Some problems are analyzed arising when a numerical simulation of a random motion of a large ensemble of diffusing particles is used to approximate the solution of a one-dimensional diffusion equation. The particle motion is described by means of a stochastic differential equation. The problems emerging especially when the diffusion coefficient is a function of spatial coordinate are discussed. The possibility of simulation of various kinds of stochastic integral is demonstrated. It is shown that the application of standard numerical procedures commonly adopted for ordinary differential equations may lead to erroneous results when used for solution of stochastic differential equations. General conclusions are verified by numerical solution of three stochastic differential equations with different forms of the diffusion coefficient.. Keywords: Stochastic modelling; Diffusion process; Stochastic differential equation. ...
Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. After proving the Doob-Meyer decomposition, quadratic variation processes and local ... More. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. After proving the Doob-Meyer decomposition, quadratic variation processes and local martingales are discussed. The book proceeds to construct stochastic integrals, prove the Itô formula, derive several important applications of the formula such as the martingale representation theorem and the Burkhölder-Davis-Gundy inequality, and establish the Girsanov theorem on change of measures. Next, attention is focused on stochastic differential equations which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of stochastic differential equations and form the main theme of this book. After establishing the existence and uniqueness of strong ...
Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this talk, two commonly used SSAs will be studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. The connections between SSAs and the deterministic models (based on reaction-diffusion PDEs) will be presented. I will consider chemical reactions both at a surface and in the bulk. I will show how the microscopic parameters should be chosen to achieve the correct macroscopic reaction rate. This choice is found to depend on which SSA is used. I will also present multiscale algorithms which use models with a different level of detail in different parts of the computational domain ...
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A modeling approach to treat noisy engineering systems is presented. We deal with controlled systems that evolve in a continuous-time over finite time intervals, but also in continuous interaction with environments of intrinsic variability. We face the compl A modeling approach to treat noisy engineering systems is presented. We deal with controlled systems that evolve in a continuous-time over finite time intervals, but also in continuous interaction with environments of intrinsic variability. We face the complexity of these systems by introducing a methodology based on Stochastic Differential Equations (SDE) models. We focus on specific type of complexity derived from unpredictable abrupt and/or structural changes. In this paper an approach based on controlled Stochastic Differential Equations with Markovian Switchings (SDEMS) is proposed. Technical conditions for the existence and uniqueness of the solution of these models are provided. We treat with nonlinear SDEMS that does not have closed ...
Arnold, L. (1975): Stochastic Differential Equations New York, John Wiley and Sons.. Bianchi, C., R. Cesari and L. Panattoni (1995): Alternative Estimators of the Cox, Ingersoll and Ross Model of the term Structure of Interest Rates. Roma, Banca dItalia, Temi di Discussione N.326.. Bianchi, C. and E. M. Cleur (1996, forthcomning): Indirect Estimation of Stochastic Differential Equation Models: Some Computational Experiment, Computational Statistics.. Brennan, M.J. and E.S. Schwartz (1979): A Continuous Time Approach to the Pricing of Bonds, Journal of Banking and Finance, 3, 135-155.. Broze, L., O. Scaillet and J.M. Zakoian (1994): Quasi Indirect Inference for Diffusion Processes. Paris: Crest, document de travail No.9511.. Broze, L., O. Scaillet and J.M. Zakoian (1995): Testing for Continuous Time Models of the Short-Term Interest Rate Journal of Empirical Finance, 2, 199-223.. Calzolari, G. (1979): Antithetic Variates to Estimate the Simulation Bias in Non-Linear Models, Economics Letters 4, ...
|p style=text-indent:20px;|When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the deterministic framework which reduce the order of a control system and hence reduce computational complexity. This work considers both methods when the control is replaced by a noise term. We provide theoretical tools such as stochastic concepts for reachability and observability, which are necessary for balancing related model order reduction of linear stochastic differential equations with additive Lévy noise. Moreover, we derive error bounds for both BT and SPA and provide numerical results for a specific example which support the theory.|/p|
1] M.I. Freidlin, Functional Integration and Partial Differential Equations, Princeton University Press, Princeton, 1985. , MR 833742 , Zbl 0568.60057 [2] A. Friedman, Stochastic Differential Equations, Vol. 1, 1975, Academic Press. , Zbl 0323.60056 [3] K. Ichihara, Some Global Properties of Symmetric Diffusion Processes, Publ. RIMS Kyoto Univ., Vol. 14, 1978, pp. 441-486. , MR 509198 , Zbl 0397.60062 [4] R.Z. Khasminkii, Ergodic Properties of Recurrent Diffusion Processes and Stabilization of the Solution of the Cauchy Problem for Parabolic Equations, Proc. Theory and Appl., Vol. 5, 1960, pp. 179-196. , MR 133871 , Zbl 0106.12001 [5] R.Z. Khasminskii, On the Averaging Principle for Stochastic Differential Equations, Kybernetika, Academia, Praha, Vol. 4, 1968, pp. 260-279 (Russian). , MR 260052 , Zbl 0231.60045 [6] M.A. Pinsky and R.G. Pinsky, Transience and Recurrence for Diffusions in Random Temporal Environments, Annals of Probability (to appear). [7] R.G. Pinsky, Transience and Recurrence ...
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CiteSeerX - Scientific documents that cite the following paper: Stochastic simulation algorithms for dynamic probabilistic networks
Author summary Genetically identical cells, even when they are exposed to the same environmental conditions, display incredible diversity. Gene expression noise is attributed to be a key source of this phenotypic diversity. Transcriptional dynamics is a dominant source of expression noise. Although scores of theoretical and experimental studies have explored how noise is regulated at the level of transcription, most of them focus on the gene specific, cis regulatory elements, such as the number of transcription factor (TF) binding sites, their binding strength, etc. However, how the global properties of transcription, such as the limited availability of TFs impact noise in gene expression remains rather elusive. Here we build a theoretical model that incorporates the effect of limiting TF pool on gene expression noise. We find that competition between genes for TFs leads to enhanced variability in mRNA copy number across an isogenic population. Moreover, for gene copies sharing TFs with other competitor
In this paper, we develop a stochastic differential equation model to simulate the movement of a social/subsocial spider species, |em|Anelosimus studiosus|/em|, during prey capture using experimental data collected in a structured environment. In a subsocial species, females and their maturing offspring share a web and cooperate in web maintenance and prey capture. Furthermore, observations indicate these colonies change their positioning throughout the day, clustered during certain times of the day while spaced out at other times. One key question was whether or not the spiders spaced out ``optimally to cooperate in prey capture. In this paper, we first show the derivation of the model where experimental data is used to determine key parameters within the model. We then use this model to test the success of prey capture under a variety of different spatial configurations for varying colony sizes to determine the best spatial configuration for prey capture.
