reflection of the similarity of the underlying neural representations. Uncertainty fundamentally affects both sensory integration and learning and is at the heart of many theories of neural representation. However, little is known about how uncertainty, resulting from variability in the environment, affects generalization curves. Here we extend standard movement generalization experiments to ask how uncertainty affects the generalization of visuomotor rotations. We find that although uncertainty affects how fast subjects learn, the perturbation generalizes independently of uncertainty.

Note on path integral quantization of hydrogen atom

International Nuclear Information System (INIS)

Storchak, S.N.

1988-01-01

For path integrals whose integration measures are generated by stochastic processes of a definite form (Stratonovich-type equations are a local form for stochastic differential equations of these processes) it has been shown that under quantization of hydrogen atom the reparametrization and reduction Jacobians are mutually cancelled. 12 refs

Unified Stochastic Geometry Model for MIMO Cellular Networks with Retransmissions

KAUST Repository

Afify, Laila H.

2016-10-11

This paper presents a unified mathematical paradigm, based on stochastic geometry, for downlink cellular networks with multiple-input-multiple-output (MIMO) base stations (BSs). The developed paradigm accounts for signal retransmission upon decoding errors, in which the temporal correlation among the signal-to-interference-plus-noise-ratio (SINR) of the original and retransmitted signals is captured. In addition to modeling the effect of retransmission on the network performance, the developed mathematical model presents twofold analysis unification for MIMO cellular networks literature. First, it integrates the tangible decoding error probability and the abstracted (i.e., modulation scheme and receiver type agnostic) outage probability analysis, which are largely disjoint in the literature. Second, it unifies the analysis for different MIMO configurations. The unified MIMO analysis is achieved by abstracting unnecessary information conveyed within the interfering signals by Gaussian signaling approximation along with an equivalent SISO representation for the per-data stream SINR in MIMO cellular networks. We show that the proposed unification simplifies the analysis without sacrificing the model accuracy. To this end, we discuss the diversity-multiplexing tradeoff imposed by different MIMO schemes and shed light on the diversity loss due to the temporal correlation among the SINRs of the original and retransmitted signals. Finally, several design insights are highlighted.

Unified Stochastic Geometry Model for MIMO Cellular Networks with Retransmissions

KAUST Repository

Afify, Laila H.; Elsawy, Hesham; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim

2016-01-01

This paper presents a unified mathematical paradigm, based on stochastic geometry, for downlink cellular networks with multiple-input-multiple-output (MIMO) base stations (BSs). The developed paradigm accounts for signal retransmission upon decoding errors, in which the temporal correlation among the signal-to-interference-plus-noise-ratio (SINR) of the original and retransmitted signals is captured. In addition to modeling the effect of retransmission on the network performance, the developed mathematical model presents twofold analysis unification for MIMO cellular networks literature. First, it integrates the tangible decoding error probability and the abstracted (i.e., modulation scheme and receiver type agnostic) outage probability analysis, which are largely disjoint in the literature. Second, it unifies the analysis for different MIMO configurations. The unified MIMO analysis is achieved by abstracting unnecessary information conveyed within the interfering signals by Gaussian signaling approximation along with an equivalent SISO representation for the per-data stream SINR in MIMO cellular networks. We show that the proposed unification simplifies the analysis without sacrificing the model accuracy. To this end, we discuss the diversity-multiplexing tradeoff imposed by different MIMO schemes and shed light on the diversity loss due to the temporal correlation among the SINRs of the original and retransmitted signals. Finally, several design insights are highlighted.

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

International Nuclear Information System (INIS)

Luhur, M.R.

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

Muhammad Ramzan Luhur

2014-01-01

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

The stochastic finite element methods with applications in geotechnics and rupture mechanics

International Nuclear Information System (INIS)

Baldeweck, Herve

1999-01-01

After having presented and classified the various stochastic finite elements methods, notably by distinguishing reliability methods (first order and second order reliability methods, response surfaces, Monte Carlo) and sensitivity methods (Monte Carlo, spectral development, perturbation, weighted integrals), the author of this research thesis presents basic tools needed for different theoretical developments: hazard representation and method of moments. He also presents the problem which is used all along this work to compare and assess the different sensitivity methods. Then, he reports the theoretical development of these sensitivity methods: the Monte Carlo method, the spectral development method, the perturbation method, and the quadrature method. This last one is a new one aimed at the assessment of statistical moments. The author highlights the relationships between reliability and sensitivity methods. In the third part, several applications and calculations are reported. Applications are in geotechnics (soil-structure interaction, calculation of soil stiffness, application in the field of geo-materials with the calculation of an underground gallery), and in rupture mechanics (international benchmark on the reliability of a nuclear reactor, non linear calculation of a cracked straight pipe, reliability calculation of a cracked plate with a Young modulus being a random field) [fr

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

Interaction and Representational Integration: Evidence from Speech Errors

Science.gov (United States)

Goldrick, Matthew; Baker, H. Ross; Murphy, Amanda; Baese-Berk, Melissa

2011-01-01

We examine the mechanisms that support interaction between lexical, phonological and phonetic processes during language production. Studies of the phonetics of speech errors have provided evidence that partially activated lexical and phonological representations influence phonetic processing. We examine how these interactive effects are modulated…

SELANSI: a toolbox for simulation of stochastic gene regulatory networks.

Science.gov (United States)

Pájaro, Manuel; Otero-Muras, Irene; Vázquez, Carlos; Alonso, Antonio A

2018-03-01

Gene regulation is inherently stochastic. In many applications concerning Systems and Synthetic Biology such as the reverse engineering and the de novo design of genetic circuits, stochastic effects (yet potentially crucial) are often neglected due to the high computational cost of stochastic simulations. With advances in these fields there is an increasing need of tools providing accurate approximations of the stochastic dynamics of gene regulatory networks (GRNs) with reduced computational effort. This work presents SELANSI (SEmi-LAgrangian SImulation of GRNs), a software toolbox for the simulation of stochastic multidimensional gene regulatory networks. SELANSI exploits intrinsic structural properties of gene regulatory networks to accurately approximate the corresponding Chemical Master Equation with a partial integral differential equation that is solved by a semi-lagrangian method with high efficiency. Networks under consideration might involve multiple genes with self and cross regulations, in which genes can be regulated by different transcription factors. Moreover, the validity of the method is not restricted to a particular type of kinetics. The tool offers total flexibility regarding network topology, kinetics and parameterization, as well as simulation options. SELANSI runs under the MATLAB environment, and is available under GPLv3 license at https://sites.google.com/view/selansi. antonio@iim.csic.es. © The Author(s) 2017. Published by Oxford University Press.

