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|
ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV) publishes rapidly and efficiently papers and surveys in the areas of control, optimisation and calculus of variations
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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.
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.) ...
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 ...
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 ...
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 ...
... 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 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:
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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.
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 ...
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...
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. ...
The workshop aims to contribute to the development of this area and will bring together leading researchers in the field. They will overview recent progress achieved in inference methods for L vy processes, identify problems of interest and outline future research directions. Topics like inverse statistical problems, regularisation techniques, semi- and nonparametric statistics, adaptive inference, are expected to play a major role. Among many open problems and challenges facing the area we mention e.g. devising computationally efficient inference strategies for L vy processes, implementation and theoretical analysis of (non-parametric) Bayesian approach to inference in L vy models, handling multivariate L vy processes and stochastic differential equations driven by L vy processes, statistical investigation of L vy copulas, incorporation of techniques and themes current in other branches of statistics (e.g. sparsity), and others. However, the workshop themes will not be limited to statistics ...
Aase, Knut K.; Bjuland, Terje & Øksendal, Bernt (2010). An anticipative linear filtering equation. Vis sammendrag In the classical Kalman-Bucy filter and in the subsequent literature so far, it has been assumed that the initial value of the signal process is independent of both the noise of the signal and of the noise of the observations.The purpose of this paper is to prove a filtering equation for a linear system where the (normally distributed) initial value X0 of the signal process Xt has a given correlation function with the noise (Brownian motion Bt) of the observation process Zt. This situation is of interest in applications to insider trading in finance. We prove a Riccati type equation for the mean square error S(t):= E[(Xt - ^Xt)**2]; 0 ,= t ,= T; where ^Xt is the filtered estimate for Xt. Moreover, we establish a stochastic differential equation for ^Xt based on S(t). Our method is based on an enlargement of filtration technique, which allows us to put the anticipative linear filter ...
This book deals with the optimal control of solutions of fully observable Itô-type stochastic differential equations. The validity of the Bellman
Maximal upper bounds for the moments of stochastic integrals and solutions of stochastic differential equations with respect to fractional Brownian motion with Hurst index $H,1/2$. II ...
Downloadable (with restrictions)! A self-contained theory is presented for pricing and hedging LIBOR and swap derivatives by arbitrage. Appropriate payoff homogeneity and measurability conditions are identified which guarantee that a given payoff can be attained by a self-financing trading strategy. LIBOR and swap derivatives satisfy this condition, implying they can be priced and hedged with a finite number of zero-coupon bonds, even when there is no instantaneous saving bond. Notion of locally arbitrage-free price system is introduced and equivalent criteria established. Stochastic differential equations are derived for term structures of forward libor and swap rates, and shown to have a unique positive solution when the percentage volatility function is bounded, implying existence of an arbitrage-free model with such volatility specification. The construction is explicit for the lognormal LIBOR and swap market models, the former following Musiela and Rutkowski (1995). Primary examples of LIBOR and
Fanda Yang at University of Minnesota, Applied Economics PhD student, studies financial mathematics, commodity risk management, agribusiness, dairy economics, macro time series, volatility models, stochastic differential equations, copula, financial derivatives, options, multivariate distribution, c#
Heterogeneous chemistry of carbon aerosols. Stochastic simulation of chemical kinetics. Raman crystallography and other biochemical applications of Raman microscopy
Title: Stochastic analysis of biochemical reaction networks with absolute concentration robustness Abstract: It has recently been shown that structural conditions on the reaction network, rather than a fine-tuning of system parameters, often suffice to impart "absolute concentration robustness" on a wide class of biologically relevant, deterministically modeled mass-action systems [Shinar and Feinberg, Science, 2010]. Many biochemical networks, however, operate on a scale insufficient to justify the assumptions of the deterministic mass-action model, which raises the question of whether the long-term dynamics of the systems are being accurately captured when the deterministic model predicts stability. I will discuss recent results that show that fundamentally different conclusions about the long-term behavior of such systems are reached if the systems are instead modeled with stochastic dynamics and a discrete state space. Specifically we characterize a large class of models which exhibit ...