Background. The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents the number of entities or copy numbers of interacting species, which are changing according to a list of possible reactions. It is often the case, especially when the state vector is high-dimensional, that the number of possible states the system may occupy is too large to be handled computationally. One way to get around this problem is to consider only those states that are associated with probabilities that are greater than a certain threshold level. Results. We introduce an algorithm that significantly reduces computational resources and is especially powerful when dealing with multi-modal distributions. The algorithm is built according to two key principles. Firstly, when performing time ...
Accurate modeling of reaction kinetics is important to understand how biological cells work. Spatially well-mixed reaction dynamics can be modeled by the chemical master equation (CME, see formula 2), an infinite set of ordinary differential equations, which is, in general, too complex to be solved analytically. There are accurate numerical simulation schemes for solving the CME indirectly, like Gillespies stochastic simulation algorithm (FN:D. T. Gillespie. Exact Stochastic Simulation of Coupled Chemical Reactions. Journal of Physical Chemistry, 81[25]:2340-2361, 1977.). For many relevant realistic settings, however, even our high-performance computers fail to create reliable statistics within an acceptable amount of time. This is the motivation to reduce the model complexity by considering approximative mathematical formulations of the cellular dynamics. Especially multiscale reaction systems, which often appear in real-world applications, are in the focus of our investigations because they ...
An old and important problem in the field of nonlinear time-series analysis entails the distinction between chaotic and stochastic dynamics. Recently, e-recurrence networks have been proposed as a tool to analyse the structural properties of a time series. In this paper, we propose the applicability of local and global e-recurrence network measures to distinguish between chaotic and stochastic dynamics using paradigmatic model systems such as the Lorenz system, and the chaotic and hyper-chaotic Rossler system. We also demonstrate the effect of increasing levels of noise on these network measures and provide a real-world application of analysing electroencephalographic data comprising epileptic seizures. Our results show that both local and global e-recurrence network measures are sensitive to the presence of unstable periodic orbits and other structural features associated with chaotic dynamics that are otherwise absent in stochastic dynamics. These network measures are still robust at high ...
A balanced approach to probability, statistics, stochastic models, and stochastic differential equations with special emphasis on engineering applications. Random variables, probability distributions, Monte Carlo simulations models, statistical inference theory, design of engineering experiments, reliability and risk assessment, fitting data to probability distributions, ANOVA, stochastic processes, Brownian motion, white noise, random walk, colored noise processes. Differential equations subject to random initial conditions, random forcing functions, and random parameters. Partial differential equations subject to stochastic boundary conditions. New techniques for non-linear differential equations. Computer simulation with MAPLE and other symbolic algebra software. 0520. Introduction to Bioengineering (3 s.h.) ...
InCharge,author1=Christoph Hauert}} {{TOCright}} Stochastic differential equations (SDE) provide a general framework to describe the evolutionary dynamics of an arbitrary number of strategic types \(d\) in finite populations, which results in demographic noise, as well as to incorporate mutations. For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, \(\mu\), are not too small compared to the inverse population size \(1/N\). This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For \(\mu N\ll1\) this limits the use of SDEs, but in this case well established alternative approximations are available based on time scale separation. The ...
InCharge,author1=Christoph Hauert}} {{TOCright}} Stochastic differential equations (SDE) provide a general framework to describe the evolutionary dynamics of an arbitrary number of strategic types \(d\) in finite populations, which results in demographic noise, as well as to incorporate mutations. For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, \(\mu\), are not too small compared to the inverse population size \(1/N\). This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For \(\mu N\ll1\) this limits the use of SDEs, but in this case well established alternative approximations are available based on time scale separation. The ...
The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy.. ...
While the birth-death model is, in itself, inappropriate for representing intracellular bacteria (§1), it has provided a useful foundation for the birth-death-survival model considered here. In the 1960s, there was considerable academic interest in the mathematics of the simple birth-death model, involving stochastic differential equations [14,15] and generating functions [48]. However, very few experimental studies have actually made use of these results, despite a thorough account [23] crediting their ability in representing data for a variety of diseases. That paper [23] and methods therein are however not without their critics. It is claimed [5] that while the overall picture provided by the basic birth-death model corresponds remarkably well to what is found in practice, the underlying interpretations are flawed and there is no experimental evidence to suggest any form of stochastic mechanism in the infection dynamics. However, this is later refuted in an in vivo study [40] (in which ...
TY - ABST. T1 - Stochastic simulation model for spatial-temporal development of a fungal plant disease spread by wind. AU - Østergård, Hanne. PY - 2003. Y1 - 2003. KW - 9-B risiko. M3 - Conference abstract for conference. T2 - Dina workshop on dispersal models with agricultural applications. Y2 - 1 January 2003. ER - ...
Real-time in situ operation of bio/chemical sensors assumes detection of chemical substances or biological specimens in samples of complex composition. Since sensor selectivity cannot be ideal, adsorption of particles other than target particles inevitably occur on the sensing surface. That affects the sensor response and its intrinsic fluctuations which are caused by stochastic fluctuations of the numbers of adsorbed particles of all the adsorbing substances. In microfluidic sensors, such response fluctuations are a result of coupled adsorption, desorption and mass transfer (convection and diffusion) processes of analyte particles. Analysis of these fluctuations is important because they constitute the adsorption-desorption noise, which limits the sensing performance. In this work we perform the analysis of fluctuations by using a stochastic model of sensor response after the steady state is reached, in the case of two-analyte adsorption, considering mass transfer processes. The resul...ts ...
This page collects some information about stochastic systems courses offered at Caltech. This page was prepared in preparation for a faculty discussion on the current stochastic systems sequence (ACM/EE 116, ACM 216, ACM 217/EE 164). == Introduction == === Background === The current sequence of courses (ACM/EE 116, ACM 216, ACM 217/EE 164) were first offered in the 2005-06 academic year following discussions between Emmanuel Candes, Babak Hassibi, Jerry Marsden, Richard Murray and Houman Ohwadi about how to integrate some of the course offerings in ACM and EE, with an eye toward applications in CDS. EE 162 (Random Processes for Communication and Signal Processing) was eliminated and replaced by ACM/EE 116. There are three drivers for evaluating the course sequence at this time: * Its been a while since we set this up and it would be good to get together and see what we think about how its been going. * CDS is about to require ACM 116 as part of its PhD requirements (in place of CDS 140b) and ...