Nambu mechanics for stochastic magnetization dynamics

Energy Technology Data Exchange (ETDEWEB)

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

2017-06-15

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

A combined stochastic feedforward and feedback control design methodology with application to autoland design

Science.gov (United States)

Halyo, Nesim

1987-01-01

A combined stochastic feedforward and feedback control design methodology was developed. The objective of the feedforward control law is to track the commanded trajectory, whereas the feedback control law tries to maintain the plant state near the desired trajectory in the presence of disturbances and uncertainties about the plant. The feedforward control law design is formulated as a stochastic optimization problem and is embedded into the stochastic output feedback problem where the plant contains unstable and uncontrollable modes. An algorithm to compute the optimal feedforward is developed. In this approach, the use of error integral feedback, dynamic compensation, control rate command structures are an integral part of the methodology. An incremental implementation is recommended. Results on the eigenvalues of the implemented versus designed control laws are presented. The stochastic feedforward/feedback control methodology is used to design a digital automatic landing system for the ATOPS Research Vehicle, a Boeing 737-100 aircraft. The system control modes include localizer and glideslope capture and track, and flare to touchdown. Results of a detailed nonlinear simulation of the digital control laws, actuator systems, and aircraft aerodynamics are presented.

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

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

Derivation of the Schroedinger equation from stochastic mechanics

International Nuclear Information System (INIS)

Wallstrom, T.C.

1988-01-01

The thesis is divided into four largely independent chapters. The first three chapters treat mathematical problems in the theory of stochastic mechanics. The fourth chapter deals with stochastic mechanisms as a physical theory and shows that the Schroedinger equation cannot be derived from existing formulations of stochastic mechanics, as had previously been believed. Since the drift coefficients of stochastic mechanical diffusions are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In Chapter 1, it is shown that for a smooth wavefunction, the closest approach to the nodes can be bounded solely in terms of the time-integrated energy. The ergodic properties of stochastic mechanical diffusions are greatly complicated by the tendency of the particles to avoid the nodes. In Chapter 2, it is shown that a sufficient condition for a stationary process to be ergodic is that there exist positive t and c such that for all x and y, p t (x,y) > cp(y), and this result is applied to show that the set of spin-1/2 diffusions is uniformly ergodic. Nelson has conjectured that in the limit as the particle's moment of inertia I goes to zero, the projections of the Bopp-Haag-Dankel diffusions onto IR 3 converge to a Markovian limit process. This conjecture is proved for the spin-1/2 case in Chapter 3, and the limit process identified as the diffusion naturally associated with the solution to the regular Pauli equation. In Chapter 4 it is shown that the general solution of the stochastic Newton equation does not correspond to a solution of the Schroedinger equation

Mental Representation and Motor Imagery Training

Directory of Open Access Journals (Sweden)

Thomas eSchack

2014-05-01

Full Text Available Research in sports, dance and rehabilitation has shown that Basic Action Concepts (BACs are fundamental building blocks of mental action representations. BACs are based on chunked body postures related to common functions for realizing action goals. In this paper, we outline issues in research methodology and an experimental method, SDA-M (structural dimensional analysis of mental representation, to assess action-relevant representational structures that reflect the organization of BACs. The SDA-M reveals a strong relationship between cognitive representation and performance if complex actions are performed. We show how the SDA-M can improve motor imagery training and how it contributes to our understanding of coaching processes. The SDA-M capitalizes on the objective measurement of individual mental movement representations before training and the integration of these results into the motor imagery training. Such motor imagery training based on mental representations has been applied successfully in professional sports such as golf, volleyball, gymnastics, windsurfing, and recently in the rehabilitation of patients who have suffered a stroke.

Stochastic Levy Divergence and Maxwell's Equations

Directory of Open Access Journals (Sweden)

B. O. Volkov

2015-01-01

Full Text Available One of the main reasons for interest in the Levy Laplacian and its analogues such as Levy d'Alembertian is a connection of these operators with gauge fields. The theorem proved by Accardi, Gibillisco and Volovich stated that a connection in a bundle over a Euclidean space or over a Minkowski space is a solution of the Yang-Mills equations if and only if the corresponding parallel transport to the connection is a solution of the Laplace equation for the Levy Laplacian or of the d'Alembert equation for the Levy d'Alembertian respectively (see [5, 6]. There are two approaches to define Levy type operators, both of which date back to the original works of Levy [7]. The first is that the Levy Laplacian (or Levy d'Alembertian is defined as an integral functional generated by a special form of the second derivative. This approach is used in the works [5, 6], as well as in the paper [8] of Leandre and Volovich, where stochastic Levy-Laplacian is discussed. Another approach to the Levy Laplacian is defining it as the Cesaro mean of second order derivatives along the family of vectors, which is an orthonormal basis in the Hilbert space. This definition of the Levy Laplacian is used for the description of solutions of the Yang-Mills equations in the paper [10].The present work shows that the definitions of the Levy Laplacian and the Levy d'Alembertian based on Cesaro averaging of the second order directional derivatives can be transferred to the stochastic case. In the article the values of these operators on a stochastic parallel transport associated with a connection (vector potential are found. In this case, unlike the deterministic case and the stochastic case of Levy Laplacian from [8], these values are not equal to zero if the vector potential corresponding to the stochastic parallel transport is a solution of the Maxwell's equations. As a result, two approaches to definition of the Levy Laplacian in the stochastic case give different operators. This

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

Sum-over-histories representation for the causal Green function of free scalar field theory

International Nuclear Information System (INIS)

Rudolph, O.

1995-01-01

A set of Green functions scrG α (x-y), α element-of[0,2π] for free scalar field theory is introduced, varying between the Hadamard Green function Δ 1 (x-y)==left-angle 0|{cphi(x),cphi(y)}|0 right-angle and the causal Green function scrG π (x-y)=iΔ(x-y)==[cphi(x),cphi(y)]. For every α element-of[0,2π] a path integral representation for scrG α is obtained both in configuration space and in the phase space of the classical relativistic particle. Setting α=π a sum-over-histories representation for the causal Green function is obtained. Furthermore, a reduced phase space integral representation for the scrG α 's is stated and an alternative BRST path integral representation for scrG α is presented. From these path integral representations the composition laws for the scrG α 's are derived using a modified path decomposition expansion

Stochastic Differential Equation-Based Flexible Software Reliability Growth Model

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P. K. Kapur

2009-01-01

Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.

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…

How lexical is the lexicon? Evidence for integrated auditory memory representations.