We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed. © 2012 Hilborn et al ...
MAE C271A. Probability and Stochastic Processes in Dynamical Systems. (Instructor: Speyer, J.) Lecture, four hours; outside study, eight hours. Enforced requisites: courses 107, 182A. Probability spaces, random variables, stochastic sequences and processes, expectation, conditional expectation, Gauss/Markov sequences, and minimum variance estimator (Kalman filter) with applications. Concurrently scheduled with course C175A ...
Get this from a library! Probability and random processes. [Venkatarama Krishnan] -- A resource for probability AND random processes, with hundreds of worked examples and probability and Fourier transform tablesThis survival guide in probability and random processes eliminates the ...
This book presents applied probability and stochastic processes in an elementary but mathematically precise manner, with numerous examples and exercises to illustrate the range of engineering and scie
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DNA walkers are designed with the structural specificity and functional diversity of oligonucleotides to actively convert chemical energy into mechanical translocation. Compared to natural protein motors, DNA walkers small translocation distance (mostly ,100 nm) and slow reaction rate (,0.1 nm s−1) make single-molecule characterization of their kinetics elusive. An important indication of single-walker kinetics is the rate-limiting reactions that a particular walker design bears. We introduce an integrated super-resolved fluorescence microscopy approach that is capable of long-term imaging to investigate the stochastic behavior of DNA walkers. Subdiffraction tracking and imaging in the visible and second near-infrared spectra resolve walker structure and reaction rates. The distributions of walker kinetics are analyzed using a stochastic model to reveal reaction randomness and the rate-limiting biochemical reaction steps. ...
It is now well established that most if not all enzymatic proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. A hypothesis is stated that the protein conformational transition networks, as just as higher-level biological networks, the protein interaction network, and the metabolic network, have evolved in the process of self-organized criticality. Here, the criticality means that all the three classes of networks are scale-free and, moreover, display a transition from the fractal organization on a small length-scale to the small-world organization on the large length-scale. Good mathematical models of such networks are stochastic critical branching trees extended by long-range shortcuts. Biological molecular machines are proteins that operate under isothermal conditions and hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the
Contents: Chemical Kinetics in a Reentry Flow Field The Role of Chemical Kinetics The Principles of Chemical Kinetics Relaxation Processes The Chemical System of the Flow Field Reaction Rate Constants Dissociation Reactions Rearrangement Reactions Associative Ionization Collisional Ionization Charge Exchange Reactions Attachment Other Ion reactions Calculations Impurities and Other Chemical Systems The General Effect of Impurities Sodium Planetary Entry Table of Suggested Rate Constants(*REACTION KINETICS
154 Hurley. Computational Methods for Parameter Sensitivities of Stochastic Chemical Reaction Networks. Stochastic models are commonly used to simulate and analyze biochemical networks, in particular when the abundances of the constituent molecules are small and ordinary differential equations cease to provide a good description of system behavior. Example networks include the transcription and translation of DNA, and genetic switching. A common modeling choice is to use a continuous time Markov chain (CTMC). As solving analytically for the expectations of model quantities is usually intractable or impossible, one typically uses simulation methods to generate sample paths for analysis.. Even when biochemical knowledge suggests an appropriate model, parameter values are typically unknown and must be estimated experimentally. Therefore, parameter sensitivity estimation is a valuable tool as it provides a quantitative method for understanding how perturbations in model parameters affect different ...