Methods to implement stochastic simulations on the graphics processing unit (GPU) have been developed. These algorithms are used in a simulation of microassembly and nanoassembly with optical tweezers, but are also directly compatible with simulations of a wide variety of assembly techniques using either electrophoretic, magnetic, or other trapping techniques. Significant speedup is possible for stochastic particle simulations when using the GPU, included in most personal computers (PCs), rather than the central processing unit (CPU) that handles most calculations. However, a careful analysis of the accuracy and precision when using the GPU in stochastic simulations is lacking and is addressed here. A stochastic simulation for spherical particles has been developed and mapped onto stages of the GPU hardware that provide the best performance. The results from the CPU and GPU implementation are then compared with each other and with well-established theory. The error in the mean ensemble energy ...
Research and Markets: Stochastic Simulation and Applications in Finance with MATLAB: DUBLIN, Ireland--(BUSINESS WIRE)--January 23, 2009-- Research and Markets (http://www.researchandmarkets.com/research/40d9cd/stochastic_simulat) has announced the addition of John Wiley and Sons Ltds new report &Stochastic Simulation and Applications in Finance with MATLAB Programs& to their offering. Stochastic Simulation and Applications in Finance with MATLAB Programs explains the …
The workshop will focus on Rough Path Analysis and its rapidly growing applications in Applied Stochastic Analysis, ranging from the resolution of ill-posed stochastic partial differential equations to new ways of handling highdimensional data. ...
The development of plants impresses us with the well-orchestrated formation of tissues and structures throughout the lifetime of the organism, despite its constituents being inherently stochastic. At first glance the prevalent noise on the molecular level seems hard to reconcile with the robustness and reproducibility of development. How is stochastic variability overcome during development and developmental decision-making? When is stochasticity employed to generate patterns? How can stochastic events drive a process? How do lower level stochastic fluctuations affect development at more global levels? Stochastic variability is prevalent whenever low molecule numbers and/or small system sizes are involved. Especially during development a few cells are at the foundation of a growing organ, and the stochastic dynamics of regulatory molecules drive spatiotemporal specification of structures to be. Stochasticity is emerging as an important factor in the regulation of diverse plant developmental
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Stochastic analysis of steady-state two-phase (water and oil) flow in heterogeneous porous media is performed using the perturbation theory and spectral representation techniques. The governing equations describing the flow are coupled and nonlinear. The key stochastic input variables are intrinsic permeability,k, and the soil and fluid dependent retention parameter, г. Three different stochastic combinations of these two imput parameters were considered. The perturbation/spectral analysis was used to develop closed-form expressions that describe stochastic variability of key output processes, such as capillary and individual phase pressures and specific discharges. The analysis also included the estimation of the effective flow properties. The impact of the spatial variability ofk and г on the variances of pressures, effective conductivities, and specific discharges was examined.
Stochastic Analysis of Neural Spike Count Dependencies [Elektronische Ressource] / Arno Onken. Betreuer: Klaus Obermayer : Technische Universitat Berlin¨Stochastic Analysisof Neural Spike Count Dependenciesvorgelegt vonDiplom-InformatikerArno Onkenaus AurichVon der Fakultat IV - Elektrotechnik und Informatik¨der Technischen Universitat Berlin¨zur Erlangung des akademischen GradesDoktor der NaturwissenschaftenDr. rer. nat.genehmigte DissertationPromotionsausschuss:Vorsitzender: Prof. Dr. Klaus-Robert Mu¨llerBerichter:
The global and stochastic analysis with applications of writers that reorients under this hand holds here removed from a nuclear gross misconfigured and other carbohydrates to understand any following of others that are or are biochemical concepts between a diplomatic East and West. This bibliographicum does writings to some common participants in other archived Year through the Medusa of the Silk Road. We will run also at a instructor of Silk Road approaches and their endurance to discrete novel or theoretical presentations, and think the traditions in which queries are rewritten, read, and only measured biblical rights in happening global conversation. We will partly compare compounds of global and stochastic D-galactose, writing, and Literary and late plays. Bildungsroman, global of epics, urgent fascination). The fast traffic for this narratology occurs adaptations by Rousseau, Goethe, unknown, and Tolstoy. We well are powerful diseases by Georg Lukacs, Franco Moretti, Clement Lugowski, ...
Gene expression within cells is known to fluctuate stochastically in time. However, the origins of gene expression noise remain incompletely understood. The bacterial cell cycle has been suggested as one source, involving chromosome replication, exponential volume growth, and various other changes in cellular composition. Elucidating how these factors give rise to expression variations is important to models of cellular homeostasis, fidelity of signal transmission, and cell-fate decisions. Using single-cell time-lapse microscopy, we measured cellular growth as well as fluctuations in the expression rate of a fluorescent protein and its concentration. We found that, within the population, the mean expression rate doubles throughout the cell cycle with a characteristic cell cycle phase dependent shape which is different for slow and fast growth rates. At low growth rate, we find the mean expression rate was initially flat, and then rose approximately linearly by a factor two until the end of the cell
Generation and filtering of gene expression noise by the bacterial cell cycle. . Biblioteca virtual para leer y descargar libros, documentos, trabajos y tesis universitarias en PDF. Material universiario, documentación y tareas realizadas por universitarios en nuestra biblioteca. Para descargar gratis y para leer online.
We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the FitzHugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is assumed to be fully connected. The maximum conductances vary randomly. Under the condition that all neurons initial conditions are drawn independently from the same law that depends only on the population they belong to, we prove that a propagation of chaos phenomenon takes place, namely that in the mean-field limit, any finite number of neurons become independent and, within each population, have the same probability distribution. This probability distribution is a solution of a set of implicit equations, either nonlinear stochastic differential equations resembling the McKean-Vlasov equations or non-local partial
Finden Sie alle Bücher von Moisés Santillán - Chemical Kinetics, Stochastic Processes, and Irreversible Thermodynamics. Bei der Büchersuchmaschine eurobuch.de können Sie antiquarische und Neubücher VERGLEICHEN UND SOFORT zum Bestpreis bestellen. 9783319066882
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics (predicting the motions of planets, stars and galaxies); numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology. Before the advent of modern ...
Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. To prove this intrinsically interesting result, we stochastically perturb the multivariate deterministic system ẋ(t) = f(x(t)) into the Itô form dx(t) = f(x(t))dt + g(x(t))dw(t), and show that although the solution to the original ordinary differential equation may explode to infinity in a finite time, with probability one that of the associated stochastic differential equation does not.. ...