Science.gov (United States)

Pufahl, April; Samuel, Arthur G

2014-05-01

Previous research has shown that lexical representations must include not only linguistic information (what word was said), but also indexical information (how it was said, and by whom). The present work demonstrates that even this expansion is not sufficient. Seemingly irrelevant information, such as an unattended background sound, is retained in memory and can facilitate subsequent speech perception. We presented participants with spoken words paired with environmental sounds (e.g., a phone ringing), and had them make an "animate/inanimate" decision for each word. Later performance identifying filtered versions of the words was impaired to a similar degree if the voice changed or if the environmental sound changed. Moreover, when quite dissimilar words were used at exposure and test, we observed the same result when we reversed the roles of the words and the environmental sounds. The experiments also demonstrated limits to these effects, with no benefit from repetition. Theoretically, our results support two alternative possibilities: (1) Lexical representations are memory representations, and are not walled off from those for other sounds. Indexical effects reflect simply one type of co-occurrence that is incorporated into such representations. (2) The existing literature on indexical effects does not actually bear on lexical representations - voice changes, like environmental sounds heard with a word, produce implicit memory effects that are not tied to the lexicon. We discuss the evidence and implications of these two theoretical alternatives. Copyright © 2014 Elsevier Inc. All rights reserved.

GillesPy: A Python Package for Stochastic Model Building and Simulation.

Science.gov (United States)

Abel, John H; Drawert, Brian; Hellander, Andreas; Petzold, Linda R

2016-09-01

GillesPy is an open-source Python package for model construction and simulation of stochastic biochemical systems. GillesPy consists of a Python framework for model building and an interface to the StochKit2 suite of efficient simulation algorithms based on the Gillespie stochastic simulation algorithms (SSA). To enable intuitive model construction and seamless integration into the scientific Python stack, we present an easy to understand, action-oriented programming interface. Here, we describe the components of this package and provide a detailed example relevant to the computational biology community.

Parental representations and dimensions of personality: empirical relations and assessment implications.

Science.gov (United States)

Pincus, A L; Ruiz, M A

1997-04-01

Research on the relations between parental representations, personality traits, and psychopathology was discussed with reference to their integration for clinical personality assessment. Empirical results linking parental representations assessed by the Structural Analysis of Social Behavior and the Five-Factor Model of personality traits in a young adult population supported the position that parental representations significantly relate to adult personality. Individuals whose parental representations were generally affiliative described themselves as less prone to emotional distress (lower neuroticism); more interpersonally oriented and experiencing of positive emotions (higher extraversion); more peaceable and trustworthy (higher agreeableness); and more dutiful, resourceful, and dependable (higher conscientiousness). Parental representations colored by autonomy granting and autonomy taking were related to higher levels of openness to experience but lower levels of conscientiousness and extraversion in self-descriptions. Assessment implications and an integrative assessment strategy were presented along with a clinical case example.

Remarks on the history of the terms "object representation" and "self representation".

Science.gov (United States)

May, Ulrike

2005-01-01

This paper reconstructs the history of the term "object representation" and "self representation". It seeks to show that "Objektrepräsentanz" was introduced by Fenichel in 1926, following on from Radó, in order to be able to integrate identification (and the superego) into metapsychology. Freud himself never used "Objektrepräsentanz". Fenichel's pioneering role is not discernible in the English literature mainly because of the diverging approaches used in the translation of this term (object representative versus object representation). It is generally acknowledged that "self representation" was first used by Hartmann but this paper suggests that it actually played a more crucial role in Jacobson's work than it did in Hartmann's. In addition, this paper sees the terms of self and object representation as a reflection of the paradigm change in the 1920s that ensued after the publication of Freud's "The Ego and the Id". In tracing the history of the terms, the significance of the Berlin Psychoanalytical Institute in the 1920s emerges as do the Berlin roots of the works written in the USA in the 1950s and 1960s by Edith Jacobson. She received her analytical training in Berlin. Fenichel was her analyst, Radó was one of her teachers, and she was closely involved with the work of her fellow analysts there.

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.

A collection of integrable systems of the Toda type in continuous and discrete time, with 2x2 Lax representations

OpenAIRE

Suris, Yuri B.

1997-01-01

A fairly complete list of Toda-like integrable lattice systems, both in the continuous and discrete time, is given. For each system the Newtonian, Lagrangian and Hamiltonian formulations are presented, as well as the 2x2 Lax representation and r-matrix structure. The material is given in the "no comment" style, in particular, all proofs are omitted.

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...

Efficiency in the Community College Sector: Stochastic Frontier Analysis

Science.gov (United States)

Agasisti, Tommaso; Belfield, Clive

2017-01-01

This paper estimates technical efficiency scores across the community college sector in the United States. Using stochastic frontier analysis and data from the Integrated Postsecondary Education Data System for 2003-2010, we estimate efficiency scores for 950 community colleges and perform a series of sensitivity tests to check for robustness. We…

Structure factors for tunneling ionization rates of molecules: General Hartree-Fock-based integral representation

Science.gov (United States)

Madsen, Lars Bojer; Jensen, Frank; Dnestryan, Andrey I.; Tolstikhin, Oleg I.

2017-07-01

In the leading-order approximation of the weak-field asymptotic theory (WFAT), the dependence of the tunneling ionization rate of a molecule in an electric field on its orientation with respect to the field is determined by the structure factor of the ionizing molecular orbital. The WFAT yields an expression for the structure factor in terms of a local property of the orbital in the asymptotic region. However, in general quantum chemistry approaches molecular orbitals are expanded in a Gaussian basis which does not reproduce their asymptotic behavior correctly. This hinders the application of the WFAT to polyatomic molecules, which are attracting increasing interest in strong-field physics. Recently, an integral-equation approach to the WFAT for tunneling ionization of one electron from an arbitrary potential has been developed. The structure factor is expressed in an integral form as a matrix element involving the ionizing orbital. The integral is not sensitive to the asymptotic behavior of the orbital, which resolves the difficulty mentioned above. Here, we extend the integral representation for the structure factor to many-electron systems treated within the Hartree-Fock method and show how it can be implemented on the basis of standard quantum chemistry software packages. We validate the methodology by considering noble-gas atoms and the CO molecule, for which accurate structure factors exist in the literature. We also present benchmark results for CO2 and for NH3 in the pyramidal and planar geometries.

System Entropy Measurement of Stochastic Partial Differential Systems

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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.

Measures of thermodynamic irreversibility in deterministic and stochastic dynamics

International Nuclear Information System (INIS)

Ford, Ian J

2015-01-01

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

A symplectic integration method for elastic filaments

Science.gov (United States)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

Stochastic Optimization in The Power Management of Bottled Water Production Planning

Science.gov (United States)

Antoro, Budi; Nababan, Esther; Mawengkang, Herman

2018-01-01

This paper review a model developed to minimize production costs on bottled water production planning through stochastic optimization. As we know, that planning a management means to achieve the goal that have been applied, since each management level in the organization need a planning activities. The built models is a two-stage stochastic models that aims to minimize the cost on production of bottled water by observing that during the production process, neither interfernce nor vice versa occurs. The models were develop to minimaze production cost, assuming the availability of packing raw materials used considered to meet for each kind of bottles. The minimum cost for each kind production of bottled water are expressed in the expectation of each production with a scenario probability. The probability of uncertainly is a representation of the number of productions and the timing of power supply interruption. This is to ensure that the number of interruption that occur does not exceed the limit of the contract agreement that has been made by the company with power suppliers.