Application of Single Electron Devices Utilizing Stochastic Dynamics: 10.4018/jnmc.2009040102: Single electron devices utilizing the Coulomb blockade phenomenon have attractive features such as extreme low power consumption, one by one electron flow
As a consequence of the rugged landscape of RNA molecules their folding is described by the kinetic partitioning mechanism according to which only a small fraction ($\phi_F$) reaches the folded state while the remaining fraction of molecules is kinetically trapped in misfolded intermediates. The transition from the misfolded states to the native state can far exceed biologically relevant time. Thus, RNA folding in vivo is often aided by protein cofactors, called RNA chaperones, that can rescue RNAs from a multitude of misfolded structures. We consider two models, based on chemical kinetics and chemical master equation, for describing assisted folding. In the passive model, applicable for class I substrates, transient interactions of misfolded structures with RNA chaperones alone are sufficient to destabilize the misfolded structures, thus entropically lowering the barrier to folding. For this mechanism to be efficient the intermediate ribonucleoprotein (RNP) complex between collapsed RNA and ...
INPROCEEDINGS{novotni-2003-stochastic, author = {Novotni, Dominik and Weber, Andreas}, editor = {Valafar, F. and Valafar, H.}, title = {A Stochastic Method for Solving Inverse Problems in Epidemic Modelling}, booktitle = {Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS03)}, year = {2003}, month = jun, publisher = {CSREA Press}, abstract = {We describe a stochastic optimization method that can be used to solve inverse problems in epidemic modelling. Although in general it cannot be expected, that these inverse problems have solutions and that possible solutions can be approximated by local optimization methods, our optimization method worked well when applied to a model for the epidemics caused by Respiratory Syncytial Virus (RSV) and the empirical data of various locations. We conjecture that similar results can be obtained for other epidemics and other models.}, isbn = {1-932415-04-1 ...
In microscopic systems formed by living cells, the small numbers of some reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical characteristics is the stochastic simulation algorithm (SSA). Despite recent improvements, as a procedure that simulates every reaction event, the SSA is necessarily inefficient for most realistic problems. There are two main reasons for this, both arising from the multi-scale nature of the underlying problem: (1) the presence of multiple timescales (both fast and slow reactions); and (2) the need to include in the simulation both chemical species that are present in relatively small quantities and should be modeled by a discrete stochastic process, and species that are present in larger quantities and are more efficiently modeled by a deterministic differential equation. In the first half of the session, we will first describe the SSA, and then outline ...
In microscopic systems formed by living cells, the small numbers of some reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical characteristics is the stochastic simulation algorithm (SSA). Despite recent improvements, as a procedure that simulates every reaction event, the SSA is necessarily inefficient for most realistic problems. There are two main reasons for this, both arising from the multi-scale nature of the underlying problem: (1) the presence of multiple timescales (both fast and slow reactions); and (2) the need to include in the simulation both chemical species that are present in relatively small quantities and should be modeled by a discrete stochastic process, and species that are present in larger quantities and are more efficiently modeled by a deterministic differential equation. In the first half of the session, we will first describe the SSA, and then outline ...
Abhishek Garg Looking at stochasticity in nodes and in functions within GR networks. For T-helper differentiation, the GR network is reasonably complex (hes using this as the example for the talk). How does the system behave when it is subjected to stochastic behaviour? Start by looking at the robustness of the system. Robustness is maintenance…
In the noisy cellular environment, expression of genes has been shown to be stochastic across organisms ranging from prokaryotic to human cells. Stochastic expression manifests as cell-to-cell variability in the levels of RNAs/proteins, in spite of the fact that cells are genetically identical and are exposed to the same environment. Development of computationally tractable frameworks for modeling stochastic fluctuations in gene product levels is essential to understand how noise at the cellular level affects biological function and phenotype. I will introduce state-of-the-art computational tools for stochastic modeling, analysis and inferences of biomolecular circuits. Mathematical methods will be combined with experiments to study infection dynamics of two viral systems in single cells. First, I will show how stochastic expression of proteins results in intercellular lysis time and viral burst size variations in the bacterial virus, lambda phage. Next, I will describe our efforts in stochastic ...