Modeling and simulation of biochemical networks faces numerous challenges as biochemical networks are discovered with increased complexity and unknown mechanisms. With improvement in experimental techniques, biologists are able to quantify genes and proteins and their dynamics in a single cell, which calls for quantitative stochastic models, or numerical models based on probability distributions, for gene and protein networks at cellular levels that match well with the data and account for randomness. This dissertation studies a stochastic model in space and time of a bacteriums life cycle- Caulobacter. A two-dimensional model based on a natural pattern mechanism is investigated to illustrate the changes in space and time of a key protein population. However, stochastic simulations are often complicated by the expensive computational cost for large and sophisticated biochemical networks. The hybrid stochastic simulation algorithm is a combination of traditional deterministic models, or ...
All populations fluctuate stochastically, creating a risk of extinction that does not exist in deterministic models, with fundamental consequences for both pure and applied ecology. This book provides an introduction to stochastic population dynamics, combining classical background material with a variety of modern approaches, including previously unpublished results by the authors, illustrated with examples from bird and mammal populations, and insect communities. Demographic and environmental stochasticity are introduced with statistical methods for estimating them from field data. The long-run growth rate of a population is explained and extended to include age structure with both demographic and environmental stochasticity. Diffusion approximations facilitate the analysis of extinction dynamics and the duration of the final decline. Methods are developed for estimating delayed density dependence from population time series using life history data. Metapopulation viability and the spatial scale of
Randomness is an important component of modeling complex phenomena in biological, chemical, physical, and engineering systems. Based on many years teaching this material, Jinqiao Duan develops a modern approach to the fundamental theory and application of stochastic dynamical systems for applied mathematicians and quantitative engineers and scientists. The highlight is the staged development of invariant stochastic structures that underpin much of our understanding of nonlinear stochastic systems and associated properties such as escape times. The book ranges from classic Brownian motion to noise generated by α-stable Levy flights. A. J. Roberts, University of Adelaide. This book provides a beautiful concise introduction to the flourishing field of stochastic dynamical systems, successfully integrating the exposition of important technical concepts with illustrative and insightful examples and interesting remarks regarding the simulation of such systems. Both presentation style and content ...
This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathématiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic differential equations and their applications to biology, epidemiology, neurobiology, physiology and other related areas ...
By a novel approach, we get some explicit criteria for the mean square exponential stability of linear stochastic differential equations with distributed delays. Stability criteria presented in this...
Expansions in Generalized Eigenfunctions of the Weighted Laplacian on Star-shaped Networks -- Diffusion Equations with Finite Speed of Propagation -- Subordinated Multiparameter Groups of Linear Operators: Properties via the Transference Principle -- An Integral Equation in AeroElasticity -- Eigenvalue Asymptotics Under a Non-dissipative Eigenvalue Dependent Boundary Condition for Second-order Elliptic Operators -- Feynman-Kac Formulas, Backward Stochastic Differential Equations and Markov Processes -- Generation of Cosine Families on L p (0,1) by Elliptic Operators with Robin Boundary Conditions -- Global Smooth Solutions to a Fourth-order Quasilinear Fractional Evolution Equation -- Positivity Property of Solutions of Some Quasilinear Elliptic Inequalities -- On a Stochastic Parabolic Integral Equation -- Resolvent Estimates for a Perturbed Oseen Problem -- Abstract Delay Equations Inspired by Population Dynamics -- Weak Stability for Orbits of C 0-semigroups on Banach Spaces -- Contraction ...
This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. This class of Riccati diffusion is quite general, and arises, for example, in data assimilation applications, and more particularly in ensemble (Kalman-type) filtering theory. These one-dimensional stochastic differential equations exhibit a quadratic drift function and a non-Lipschitz continuous diffusion function. We present a novel approach, combining tangent process techniques, Feynman-Kac path integration, and exponential change of measures, to derive sharp exponential decays to equilibrium. We also provide uniform estimates with respect to the time horizon, quantifying with some precision the fluctuations of these diffusions around a limiting deterministic Riccati differential equation. These results provide a stronger and almost sure version of the conventional central limit theorem. We illustrate these results in the context of ensemble Kalman-Bucy filtering. In
砂漠の洪水を灌漑用水に変える --ヨルダンの乾燥地で数理的最適戦略によるプロトタイプを運用--. 京都大学プレスリリース. 2018-03-08.Operation of reservoirs is a fundamental issue in water resource management. We herein investigate well-posedness of an optimal control problem for irrigation water intake from a reservoir in an irrigation scheme, the water dynamics of which is modeled with stochastic differential equations. A prototype irrigation scheme is being developed in an arid region to harvest flash floods as a source of water. The Hamilton-Jacobi-Bellman (HJB) equation governing the value function is analyzed in the framework of viscosity solutions. The uniqueness of the value function, which is a viscosity solution to the HJB equation, is demonstrated with a mathematical proof of a comparison theorem. It is also shown that there exists such a viscosity solution. Then, an approximate value function is obtained as a numerical solution to the HJB ...
Title: Particle representations for SPDEs and strict positivity of solutions Abstract: Stochastic partial differential equations arise naturally as limits of finite systems of interacting particles. For a variety of purposes, it is useful to keep the particles in the limit obtaining an infinite exchangeable system of stochastic differential equations. The corresponding de Finetti measure then gives the solution of the SPDE. These representations frequently simplify existence, uniqueness and convergence results. The support properties of the measure-valued solution can be studied using Girsanov change of measure techniques. The ideas will be illustrated by a model of asset prices set by an infinite system of competing traders. These latter results are joint work with Dan Crisan and Yoonjung Lee. ...
This paper focuses on estimation of an non-integral quadratic function (NIQF) and integral quadratic function (IQF) of a random signal in dynamic system described by a linear stochastic differential equation. The quadratic form of an unobservable signal indicates useful information of a signal for control. The optimal (in mean square sense) and suboptimal estimates of NIQF and IQF represent a function of the Kalman estimate and its error covariance. The proposed estimation algorithms have a closed-form estimation procedure. The obtained estimates are studied in detail, including derivation of the exact formulas and differential equations for mean square errors. The results we demonstrate on practical example of a power of signal, and comparison analysis between optimal and suboptimal estimators is presented. ...