Making Implicit Multivariable Calculus Representations Explicit: A Clinical Study

Science.gov (United States)

McGee, Daniel; Moore-Russo, Deborah; Martinez-Planell, Rafael

2015-01-01

Reviewing numerous textbooks, we found that in both differential and integral calculus textbooks the authors commonly assume that: (i) students can generalize associations between representations in two dimensions to associations between representations of the same mathematical concept in three dimensions on their own; and (ii) explicit…

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Directory of Open Access Journals (Sweden)

Peng Jiang

2013-01-01

Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

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...

Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients

CERN Document Server

Hutzenthaler, Martin

2015-01-01

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation method

SLUG-STOCHASTICALLY LIGHTING UP GALAXIES. I. METHODS AND VALIDATING TESTS

Energy Technology Data Exchange (ETDEWEB)

Da Silva, Robert L.; Fumagalli, Michele; Krumholz, Mark [Department of Astronomy and Astrophysics, UCO/Lick Observatory, University of California, 1156 High Street, Santa Cruz, CA 95064 (United States)

2012-02-01

The effects of stochasticity on the luminosities of stellar populations are an often neglected but crucial element for understanding populations in the low-mass or the low star formation rate regime. To address this issue, we present SLUG, a new code to 'Stochastically Light Up Galaxies'. SLUG synthesizes stellar populations using a Monte Carlo technique that properly treats stochastic sampling including the effects of clustering, the stellar initial mass function, star formation history, stellar evolution, and cluster disruption. This code produces many useful outputs, including (1) catalogs of star clusters and their properties such as their stellar initial mass distributions and their photometric properties in a variety of filters, (2) two dimensional histograms of color-magnitude diagrams of every star in the simulation, and (3) the photometric properties of field stars and the integrated photometry of the entire simulated galaxy. After presenting the SLUG algorithm in detail, we validate the code through comparisons with STARBURST99 in the well-sampled regime, and with observed photometry of Milky Way clusters. Finally, we demonstrate SLUG's capabilities by presenting outputs in the stochastic regime. SLUG is publicly distributed through the Web site http://sites.google.com/site/runslug/.

Numerical functional integration method for studying the properties of the physical vacuum

International Nuclear Information System (INIS)

Lobanov, Yu.Yu.

1998-01-01

The new approach to investigate the physical vacuum in quantum theories including its nonperturbative topological structure is discussed. This approach is based on the representation of the matrix element of the evolution operator in Euclidean metrics in a form of the functional integral with a certain measure in the corresponding space and on the use of approximation formulas which we constructed for this kind of integral. No preliminary discretization of space and time is required, as well as no simplifying assumptions like semiclassical approximation, collective excitations, introduction of ''short-time'' propagators, etc. are necessary in this approach. The method allows to use the more preferable deterministic algorithms instead of the traditional stochastic technique. It has been proven that our approach has important advantages over the other known methods, including the higher efficiency of computations. Examples of application of the method to the numerical study of some potential nuclear models and to the computation of the topological susceptibility and the θ-vacua energy are presented. (author)

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth.

Science.gov (United States)

Lv, Qiming; Schneider, Manuel K; Pitchford, Jonathan W

2008-08-01

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.

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).

STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB.

Science.gov (United States)

Klingbeil, Guido; Erban, Radek; Giles, Mike; Maini, Philip K

2011-04-15

The importance of stochasticity in biological systems is becoming increasingly recognized and the computational cost of biologically realistic stochastic simulations urgently requires development of efficient software. We present a new software tool STOCHSIMGPU that exploits graphics processing units (GPUs) for parallel stochastic simulations of biological/chemical reaction systems and show that significant gains in efficiency can be made. It is integrated into MATLAB and works with the Systems Biology Toolbox 2 (SBTOOLBOX2) for MATLAB. The GPU-based parallel implementation of the Gillespie stochastic simulation algorithm (SSA), the logarithmic direct method (LDM) and the next reaction method (NRM) is approximately 85 times faster than the sequential implementation of the NRM on a central processing unit (CPU). Using our software does not require any changes to the user's models, since it acts as a direct replacement of the stochastic simulation software of the SBTOOLBOX2. The software is open source under the GPL v3 and available at http://www.maths.ox.ac.uk/cmb/STOCHSIMGPU. The web site also contains supplementary information. klingbeil@maths.ox.ac.uk Supplementary data are available at Bioinformatics online.

The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems

CERN Document Server

Etingof, Pavel

2005-01-01

The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer

Object representation in the bottlenose dolphin (Tursiops truncatus): integration of visual and echoic information.

Science.gov (United States)

Harley, H E; Roitblat, H L; Nachtigall, P E

1996-04-01

A dolphin performed a 3-alternative matching-to-sample task in different modality conditions (visual/echoic, both vision and echolocation: visual, vision only; echoic, echolocation only). In Experiment 1, training occurred in the dual-modality (visual/echoic) condition. Choice accuracy in tests of all conditions was above chance without further training. In Experiment 2, unfamiliar objects with complementary similarity relations in vision and echolocation were presented in single-modality conditions until accuracy was about 70%. When tested in the visual/echoic condition, accuracy immediately rose (95%), suggesting integration across modalities. In Experiment 3, conditions varied between presentation of sample and alternatives. The dolphin successfully matched familiar objects in the cross-modal conditions. These data suggest that the dolphin has an object-based representational system.

A Rigorous Temperature-Dependent Stochastic Modelling and Testing for MEMS-Based Inertial Sensor Errors

Directory of Open Access Journals (Sweden)

Spiros Pagiatakis

2009-10-01

Full Text Available In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times. It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF. It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at −40 °C, −20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.

A Rigorous Temperature-Dependent Stochastic Modelling and Testing for MEMS-Based Inertial Sensor Errors.

Science.gov (United States)

El-Diasty, Mohammed; Pagiatakis, Spiros

2009-01-01

In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM) models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times). It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF). It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at -40 °C, -20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.

A stochastic model for the simulation of wind turbine blades in static stall

DEFF Research Database (Denmark)

Bertagnolio, Franck; Rasmussen, Flemming; Sørensen, Niels N.

2010-01-01

The aim of this work is to improve aeroelastic simulation codes by accounting for the unsteady aerodynamic forces that a blade experiences in static stall. A model based on a spectral representation of the aerodynamic lift force is defined. The drag and pitching moment are derived using...... a conditional simulation technique for stochastic processes. The input data for the model can be collected either from measurements or from numerical results from a Computational Fluid Dynamics code for airfoil sections at constant angles of attack. An analysis of such data is provided, which helps to determine...