Probability, Statistics and Random Processes is designed to meet the requirements of students and is intended for beginners to help them understand the concepts from the first principles. Spread across … - Selection from Probability, Statistics and Random Processes [Book]
EDIT (original answer below):. WHubers comment is dead on. A stochastic process is a statistical description of the values. A realization is a particular set of values that adhere to this description. You can create an ensemble of randomly generated realizations for a given process. (In physics we talk about ensembles. Do probabilists?). In the ensemble, ALL values in the process are (or at least can be) random variables. That being said, you could speak of the subset of all realizations such that the first day is sunny. Perhaps this is a new stochastic process based on the original, but conditioned on the first day being sunny. I think this is what I hastily put in my original answer.. I suppose one could define a discrete stochastic process such that every 10th value is equal to $\pi$ or something, in which case these would have a fixed value in each realization. Such a process would not strictly fit the definition in your question. But that seems somewhat pathological.. ...
A stochastic model to investigate the underlying mechanisms leading to greater cell-to-cell variation in the IFNB1 mRNA than in a housekeeping gene, another induced transcript and viral RNA. The model suggests that the surprisingly high levels of IFNB1 transcript noise originate from the complexity of IFNB1 enhanceosome formation, which leads to a range up to many minutes in the differences within each cell in the time of activation of each allele (Chromosome-specific and noisy IFNB1 transcription in individual virus-infected human primary dendritic cells, Hu, Jianzhong et al., Nucleic Acids Research (2007), Volume 35, Issue 15, p.5232 - 5241). The complexity of IFNB1 enhanceosome formation prior to transcription initiation is assumed to provide the dominant contribution to the stochastic behavior. This assembly involves binding of NFKB, AP-1, IRF, and HMG-I(Y) to form the enhanceosome. We denote HMG-I(Y) by P1, NFKB by P2, AP1 by P3 and the IRFs by P4. The model comprises four proteins P1, P2, ...
Random Processes and Visual Perception: Stochastic Art: 10.4018/978-1-4666-8142-2.ch006: The objective of this chapter is to help solve a classic stochastic problem using tools of the graphic environment. Stochastic processes are associated with
Understanding the community assembly mechanisms controlling biodiversity patterns is a central issue in ecology. Although it is generally accepted that both deterministic and stochastic processes play important roles in community assembly, quantifying their relative importance is challenging. Here we propose a general mathematical framework to quantify ecological stochasticity under different situations in which deterministic factors drive the communities more similar or dissimilar than null expectation. An index, normalized stochasticity ratio (NST), was developed with 50% as the boundary point between more deterministic (,50%) and more stochastic (,50%) assembly. NST was tested with simulated communities by considering abiotic filtering, competition, environmental noise, and spatial scales. All tested approaches showed limited performance at large spatial scales or under very high environmental noise. However, in all of the other simulated scenarios, NST showed high accuracy (0.90 to 1.00) and ...
Statistical physics provide a powerful tool to describe cooperative many-particle phenomena both in- and out-of-equilibrium based on a detailed atomistic-level description. Rather than just phenomena conventional physical and chemical systems (thin film growth, self-assembly of nanoclusters, spatial patterns in reaction-diffusion systems,…), this approach can also be applied to diverse biological, sociological, epidemiological, etc. systems (aggregation, flocking, traffic flow, spatial epidemic spread,…). Instead of implementing Newtonian-type dynamics to track particles, we present examples utilizing stochastic models to track just particle locations, which thereby allow access to longer experimentally-relevant time- and length- scales. Specifically, we describe self-assembly and thin film growth during surface deposition, and also concentration patterns in surface and other reaction-diffusion systems.. A related basic question is whether it is possible to systematically transition from an ...
Biological neurons are good examples of a threshold deviceâ€"this is why neural systems are in the focus when looking for realization of Stochastic Resonance (SR) and Spatiotemporal Stochastic Resonance (STSR) phenomena. There are two different ways to simulate neural systemsâ€"one based on differential equations, the other based on a simple threshold model. In this talk the effect of noise on neural systems will be discussed using both ways of modelling. The results so far suggest that SR and STSR do occur in models of neural systems. However, how significant is the role played by these phenomena and what implications might they have on neurobiology is still a question. © 2000 American Institute of Physics ...