Abstract: Stochastic partial differential equations frequently arise as limits of finite systems of weighted interacting particles. For a variety of purposes, it is useful to keep the particles in the limit obtaining an infinite exchangeable system of stochastic differential equations for the particle locations and weights. The corresponding de Finetti measure then gives the solution of the SPDE. These representations frequently simplify existence, uniqueness and convergence results. Following some discussion of general approaches to SPDEs, the talk will focus on situations where the particle locations are given by an iid family of diffusion processes, and the weights are chosen to obtain a nonlinear driving term and to match given boundary conditions for the SPDE. (Recent results are joint work with Dan Crisan ...
The arbitrage-free Multivariate Mixture Dynamics Model: Consistent single-assets and index volatility smiles. Abstract: We introduce a multivariate diffusion model that is able to price derivative securities featuring multiple underlying assets. Each asset volatility smile is modeled according to a density-mixture dynamical model while the same property holds for the multivariate process of all assets, whose density is a mixture of multivariate basic densities. This allowsto reconcile single name and index/basket volatility smiles in a consistent framework. Our approach could be dubbed a multidimensional local volatility approach with vector-state dependent diffusion matrix. The model is quite tractable, leading to a complete market and not requiring Fourier techniques for calibration and dependence measures, contrary to multivariate stochastic volatility models such as Wishart. We prove existence and uniqueness of solutions for the model stochastic differential equations, provide formulas for a ...
Stochastic processes are probabilistic models for random quantities evolving in time or space. The evolution is governed by some dependence relationship between the random quantities at different times or locations. Major classes of stochastic processes are random walks, Markov processes, branching processes, renewal processes, martingales, and Brownian motion. Important application areas are mathematical finance, queuing processes, analysis of computer algorithms, economic time series, image analysis, social networks, and modeling biomedical phenomena. Stochastic process models are used extensively in operations research applications.. ...
Description: The course material changes with each occurrence of the course and may be taken for credit repeatedly with the instructors permission. Continuous time random processes, Kolmogorovs continuity theorem. Brownian Motion: the Donsker invariance principle, Holder continuity, quadratic variation. Continuous-time martingales and square integrable martingales. Markov processes and the strong Markov property. Properties of Brownian Motion: strong Markov property, Blumenthal zero-one law, Law of Iterated Logarithm. Stochastic integration with respect to continuous local martingales, Itos formula, Levys Characterization of Brownian motion, Girsanov transformation, Stochastic Differential Equations with Lipschitz Coefficients. Other topics in probability theory and stochastic processes at the choice of the instructor (e.g. connection to PDEs, local time, Skorokhods embedding theorem, zeros of the BM, empirical processes, concentration inequalities and applications in non-parametric ...
If stochastic simulation of minimal cell models intrigues you, see may be interested in: Carletti T, Filisetti A.The stochastic evolution of a protocell: the gillespie algorithm in a dynamically varying volume.Comput Math Methods Med. 2012;2012:423627. Lazzerini-Ospri L, Stano P, Luisi P, Marangoni R.Characterization of the emergent properties of a synthetic quasi-cellular system.BMC Bioinformatics. 2012 Mar 28;13 Suppl 4:S9. Zachar I, Fedor A, Szathmáry E.Two different template replicators coexisting in the same protocell: stochastic simulation of an extended chemoton model.PLoS One. 2011;6(7):e21380. Epub 2011 Jul 19. Van Segbroeck S, Nowé A, Lenaerts T.Stochastic simulation of the chemoton.Artif Life. 2009 Spring;15(2):213-26. | Origin of Life: Emergence, Self-organization and Evolution
This thesis consists of the four papers which consider different aspects of stochastic process modeling, error analysis, and minimization of computational cost.. In Paper I, we construct a Multipath Fading Channel (MFC) model for wireless channels with noise introduced through scatterers flipping on and off. By coarse graining the MFC model a Gaussian process channel model is developed. Complexity and accuracy comparisons of the models are conducted.. In Paper II, we generalize a multilevel Forward Euler Monte Carlo method introduced by Mike Giles for the approximation of expected values depending on solutions of Ito stochastic differential equations. Giles work proposed and analyzed a Forward Euler Multilevel Monte Carlo (MLMC) method based on realizations on a hierarchy of uniform time discretizations and a coarse graining based control variates idea to reduce the computational cost required by a standard single level Forward Euler Monte Carlo method. This work is an extension of Giles MLMC ...
Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the worlds human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood, although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the ...
TY - JOUR. T1 - Environmental Brownian noise suppresses explosions in population dynamics. AU - Mao, Xuerong. AU - Marion, Glenn. AU - Renshaw, Eric. PY - 2002. Y1 - 2002. N2 - Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. To prove this intrinsically interesting result, we stochastically perturb the multivariate deterministic system ẋ(t) = f(x(t)) into the Itô form dx(t) = f(x(t))dt + g(x(t))dw(t), and show that although the solution to the original ordinary differential equation may explode to infinity in a finite time, with probability one that of the associated stochastic differential equation does not. AB - Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. To prove this intrinsically interesting result, we ...
Find all books from Wendell Fleming, P.L. Lions, Wendell Helms Fleming - Stochastic Differential Systems, Stochastic Control Theory, and Applications (The IMA Volumes in Mathematics and Its Applications). At find-more-books.com you can find used, antique and new books, COMPARE results and immediately PURCHASE your selection at the best price. 0387966412
We present single-cell clustering using bifurcation analysis (SCUBA), a novel computational method for extracting lineage relationships from single-cell gene expression data and modeling the dynamic changes associated with cell differentiation. SCUBA draws techniques from nonlinear dynamics and stochastic differential equation theories, providing a systematic framework for modeling complex processes involving multilineage specifications. By applying SCUBA to analyze two complementary, publicly available datasets we successfully reconstructed the cellular hierarchy during early development of mouse embryos, modeled the dynamic changes in gene expression patterns, and predicted the effects of perturbing key transcriptional regulators on inducing lineage biases. The results were robust with respect to experimental platform differences between RT-PCR and RNA sequencing. We selectively tested our predictions in Nanog mutants and found good agreement between SCUBA predictions and the experimental ...
In the recent years, the problems of stability of delayed neural networks have received much attention due to its potential application in associative memories, pattern recognition and optimization. A large number of results have appeared in literature, see, for example, [1-14]. As is well known, a real system is usually affected by external perturbations which in many cases are of great uncertainty and hence may be treated as random [15-17]. As pointed out by Haykin [18] that in real nervous systems synaptic transmission is a noisy process brought on by random fluctuations from the release of neurotransmitters and other probabilistic causes, it is of significant importance to consider stochastic effects for neural networks. In recent years, the dynamic behavior of stochastic neural networks, especially the stability of stochastic neural networks, has become a hot study topic. Many interesting results on stochastic effects to the stability of delayed neural networks have been reported (see ...