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

Science.gov (United States)

Sedwards, Sean; Mazza, Tommaso

2007-10-15

Compartments and membranes are the basis of cell topology and more than 30% of the human genome codes for membrane proteins. While it is possible to represent compartments and membrane proteins in a nominal way with many mathematical formalisms used in systems biology, few, if any, explicitly model the topology of the membranes themselves. Discrete stochastic simulation potentially offers the most accurate representation of cell dynamics. Since the details of every molecular interaction in a pathway are often not known, the relationship between chemical species in not necessarily best described at the lowest level, i.e. by mass action. Simulation is a form of computer-aided analysis, relying on human interpretation to derive meaning. To improve efficiency and gain meaning in an automatic way, it is necessary to have a formalism based on a model which has decidable properties. We present Cyto-Sim, a stochastic simulator of membrane-enclosed hierarchies of biochemical processes, where the membranes comprise an inner, outer and integral layer. The underlying model is based on formal language theory and has been shown to have decidable properties (Cavaliere and Sedwards, 2006), allowing formal analysis in addition to simulation. The simulator provides variable levels of abstraction via arbitrary chemical kinetics which link to ordinary differential equations. In addition to its compact native syntax, Cyto-Sim currently supports models described as Petri nets, can import all versions of SBML and can export SBML and MATLAB m-files. Cyto-Sim is available free, either as an applet or a stand-alone Java program via the web page (http://www.cosbi.eu/Rpty_Soft_CytoSim.php). Other versions can be made available upon request.

Unified double- and single-sided homogeneous Green's function representations

Science.gov (United States)

Wapenaar, Kees; van der Neut, Joost; Slob, Evert

2016-06-01

In wave theory, the homogeneous Green's function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green's function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green's function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green's function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green's function retrieval.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.

2015-01-07

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.; Al-Juhani, Amnah

2015-01-01

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Symbolic Computing in Probabilistic and Stochastic Analysis

Directory of Open Access Journals (Sweden)

Kamiński Marcin

2015-12-01

Full Text Available The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i analytical derivations, (ii the classical Monte-Carlo simulation approach, (iii the stochastic perturbation technique, as well as (iv some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented in any system to derive the basic equations for the stochastic perturbation technique and how to make an efficient implementation of the semi-analytical methods using an automatic differentiation and integration provided by the computer algebra program itself. The second important illustration is probabilistic extension of the finite element and finite difference methods coded in MAPLE, showing how to solve boundary value problems with random parameters in the environment of symbolic computing. The response function method belongs to the third group, where interference of classical deterministic software with the non-linear fitting numerical techniques available in various symbolic environments is displayed. We recover in this context the probabilistic structural response in engineering systems and show how to solve partial differential equations including Gaussian randomness in their coefficients.

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.)

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

Simulating local measurements on a quantum many-body system with stochastic matrix product states

DEFF Research Database (Denmark)

Gammelmark, Søren; Mølmer, Klaus

2010-01-01

We demonstrate how to simulate both discrete and continuous stochastic evolutions of a quantum many-body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a simple representation in terms of matrix product operators...... is found. The technique is exemplified by numerical simulations of the antiferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular, we focus on local measurements with small support and nonlocal measurements, which induce long-range correlations....

Testing periodically integrated autoregressive models

NARCIS (Netherlands)

Ph.H.B.F. Franses (Philip Hans); M.J. McAleer (Michael)

1997-01-01

textabstractPeriodically integrated time series require a periodic differencing filter to remove the stochastic trend. A non-periodic integrated time series needs the first-difference filter for similar reasons. When the changing seasonal fluctuations for the non-periodic integrated series can be

A Stochastic Model for Improving Information Security in Supply Chain Systems

OpenAIRE

Ibrahim Al Kattan; Ahmed Al Nunu; Kassem Saleh

2009-01-01

This article presents a probabilistic security model for supply chain management systems (SCM) in which the basic goals of security (including confidentiality, integrity, availability and accountability, CIAA) are modeled and analyzed. Consequently, the weak points in system security are identified. A stochastic model using measurable values to describe the information system security of a SCM is introduced. Information security is a crucial and integral part of the network of supply chains. ...

Flows, scaling, and the control of moment hierarchies for stochastic chemical reaction networks

Science.gov (United States)

Smith, Eric; Krishnamurthy, Supriya

2017-12-01

Stochastic chemical reaction networks (CRNs) are complex systems that combine the features of concurrent transformation of multiple variables in each elementary reaction event and nonlinear relations between states and their rates of change. Most general results concerning CRNs are limited to restricted cases where a topological characteristic known as deficiency takes a value 0 or 1, implying uniqueness and positivity of steady states and surprising, low-information forms for their associated probability distributions. Here we derive equations of motion for fluctuation moments at all orders for stochastic CRNs at general deficiency. We show, for the standard base case of proportional sampling without replacement (which underlies the mass-action rate law), that the generator of the stochastic process acts on the hierarchy of factorial moments with a finite representation. Whereas simulation of high-order moments for many-particle systems is costly, this representation reduces the solution of moment hierarchies to a complexity comparable to solving a heat equation. At steady states, moment hierarchies for finite CRNs interpolate between low-order and high-order scaling regimes, which may be approximated separately by distributions similar to those for deficiency-zero networks and connected through matched asymptotic expansions. In CRNs with multiple stable or metastable steady states, boundedness of high-order moments provides the starting condition for recursive solution downward to low-order moments, reversing the order usually used to solve moment hierarchies. A basis for a subset of network flows defined by having the same mean-regressing property as the flows in deficiency-zero networks gives the leading contribution to low-order moments in CRNs at general deficiency, in a 1 /n expansion in large particle numbers. Our results give a physical picture of the different informational roles of mean-regressing and non-mean-regressing flows and clarify the dynamical

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.

Integral representation in the hodograph plane of compressible flow

DEFF Research Database (Denmark)

Hansen, Erik Bent; Hsiao, G.C.

2003-01-01

Compressible flow is considered in the hodograph plane. The linearity of the equation determining the stream function is exploited to derive a representation formula involving boundary data only, and a fundamental solution to the adjoint equation. For subsonic flow, an efficient algorithm...

Interaction and representational integration: Evidence from speech errors

OpenAIRE

Goldrick, Matthew; Baker, H. Ross; Murphy, Amanda; Baese-Berk, Melissa

2011-01-01

We examine the mechanisms that support interaction between lexical, phonological and phonetic processes during language production. Studies of the phonetics of speech errors have provided evidence that partially activated lexical and phonological representations influence phonetic processing. We examine how these interactive effects are modulated by lexical frequency. Previous research has demonstrated that during lexical access, the processing of high frequency words is facilitated; in contr...

A real-space stochastic density matrix approach for density functional electronic structure.