International Journal of Stochastic Analysis is a peer-reviewed, Open Access journal that publishes original research articles as well as review articles in all areas of stochastic analysis.
International Journal of Stochastic Analysis is a peer-reviewed, Open Access journal that publishes original research articles as well as review articles in all areas of stochastic analysis.
Professor of Molecular Systems Biology and Director of Warwick Integrative Synthetic Biology centre (WISB), University of Warwick, UK. [email protected] John McCarthy studied Biochemistry in Oxford and began his research career studying the biochemistry and biophysics of electron transport-dependent ATP synthesis. In subsequent years in Germany he switched to research on mechanisms underpinning the control and regulation of gene expression and became a Department Head in one of Germanys Federal Research Institutes. He also engaged with various challenges in biotechnology, collaborating with a large number of biotechnology and pharmaceutical companies. John moved to Manchester in 1996, where he was Head of the Department of Biomolecular Sciences at UMIST 1998-2000. He took on leadership of the Manchester Interdisciplinary Biocentre project in 1998, and was Director of this institute from 2004 until 2010, when he moved to become Head of Life Sciences at the University of Warwick. John ...
It is widely observed that biological systems are phenotypically robust to both genetic and environmental perturbation. However, it is also observed that a clon...
N refers to the number of individuals. Demographic stochasticity is defined by a sum of squares statistic for the relative variation among individual fitnesses in a given time interval. Environmental stochasticity is calculated by the residual of observed versus expected change, minus the difference caused by individual interactions [51], and therefore assumes a uniform response in all individuals (e.g. in our context here, an increase in background origination rates). While this binary classification forms a crass straw man, this simplistic polarization echoes the palaeobiological dichotomy into either the biotic, organismal Red Queen school [11,52] or the supposed alternative of an abiotic, environmental Court Jester [12]. The mutual dependence between the hypotheses has only recently been acknowledged [6,10,13].. Assuming that the number of species saturates following logistic growth [4], calculating environmental and demographic stochasticity statistics for evolutionary species of Cenozoic ...
Technology Networks is an internationally recognised publisher that provides access to the latest scientific news, products, research, videos and posters.
Technology Networks is an internationally recognised publisher that provides access to the latest scientific news, products, research, videos and posters.
Stochastic analysis (SPDEs, BSDEs, FBSDEs, stochastic control and stochastic differential games), Financial mathematics (models for the equity, fixed income and credit markets, commodity, energy..., Environmental ...
Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion 123 which is equivalent to the
A cell can be seen as a microscopic chemical plant, where different cellular components (mRNAs, proteins) are produced, transformed, and consumed (or degraded) to accomplish myriad cellular functions. However, unlike a typical chemical plant, cellular processes, such as gene transcription and protein translation, involve very low concentrations of molecules (on the order of nanomolar). Such low concentration means that these processes can only occur intermittently as discrete and random events. The intrinsic stochastic behavior gives rise to variations in cellular phenotype, even in clonal cell population. Thus, to understand the functioning behavior of a biological network, the intrinsic variations in cellular processes should be explicitly taken into consideration in the system modeling. Here, we are developing a reverse-engineering framework for the identification of biological models that can represent the discrete stochastic nature of processes in a cell. This framework will explicitly ...
Water supply alternatives to alleviate water shortage damages in urbanized watersheds are itemized and evaluated in terms of cost, life cycle energy (LCE), and
2 Random Variables (Discrete and Continuous) Prerequisites Before you start reading this unit, you should: Have some knowledge on definite integrals Know to solve double integrals (multiple integrals) Know about … - Selection from Probability, Statistics and Random Processes [Book]
A discrete stochastic model is proposed for thesimulation of electrical breakdown in long air gaps withextremely nonuniform electric field between theelectrodes.