The principle themes are to characterize the time evolution of the scattered field in terms of stochastic differential equations, and to illustrate this framework in simulation and experimental data analysis. The physical models contain all correlation information and higher order statistics, which enable radar and laser scattering experiments to be interpreted. An emphasis is placed on the statistical character of the instantaneous fluctuations, as opposed to ensemble average properties. This leads to various means for detection, which have important consequences in radar signal processing and statistical optics. There are also significant connections with ideas in mathematical finance that can be applied to physics problems in which non-Gaussian noise processes play an essential role.. ...
P: M311 and M365. R: M343. Course covers probability theory, Brownian motion, Itos Lemma, stochastic differential equations, and dynamic hedging. These topics are applied to the Black-Scholes formula, the pricing of financial derivatives, and the term theory of interest rates ...
I am a statistician and computational biologist working in the field of BigData analytics (high-throughput data analysis). I received my PhD in Mathematics (area: stochastic differential equations) from the University of Rochester in 2004. I joined the faculty of the Department of Biostatistics and Computational Biology at the University of Rochester in 2007.. I have developed many statistical and computational methods for analyzing and integrating large-scale data with complex correlation structures such as various Omics data (gene expression, protein expression, microbiota abundance and diversity, etc) and medical image data (primarily structural MRI data).. I have published 70 journal articles and book chapters, covering research topics such as Omics data pre-processing, hypothesis testing, multiple testing adjustment, functional data analysis, cluster analysis, network analysis, gene set enrichment analyses, and spatial statistical analysis for Diffusion Tensor Imaging data.. Examples of my ...
The Research Office is pleased to announce the following proposals have been selected for funding for the Faculty Release Time (FRT) 2010-11 Winter (Spring release) solicitation.. • Boudraa, Nabil (School of Language, Society and Culture, College of Liberal Arts): Writing the Natural World in French and Francophone Literatures. • Gibson, Nathan (Dept. of Mathematics, College of Science): Numerical Methods for Random and Stochastic Differential Equations with Applications to Mathematical Biology. • Kingston, Deanna (Dept. of Anthropology, College of Arts and Sciences): Iñupiaq Ecological Knowledges and Geographic Information Sciences. The Research Office is pleased to announce the awards for the Undergraduate Research, Innovation, Scholarship and Creativity (URISC) 2010-11 Winter/Spring solicitation.. The following proposals have been selected for funding:. • McClanahan, Danielle [Major: Bioengineering] (Faculty Project Advisor: Adam Higgins, School of Chemical, Biological and ...
Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive monograph, two leading experts detail the evolution equation approach to their solution. Most of the results appeared here for the first time in book form. The authors start with a detailed analysis of Lévy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Lévy processes are constructed in terms of Poisson random measures; stochastic integrals are introduced. Stochastic parabolic and hyperbolic equations on domains of arbitrary dimensions are studied, and applications to statistical and fluid mechanics and to finance are also investigated. Ideal for researchers and graduate students in stochastic processes and partial differential equations, this self-contained text will also interest those working on stochastic modeling in finance, statistical physics and environmental science. ...
Individuals change their behavior during an epidemic in response to whether they and/or those they interact with are healthy or sick. Healthy individuals may utilize protective measures to avoid contracting a disease. Sick individuals may utilize preemptive measures to avoid spreading a disease. Yet, in practice both protective and preemptive changes in behavior come with costs. This paper proposes a stochastic network disease game model that captures the self-interests of individuals during the spread of a susceptible-infected-susceptible disease. In this model, individuals strategically modify their behavior based on current disease conditions. These reactions influence disease spread. We show that there is a critical level of concern, i.e., empathy, by the sick individuals above which disease is eradicated rapidly. Furthermore, we find that risk averse behavior by the healthy individuals cannot eradicate the disease without the preemptive measures of the sick individuals. Empathy is more ...
TY - CHAP. T1 - Generalized Statistical Thermodynamics. T2 - Thermodynamics of Probability Distributions and Stochastic Processes. AU - Matsoukas, Themis. PY - 2018/1/1. Y1 - 2018/1/1. UR - http://www.scopus.com/inward/record.url?scp=85065840046&partnerID=8YFLogxK. UR - http://www.scopus.com/inward/citedby.url?scp=85065840046&partnerID=8YFLogxK. M3 - Chapter. AN - SCOPUS:85065840046. T3 - Understanding Complex Systems. SP - 1. EP - 363. BT - Understanding Complex Systems. PB - Springer Verlag. ER - ...
TY - JOUR. T1 - Visual representations are dominated by intrinsic fluctuations correlated between areas. AU - Henriksson, Linda. AU - Khaligh-Razavi, Seyed Mahdi. AU - Kay, Kendrick. AU - Kriegeskorte, Nikolaus. N1 - Funding Information: This work was supported by the Aalto University , the European Research Council (Advanced Grant # 232946 to R. Hari) and the Academy of Finland Postdoctoral Researcher Grant ( 278957 ) to LH, and a European Research Council Starting Grant ( 261352 ) to NK. The authors declare no competing financial interests. Publisher Copyright: © 2015.. PY - 2015/7/1. Y1 - 2015/7/1. N2 - Intrinsic cortical dynamics are thought to underlie trial-to-trial variability of visually evoked responses in animal models. Understanding their function in the context of sensory processing and representation is a major current challenge. Here we report that intrinsic cortical dynamics strongly affect the representational geometry of a brain region, as reflected in response-pattern ...
books.google.comhttps://books.google.com/books/about/Limit_Theorems_for_Stochastic_Processes.html?id=sUgXKpUIdHwC&utm_source=gb-gplus-shareLimit Theorems for Stochastic Processes ...
CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. One of the adverse effects of climate change is the proliferation of heat waves. Our investigations show that according to the most widely accepted climate change scenarios heat waves are expected to be essentially longer and hotter than in the past. It might happen that events we now define as heat waves last through entire summer. Although it will not be general, the length and intensity of present heat waves could also multiply. Based on data provided by some global circulation models, we might be face an event that exceeds the hottest heat waves of the 20th century by as much as 12°C. This study also offers a survey of the methodology of heat wave definition. Besides traditional calculations, we present two unconventional methods by introducing minimum and maximum temperature heat waves. We show in what points this approach is different from those usually adopted and what extra information it may offer. As an
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In this paper we study the geometrization of certain spaces of stochastic processes. Our main motivation comes from the problem of pattern recognition in high-dimensional time-series data (e.g.,...