Science.gov (United States)

Beck, Thomas L

2015-12-21

The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

Tsunami evacuation plans for future megathrust earthquakes in Padang, Indonesia, considering stochastic earthquake scenarios

Directory of Open Access Journals (Sweden)

A. Muhammad

2017-12-01

Full Text Available This study develops tsunami evacuation plans in Padang, Indonesia, using a stochastic tsunami simulation method. The stochastic results are based on multiple earthquake scenarios for different magnitudes (Mw 8.5, 8.75, and 9.0 that reflect asperity characteristics of the 1797 historical event in the same region. The generation of the earthquake scenarios involves probabilistic models of earthquake source parameters and stochastic synthesis of earthquake slip distributions. In total, 300 source models are generated to produce comprehensive tsunami evacuation plans in Padang. The tsunami hazard assessment results show that Padang may face significant tsunamis causing the maximum tsunami inundation height and depth of 15 and 10 m, respectively. A comprehensive tsunami evacuation plan – including horizontal evacuation area maps, assessment of temporary shelters considering the impact due to ground shaking and tsunami, and integrated horizontal–vertical evacuation time maps – has been developed based on the stochastic tsunami simulation results. The developed evacuation plans highlight that comprehensive mitigation policies can be produced from the stochastic tsunami simulation for future tsunamigenic events.

Multiobjective Output Feedback Control of a Class of Stochastic Hybrid Systems with State-Dependent Noise

Directory of Open Access Journals (Sweden)

S. Aberkane

2007-01-01

Full Text Available This paper deals with dynamic output feedback control of continuous-time active fault tolerant control systems with Markovian parameters (AFTCSMP and state-dependent noise. The main contribution is to formulate conditions for multiperformance design, related to this class of stochastic hybrid systems, that take into account the problematic resulting from the fact that the controller only depends on the fault detection and isolation (FDI process. The specifications and objectives under consideration include stochastic stability, ℋ2 and ℋ∞ (or more generally, stochastic integral quadratic constraints performances. Results are formulated as matrix inequalities. The theoretical results are illustrated using a classical example from literature.

Nonzero-Sum Stochastic Differential Portfolio Games under a Markovian Regime Switching Model

Directory of Open Access Journals (Sweden)

Chaoqun Ma

2015-01-01

Full Text Available We consider a nonzero-sum stochastic differential portfolio game problem in a continuous-time Markov regime switching environment when the price dynamics of the risky assets are governed by a Markov-modulated geometric Brownian motion (GBM. The market parameters, including the bank interest rate and the appreciation and volatility rates of the risky assets, switch over time according to a continuous-time Markov chain. We formulate the nonzero-sum stochastic differential portfolio game problem as two utility maximization problems of the sum process between two investors’ terminal wealth. We derive a pair of regime switching Hamilton-Jacobi-Bellman (HJB equations and two systems of coupled HJB equations at different regimes. We obtain explicit optimal portfolio strategies and Feynman-Kac representations of the two value functions. Furthermore, we solve the system of coupled HJB equations explicitly in a special case where there are only two states in the Markov chain. Finally we provide comparative statics and numerical simulation analysis of optimal portfolio strategies and investigate the impact of regime switching on optimal portfolio strategies.

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

Effects of stochastic interest rates in decision making under risk: A Markov decision process model for forest management

Science.gov (United States)

Mo Zhou; Joseph Buongiorno

2011-01-01

Most economic studies of forest decision making under risk assume a fixed interest rate. This paper investigated some implications of this stochastic nature of interest rates. Markov decision process (MDP) models, used previously to integrate stochastic stand growth and prices, can be extended to include variable interest rates as well. This method was applied to...

Multi-Period Natural Gas Market Modeling. Applications, Stochastic Extensions and Solution Approaches

International Nuclear Information System (INIS)

Egging, R.G.

2010-11-01

This dissertation develops deterministic and stochastic multi-period mixed complementarity problems (MCP) for the global natural gas market, as well as solution approaches for large-scale stochastic MCP. The deterministic model is unique in the combination of the level of detail of the actors in the natural gas markets and the transport options, the detailed regional and global coverage, the multi-period approach with endogenous capacity expansions for transportation and storage infrastructure, the seasonal variation in demand and the representation of market power according to Nash-Cournot theory. The model is applied to several scenarios for the natural gas market that cover the formation of a cartel by the members of the Gas Exporting Countries Forum, a low availability of unconventional gas in the United States, and cost reductions in long-distance gas transportation. The results provide insights in how different regions are affected by various developments, in terms of production, consumption, traded volumes, prices and profits of market participants. The stochastic MCP is developed and applied to a global natural gas market problem with four scenarios for a time horizon until 2050 with nineteen regions and containing 78,768 variables. The scenarios vary in the possibility of a gas market cartel formation and varying depletion rates of gas reserves in the major gas importing regions. Outcomes for hedging decisions of market participants show some significant shifts in the timing and location of infrastructure investments, thereby affecting local market situations. A first application of Benders decomposition (BD) is presented to solve a large-scale stochastic MCP for the global gas market with many hundreds of first-stage capacity expansion variables and market players exerting various levels of market power. The largest problem solved successfully using BD contained 47,373 variables of which 763 first-stage variables, however using BD did not result in

Learning STEM Through Integrative Visual Representations

Science.gov (United States)

Virk, Satyugjit Singh

Previous cognitive models of memory have not comprehensively taken into account the internal cognitive load of chunking isolated information and have emphasized the external cognitive load of visual presentation only. Under the Virk Long Term Working Memory Multimedia Model of cognitive load, drawing from the Cowan model, students presented with integrated animations of the key neural signal transmission subcomponents where the interrelationships between subcomponents are visually and verbally explicit, were hypothesized to perform significantly better on free response and diagram labeling questions, than students presented with isolated animations of these subcomponents. This is because the internal attentional cognitive load of chunking these concepts is greatly reduced and hence the overall cognitive load is less for the integrated visuals group than the isolated group, despite the higher external load for the integrated group of having the interrelationships between subcomponents presented explicitly. Experiment 1 demonstrated that integrating the subcomponents of the neuron significantly enhanced comprehension of the interconnections between cellular subcomponents and approached significance for enhancing comprehension of the layered molecular correlates of the cellular structures and their interconnections. Experiment 2 corrected time on task confounds from Experiment 1 and focused on the cellular subcomponents of the neuron only. Results from the free response essay subcomponent subscores did demonstrate significant differences in favor of the integrated group as well as some evidence from the diagram labeling section. Results from free response, short answer and What-If (problem solving), and diagram labeling detailed interrelationship subscores demonstrated the integrated group did indeed learn the extra material they were presented with. This data demonstrating the integrated group learned the extra material they were presented with provides some initial

The Early Exercise Premium Representation for American Options on Multiply Assets

International Nuclear Information System (INIS)

Klimsiak, Tomasz; Rozkosz, Andrzej

2016-01-01

In the paper we consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follow the classical multidimensional Black and Scholes model. We provide a general early exercise premium representation formula for options with payoff functions which are convex or satisfy mild regularity assumptions. Examples include index options, spread options, call on max options, put on min options, multiply strike options and power-product options. In the proof of the formula we exploit close connections between the optimal stopping problems associated with valuation of American options, obstacle problems and reflected backward stochastic differential equations

Bistable perception modeled as competing stochastic integrations at two levels.

Science.gov (United States)

Gigante, Guido; Mattia, Maurizio; Braun, Jochen; Del Giudice, Paolo

2009-07-01

We propose a novel explanation for bistable perception, namely, the collective dynamics of multiple neural populations that are individually meta-stable. Distributed representations of sensory input and of perceptual state build gradually through noise-driven transitions in these populations, until the competition between alternative representations is resolved by a threshold mechanism. The perpetual repetition of this collective race to threshold renders perception bistable. This collective dynamics - which is largely uncoupled from the time-scales that govern individual populations or neurons - explains many hitherto puzzling observations about bistable perception: the wide range of mean alternation rates exhibited by bistable phenomena, the consistent variability of successive dominance periods, and the stabilizing effect of past perceptual states. It also predicts a number of previously unsuspected relationships between observable quantities characterizing bistable perception. We conclude that bistable perception reflects the collective nature of neural decision making rather than properties of individual populations or neurons.

Quantum noise and stochastic reduction

International Nuclear Information System (INIS)

Brody, Dorje C; Hughston, Lane P

2006-01-01

In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic component, while respecting the conservation law. According to the dynamics thus obtained, referred to as the energy-based stochastic Schroedinger equation, an arbitrary initial state collapses spontaneously to one of the energy eigenstates, thus describing the phenomenon of quantum state reduction. In this paper, two such models are investigated: one that achieves state reduction in infinite time and the other in finite time. The properties of the associated energy expectation process and the energy variance process are worked out in detail. By use of a novel application of a nonlinear filtering method, closed-form solutions-algebraic in character and involving no integration-are obtained of both these models. In each case, the solution is expressed in terms of a random variable representing the terminal energy of the system and an independent noise process. With these solutions at hand it is possible to simulate explicitly the dynamics of the quantum states of complicated physical systems

Integrating Renewables in Electricity Markets

DEFF Research Database (Denmark)

Morales González, Juan Miguel; Conejo, Antonio J.; Madsen, Henrik

in the electricity market. • The development of procedures to enable demand response and to facilitate the integration of stochastic renewable units. This book is written in a modular and tutorial manner and includes many illustrative examples to facilitate its comprehension. It is intended for advanced...... such as: • The modeling and forecasting of stochastic renewable power production. • The characterization of the impact of renewable production on market outcomes. • The clearing of electricity markets with high penetration of stochastic renewable units. • The development of mechanisms to counteract...

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...

Introduction into integral geometry and stereology

DEFF Research Database (Denmark)

Kiderlen, Markus

Statistics and Random Fields and is a self-containing introduction into integral geometry and its applications in stereology. The most important integral geometric tools for stereological applications are kinematic formulas and results of Blaschke-Petkantschin type. Therefore, Crofton's formula......This text is the extended version of two talks held at the Summer Academy Stochastic Geometry, Spatial Statistics and Random Fields in the Soellerhaus, Germany, in September 2009. It forms (with slight modifications) a chapter of the Springer lecture notes Lectures on Stochastic Geometry, Spatial...

String operator formalism and functional intergal in the holomorphic representation

International Nuclear Information System (INIS)

Losev, A.S.; Morozov, A.Yu.; Rislyj, A.A.; Shatashvili, S.L.

1989-01-01

Connection between the continual integral over open Riemann surfaces and the operator formalism on closed Riemann surfaces is discussed. States of the operator formalism are the holomorphic representation of the continual integral

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.)

Numerical solutions of stochastic Lotka-Volterra equations via operational matrices

Directory of Open Access Journals (Sweden)

F. Hosseini Shekarabi

2016-03-01

Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.

Analysis of thin plates with holes by using exact geometrical representation within XFEM.

Science.gov (United States)

Perumal, Logah; Tso, C P; Leng, Lim Thong

2016-05-01

This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique. Simulation results show that the proposed techniques help to reduce the solution error, due to the exact geometrical representation of the holes and utilization of appropriate quadrature rules. Discussion on minimum order of integration order needed to achieve good accuracy and convergence for the techniques presented in this work is also included.

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.

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.

Fuzzy Stochastic Optimization Theory, Models and Applications

CERN Document Server

Wang, Shuming

2012-01-01

Covering in detail both theoretical and practical perspectives, this book is a self-contained and systematic depiction of current fuzzy stochastic optimization that deploys the fuzzy random variable as a core mathematical tool to model the integrated fuzzy random uncertainty. It proceeds in an orderly fashion from the requisite theoretical aspects of the fuzzy random variable to fuzzy stochastic optimization models and their real-life case studies.   The volume reflects the fact that randomness and fuzziness (or vagueness) are two major sources of uncertainty in the real world, with significant implications in a number of settings. In industrial engineering, management and economics, the chances are high that decision makers will be confronted with information that is simultaneously probabilistically uncertain and fuzzily imprecise, and optimization in the form of a decision must be made in an environment that is doubly uncertain, characterized by a co-occurrence of randomness and fuzziness. This book begins...

Stochastic 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)

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

Unified double- and single-sided homogeneous Green’s function representations

Science.gov (United States)

van der Neut, Joost; Slob, Evert

2016-01-01

In wave theory, the homogeneous Green’s function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green’s function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green’s function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green’s function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green’s function retrieval. PMID:27436983

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.

Applied stochastic modelling

CERN Document Server

Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P

2008-01-01

Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...

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.

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.

Dynamics of bound vector solitons induced by stochastic perturbations: Soliton breakup and soliton switching

International Nuclear Information System (INIS)

Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying

2013-01-01

We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.

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...

NLP model and stochastic multi-start optimization approach for heat exchanger networks

International Nuclear Information System (INIS)

Núñez-Serna, Rosa I.; Zamora, Juan M.

2016-01-01

Highlights: • An NLP model for the optimal design of heat exchanger networks is proposed. • The NLP model is developed from a stage-wise grid diagram representation. • A two-phase stochastic multi-start optimization methodology is utilized. • Improved network designs are obtained with different heat load distributions. • Structural changes and reductions in the number of heat exchangers are produced. - Abstract: Heat exchanger network synthesis methodologies frequently identify good network structures, which nevertheless, might be accompanied by suboptimal values of design variables. The objective of this work is to develop a nonlinear programming (NLP) model and an optimization approach that aim at identifying the best values for intermediate temperatures, sub-stream flow rate fractions, heat loads and areas for a given heat exchanger network topology. The NLP model that minimizes the total annual cost of the network is constructed based on a stage-wise grid diagram representation. To improve the possibilities of obtaining global optimal designs, a two-phase stochastic multi-start optimization algorithm is utilized for the solution of the developed model. The effectiveness of the proposed optimization approach is illustrated with the optimization of two network designs proposed in the literature for two well-known benchmark problems. Results show that from the addressed base network topologies it is possible to achieve improved network designs, with redistributions in exchanger heat loads that lead to reductions in total annual costs. The results also show that the optimization of a given network design sometimes leads to structural simplifications and reductions in the total number of heat exchangers of the network, thereby exposing alternative viable network topologies initially not anticipated.