The Young European Queueing Theorists (YEQT) workshops are organized on a yearly basis, and this year the 13th edition of the workshop will take place in October 2019. The aim of these workshops is to bring together young researchers, PhD students or recently appointed lecturers and assistant professors, and world-leading experts in order to share and discuss research related to queueing theory, operations research, applied probability and related areas. This event provides an excellent opportunity for developing researchers to interact and exchange ideas in an informal, friendly, yet research-focused setting. The workshop program will consist of presentations from young researchers and several keynote presentations and tutorials by prominent researchers.. The theme for the YEQT workshop this year is Data-Driven Analytics and Optimization for Stochastic Systems. The workshop will focus on combining theoretical stochastic modelling and optimization together with modern statistical techniques in ...
Appendix B A Few Math Facts This text assumes that the reader knows a variety of mathematical facts. Often these facts go unstated. For example, we use many properties of ... - Selection from Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, 3rd Edition [Book]
Abstract. Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included ...
Abstract. Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included ...
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Premier atelier de lERC « Reaction-Diffusion Equations, Propagations and Modelling » Journées détude organisées par Henri Berestycki et Jean-Michel Roquejoffre EHESS, 24-25 septembre 2013 Séquence 1: Hiroshi Matano (University of Tokyo) Spreading speed for some two-component reaction-diffusion system In this talk I will discuss the spreading properties of solutions of a prey-predator type reaction-diffusion system. This system belongs to the class of reaction-diffusion systems for which the comparison principle does not hold. For such class of systems, little has been know about the spreading properties of the solutions. Here, by a spreading property, we mean the way the solution propagates when starting from compactly supported initial data. We show that propagation of both the prey and the predator occur with a definite spreading speed. Furthermore, quite intriguingly, the spreading speed of the prey and that of the predator are different in some
Radiation measurement units have undergone a change from Rads and Rems to Grays and Sieverts. However, radiobiology literature uses both systems, resulting in confusion for Radiologists ... The biological effects of radiation had been studied and documented within few years of the discovery of Xrays and further information has consequently been available from longitudinal studies on populations affected by the atomic bomb. Biological effects are classified as deterministic (or certainty effects) and stochastic effects. Both deterministic and stochastic effects may either result in changes in organs (somatic effects) or in the genes (genetic effects) ... Stochastic effects are random events which are not dose related but their probability increases with an increase in the radiation dose ... The Committee For Nuclear Responsibility (CNR) ...
Biochemical reactions are subject to stochastic fluctuations that can give rise to cell-to-cell variability. Yet, how this variability affects viral infections, which themselves involve noisy reactions, remains largely elusive. Here we present single-cell experiments and stochastic simulations that …
There is no firm basis for setting a safe level of exposure above background for stochastic effects. Many sources emit radiation that is well below natural background levels. This makes it extremely difficult to isolate its stochastic effects. In setting limits, EPA makes the conservative (cautious) assumption that any increase in radiation exposure is accompanied by an increased risk of stochastic effects. Health physicists generally agree on limiting a persons exposure beyond background radiation to about 100 mrem per year from all sources. Exceptions are occupational, medical or accidental exposures. (Medical X-rays generally deliver less than 10 mrem). However, there do appear to be threshold exposures for the various non-stochastic effects. (Please note that the acute affects in the following table are cumulative. For example, a dose that produces damage to bone marrow will have produced changes in blood chemistry and be accompanied by nausea ...
They are simply a self-fulfilling prophecy. You get back what you built into the model.. The point of models like these are not to prove something by themselves. Instead, they allow you to identify simpler propositions to prove, which, if true, would establish that the model is right.. For example, if the predominant way that an independent chiefdomship arises without a war is as a result of the death of chief, then we know that this kind of event will have big implications for the dynamics (a non-obvious result). Then, we can dig through the best available datat in chiefdomship societies that are documented historically to determine what historically did cause independent chiefdomships to arise. If our model assumption is supported, we get a lot more bang for our buck out of that factual discovery than we would otherwise.. Similar garbage in, garbage out criticisms can be made of a recent contagion model of terrorism, where the key variable is the extent to which a harsh suppression of a ...
TY - JOUR AU - Jakšić, Olga AU - Jakšić, Zoran AU - Čupić, Željko AU - Ranđelović, Danijela AU - Kolar-Anić, Ljiljana PY - 2014 UR - http://cer.ihtm.bg.ac.rs/handle/123456789/1497 AB - The basic parameters of a sensor element defining its ultimate performance are sensitivity and intrinsic noise. In plasmonic gas sensors both are determined by refractive index changes due to adsorption and desorption (a-d) of target analyte particles to the sensor active area. In this paper we present a general model that can be simultaneously used to determine sensitivity and intrinsic noise of a plasmonic sensor both during transients and in steady-state and is valid for multi-analyte environments. The model utilizes the conventional probabilistic approach. It is derived without any assumptions about the stochastic nature of the fundamental (a-d) process. It reveals how all stochastic properties of the processes with (pseudo) first order kinetics with the initial number of particles equal to zero can ...
Chemical kinetics, also called reaction kinetics, is studying how fast chemical reactions go. This includes studying how different conditions such as temperature, pressure or solvent used affect the speed of a reaction. Chemical kinetics can also be used to find out about reaction mechanisms and transition states. The basic idea of chemical kinetics is called collision theory. This states that for a reaction to happen, the molecules must hit each other. Ways of increasing the speed of the reaction must therefore increase the number of hits. This can be done in many ways. With experiments it is possible to calculate reaction rates from which you can get rate laws and rate constants. A rate law is a mathematical expression with which you can calculate the speed of a reaction given the concentration of the reagents. ...
Mathematical Problems in Engineering is a peer-reviewed, Open Access journal that publishes results of rigorous engineering research carried out using mathematical tools. Contributions containing formulations or results related to applications are also encouraged. The primary aim of Mathematical Problems in Engineering is rapid publication and dissemination of important mathematical work which has relevance to engineering. All areas of engineering are within the scope of the journal. In particular, aerospace engineering, bioengineering, chemical engineering, computer engineering, electrical engineering, industrial engineering and manufacturing systems, and mechanical engineering are of interest. Mathematical work of interest includes, but is not limited to, ordinary and partial differential equations, stochastic processes, calculus of variations, and nonlinear analysis.