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

CERN Document Server

Kulasiri, Don

2002-01-01

Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas ...

Modelling the heat dynamics of a monitored Test Reference Environment for Building Integrated Photovoltaic systems using stochastic differential equations

DEFF Research Database (Denmark)

Lodi, C.; Bacher, Peder; Cipriano, J.

2012-01-01

reduce the ventilation thermal losses of the building by pre-heating the fresh air. Furthermore, by decreasing PV module temperature, the ventilation air heat extraction can simultaneously increase electrical and thermal energy production of the building. A correct prediction of the PV module temperature...... and heat transfer coefficients is fundamental in order to improve the thermo-electrical production.The considered grey-box models are composed of a set of continuous time stochastic differential equations, holding the physical description of the system, combined with a set of discrete time measurement......This paper deals with grey-box modelling of the energy transfer of a double skin Building Integrated Photovoltaic (BIPV) system. Grey-box models are based on a combination of prior physical knowledge and statistics, which enable identification of the unknown parameters in the system and accurate...

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)

Three-point statistics of cosmological stochastic gravitational waves

International Nuclear Information System (INIS)

Adshead, Peter; Lim, Eugene A.

2010-01-01

We consider the three-point function (i.e. the bispectrum or non-Gaussianity) for stochastic backgrounds of gravitational waves. We estimate the amplitude of this signal for the primordial inflationary background, gravitational waves generated during preheating, and for gravitational waves produced by self-ordering scalar fields following a global phase transition. To assess detectability, we describe how to extract the three-point signal from an idealized interferometric experiment and compute the signal to noise ratio as a function of integration time. The three-point signal for the stochastic gravitational wave background generated by inflation is unsurprisingly tiny. For gravitational radiation generated by purely causal, classical mechanisms we find that, no matter how nonlinear the process is, the three-point correlations produced vanish in direct detection experiments. On the other hand, we show that in scenarios where the B-mode of the cosmic microwave background is sourced by gravitational waves generated by a global phase transition, a strong three-point signal among the polarization modes is also produced. This may provide another method of distinguishing inflationary B-modes. To carry out this computation, we have developed a diagrammatic approach to the calculation of stochastic gravitational waves sourced by scalar fluids, which has applications beyond the present scenario.

Research-Based Worksheets on Using Multiple Representations in Science Classrooms

Science.gov (United States)

Hill, Matthew; Sharma, Manjula

2015-01-01

The ability to represent the world like a scientist is difficult to teach; it is more than simply knowing the representations (e.g., graphs, words, equations and diagrams). For meaningful science learning to take place, consideration needs to be given to explicitly integrating representations into instructional methods, linked to the content, and…

Study of the stochastic point reactor kinetic equation

International Nuclear Information System (INIS)

Gotoh, Yorio

1980-01-01

Diagrammatic technique is used to solve the stochastic point reactor kinetic equation. The method gives exact results which are derived from Fokker-Plank theory. A Green's function dressed with the clouds of noise is defined, which is a transfer function of point reactor with fluctuating reactivity. An integral equation for the correlation function of neutron power is derived using the following assumptions: 1) Green's funntion should be dressed with noise, 2) The ladder type diagrams only contributes to the correlation function. For a white noise and the one delayed neutron group approximation, the norm of the integral equation and the variance to mean-squared ratio are analytically obtained. (author)

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.

Path integral for stochastic inflation: Nonperturbative volume weighting, complex histories, initial conditions, and the end of inflation

Science.gov (United States)

Gratton, Steven

2011-09-01

In this paper we present a path integral formulation of stochastic inflation. Volume weighting can be naturally implemented from this new perspective in a very straightforward way when compared to conventional Langevin approaches. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. The calculation can be carried to times beyond those accessible to conventional Fokker-Planck approaches. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow roll. The slow-roll end of inflation mitigates certain “Youngness Paradox”-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper-time volume weighting as a viable measure for answering at least some interesting cosmological questions.

Path integral for stochastic inflation: Nonperturbative volume weighting, complex histories, initial conditions, and the end of inflation

International Nuclear Information System (INIS)

Gratton, Steven

2011-01-01

In this paper we present a path integral formulation of stochastic inflation. Volume weighting can be naturally implemented from this new perspective in a very straightforward way when compared to conventional Langevin approaches. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. The calculation can be carried to times beyond those accessible to conventional Fokker-Planck approaches. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow roll. The slow-roll end of inflation mitigates certain ''Youngness Paradox''-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper-time volume weighting as a viable measure for answering at least some interesting cosmological questions.

Evaluation of Monte Carlo electron-Transport algorithms in the integrated Tiger series codes for stochastic-media simulations

International Nuclear Information System (INIS)

Franke, B.C.; Kensek, R.P.; Prinja, A.K.

2013-01-01

Stochastic-media simulations require numerous boundary crossings. We consider two Monte Carlo electron transport approaches and evaluate accuracy with numerous material boundaries. In the condensed-history method, approximations are made based on infinite-medium solutions for multiple scattering over some track length. Typically, further approximations are employed for material-boundary crossings where infinite-medium solutions become invalid. We have previously explored an alternative 'condensed transport' formulation, a Generalized Boltzmann-Fokker-Planck (GBFP) method, which requires no special boundary treatment but instead uses approximations to the electron-scattering cross sections. Some limited capabilities for analog transport and a GBFP method have been implemented in the Integrated Tiger Series (ITS) codes. Improvements have been made to the condensed history algorithm. The performance of the ITS condensed-history and condensed-transport algorithms are assessed for material-boundary crossings. These assessments are made both by introducing artificial material boundaries and by comparison to analog Monte Carlo simulations. (authors)

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.

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

Sum-over-histories representation for the causal Green function of free scalar field theory

International Nuclear Information System (INIS)

Rudolph, O.

1993-10-01

A set of Green functions G α (x-y), α element of [0, 2π], for free scalar field theory is introduced, varying between the Hadamard Green function Δ 1 (x-y) triple bond 0vertical stroke {φ(x), φ(y)}vertical stroke 0> and the causal Green function G π (x-y)=iΔ(x-y) triple bond [φ(x), φ(y)]. For every α element of [0, 2π] a path-integral representation for G α is obtained both in the configuration space and in the phase space of the classical relativistic particle. Especially setting α=π a sum-over-histories representation for the causal Green function is obtained. Furthermore using BRST theory an alternative path-integral representation for G α is presented. From these path integral representations the composition laws for the G α 's are derived using a modified path decomposition expansion. (orig.)

Robust authentication through stochastic femtosecond laser filament induced scattering surfaces