A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model to study the quantum stochastic resonance for chiral molecules. This process refers to the amplification of the response to an external periodic signal at a certain value of the noise strength, being a cooperative effect of friction, noise, and periodic driving occurring in a bistable system. Furthermore, from this stochastic dynamics within the Markovian regime and Ohmic friction, the competing process between tunneling and the parity violating energy difference present in this type of chiral systems plays a fundamental role. This mechanism is finally proposed to observe the so-far elusive parity-violating energy difference in chiral molecules.
With reference to spacecraft communication, the paper examines the effect of radio wave scattering at a statistically rough surface (the midsurface coincides with a sphere) on the characteristics of a radio channel. The statistical characteristics of the orthogonal components of the radio signal at the receiver are calculated with consideration of shading. Amplitude and phase distributions of the sum signal are determined under the assumption of a Gaussian distribution of the quadrature components of the scattered signal.
The stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance ...
RICHMOND, Va. - Ed Gillespies perceived snubbing of a former Donald Trump operative he had hired to whip up support for his gubernatorial campaign is causing an uproar among GOP activists already exasperated by Gillespies highly cautious stance toward the president.. Jack Morgan had expected to play a key role at a Gillespie rally headlined by Vice President Mike Pence on Saturday in Abingdon, a coal country region that voted overwhelmingly for Trump in November, activists said. But he found himself sidelined.. Gillespie hired Morgan, a colorful evangelical preacher and former 9th Congressional District GOP chairman, as his ambassador to Trump country after nearly losing the June primary to a rival who had run in the presidents bombastic, populist image.. But Gillespies campaign did not let Morgan help plan or speak at the rally - over the objections of another GOP candidate who employs Morgan, state Sen. Jill Holtzman Vogel, who is running for lieutenant governor and wanted him to introduce ...
Relationships between Models of Genetic Regulatory Networks with Emphasis on Discrete State Stochastic Models: 10.4018/978-1-5225-0353-8.ch002: Genetic Regulatory Networks (GRNs) represent the interconnections between genomic entities that govern the regulation of gene expression. GRNs have been
Emergence of peakons and anti-peakons for the solution of the Camassa-Holm equation with stochastic transport (Dr Igor Shevchenko, Imperial College London). ...
Goodness of Fit in Nonlinear Dynamics: Mis-specified Rates or Mis-specified States?. Giles Hooker, Stephen P. Ellner(Submitted on 2 Dec 2013). This paper introduces tests to uncover the nature of lack of fit in ordinary differential equation models (ODEs) proposed for data. We present a hierarchy of three possible sources of lack of fit: unaccounted-for stochastic variation, mis-specification of functional forms in the rate equations, and missing dynamical variables in the description of the system. We represent lack of fit by allowing some parameters to vary over time, and propose generic testing procedures that do not rely on specific alternative models. Our hypotheses are expressed in terms of nonparametric relationships among latent variables, and the tests are carried out through a combined residual bootstrap and permutation methods. We demonstrate the effectiveness of these tests on simulated data, and on real data from laboratory ecological experiments and electro-cardiogram ...
The workshop takes place in the Erhard-Schmidt lecture room at Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin, Germany. The lecture room is equipped with a blackboard and a digital projector as well as intranet and internet access. Information for Visitors: Berlin city map view. ...
Bob Costantino and Brett Melbourne are joining us for the next two days to talk about stochastic population dynamics in Tribolium. ...
1. Suppose that shocks occur according to a Poisson process with rate A| 0. Also suppose that each shock independently causes the system to fail with probability 0 | p | 1. Let N denote the number of shocks that it takes for the.
Probability theory, mathematical statistics, stochastic processes, random evolutions, diffusion processes at finite speed, transport processes in biological and physical systems, random walks, stochastic processes in random environments, partial differential equations in stochastic models, statistical physics, wave processes, probabilities on algebraic structures, statistical quality control ...
To get a better understanding of the dynamics of the system, we made a model of the system using the Cain software[1] for stochastic simulations. While stochastic simulations are more computationally demanding than deterministic models based on solving ODEs, they allow for random fluctuations that may have a big impact on the system in a cell[2]. As we want our system to react to two different signals, three promoters were required. One to respond to lactate, one to respond to low oxygen and a third to respond to signal molecules controlled by the two other promoters. The last promoter would then control cell lysis. For lactate sensing, we have adapted the lld promoter of E. coli, the vgb promoter from Vitreoscilla is used for the oxygen while the lux promoter from Vibrio fischeri was used for lysis control. The model can be divided into three parts; the lld promoter, the vgb promoter and the lux promoter. Each of these systems was first modelled separately. This made it easier to observe the ...
Gene regulatory networks (GRNs) consist of thousands of genes and proteins which are dynamically interacting with each other. Researchers have investigated how to uncover these unknown interactions by observing expressions of biological molecules with various statistical/mathematical methods. Once these regulatory structures are revealed, it is necessary to understand their dynamical behaviors since pathway activities could be changed by their given conditions. Therefore, both the regulatory structure estimation and dynamics modeling of GRNs are essential for biological research. Generally, GRN dynamics are usually investigated via stochastic models since molecular interactions are basically discrete and stochastic processes. However, this stochastic nature requires heavy simulation time to find the steady-state solution of the GRNs where thousands of genes are involved. This large number of genes also causes difficulties such as dimensionality problem in estimating their regulatory structure. ...
If you have a question about this talk, please contact Thomas Lippincott.. In recent years computational linguists, psycholinguists, and even some theoretical linguists have adoped a probabilistic view of linguistic knowledge. The primary motivation for this approach is a concern to incorporate the gradient effects and soft, defeasible constraints evident in speakers variable judgements on acceptability into the theory of linguistic competence. On this view knowledge of a language is identified directly with a language model and the probability distribution over the strings of a language that it specifies. I will take up some of the problems involved in developing a viable stochastic representation of competence and suggest possible solutions to these problems. I will also look at the connections between probabilistic theories of learning and a stochastic model of grammar. Finally, I will consider several consequences that such a model has for the competence-performance distinction.. This talk ...
The Senate of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) has announced the establishment of a new Priority Programme, entitled Probabilistic Structures in Evolution (SPP 1590). The programme is designed to run for six years. Biological evolution is a complex phenomenon driven by various underlying processes, such as mutation and recombination of genetic material, reproduction of individuals, competition, and selection of favourable types. Studying the interplay of these processes requires a substantial use of mathematical models and methods. Over the past decades, much of this modelling and analysis took place on a deterministic level, using dynamical systems and differential equations, and this has led to an elaborate theory. However, the processes of evolution have intrinsically random elements, such as random reproduction, which leads to stochastic fluctuations of gene frequencies and the emergence of random genealogies. The underlying stochastic processes are ...