Hidden Markov Models power many state-of-the-art tools in the field of protein bioinformatics. While excelling in their tasks, these methods of protein analysis do not convey directly information on medium and long-range residue-residue interactions. This requires an expressive power of at least context-free grammars. However, application of more powerful grammar formalisms to protein analysis has been surprisingly limited. We have developed a probabilistic grammatical framework for problem-specific protein languages, which has been already successfully applied to recognition of ligand binding sites. The core of the model consists of a probabilistic context-free grammar (PCFG), automatically inferred by a genetic algorithm from only a generic set of expert-based rules and positive training sequences. Here, we show that the PCFG approach matches state-of-the-art performance in two other tasks: classification of transmembrane helix-helix pairs and recognition of amyloidogenic peptides. First, the
The pIKE plasmid toggle switch differs from the pTAK plasmid by the P1 and R1 genes.[3] In pIKE, P1 is the PLtetO-1 promoter and R1 is tetR. This toggle switch is flipped by IPTG or aTc pulses. Gardner et al designed pIKE and pTAK with different ribosome binding sites to determine bistability under different conditions, and all but one pIKE plasmid conferred bistability which is possibly due to the fact that tetR has less efficiency than the pTAK λ repressor. To test the bistability, the plasmids were induced with IPTG for 6 hours to express fluorescence, called the high state, and then grown 5 hours without IPTG. Plasmids that remained in the high state display bistability and ones that return to low states display monostability. Afterwards, the plasmids were treated with heat or aTc as appropriate for 7 hours to turn off GFP expression then removed for 5.5 hours; plasmids that remained in low state are considered bistable. The 2011 Duke iGEM team used zinc finger nucleases to modify genetic ...
[ Chemical Kinetics And Dynamics Francisco Manual ] - Promoter Nucleosome Dynamics Regulated By Signalling Through The,Patent Us5625579 Stochastic Simulation Method For Processes,High Resolution Quantification Of Focal Adhesion Spatiotemporal
Probability, random variables, statistics, and random processes, including counting, independence, conditioning, expectation, density functions, distributions, law of large numbers, central limit theorem, confidence intervals, hypothesis testing, statistical estimation, stationary processes, Markov chains, and ergodicity.. ...
A central goal in ecology is to understand the patterns and processes that explain the organization of natural communities. A major focus investigates whether communities form as the result of stochastic processes or are constructed via assembly rules (i.e. competition; [1-3]). The former scenario is attributed to random species colonization, habitat gradients and stochastic environmental effects, while the latter deterministically generates a community with a marked and predictable signature of co-occurrence owing to species interactions [4-6]. Competitive interactions form communities with species that co-occur less often than expected by chance [1], while species that do co-occur may differ significantly in key traits (e.g. body size or trophic morphology) that relax the degree of overlap in resource use [7]. Although competition has been used synonymously with descriptions of structured communities, decreased species co-occurrence can be explained by other mechanisms. For instance, species ...
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This course is intended for CNBC students, as an additional option for fulfilling the computational core course requirement, but it will also be open to Statistics and Machine Learning students. It should be of interest to anyone wishing to see the way statistical ideas play out within the brain sciences, and it will provide a series of case studies on the role of stochastic models in scientific investigation. Statistical ideas have been part of neurophysiology and the brainsciences since the first stochastic description of spike trains, and the quantal hypothesis of neurotransmitter release, more than 50 years ago. Many contemporary theories of neural system behavior are built with statistical models. For example, integrate-and-fire neurons are usually assumed to be driven in part by stochastic noise; the role of spike timing involves the distinction between Poisson and non-Poisson neurons; and oscillations are characterized by decomposing variation into frequency-based components. In the ...
The Molecular Word: Chemical Kinetics and Mechanism 2004 , The Molecular Word: Chemical Kinetics and Mechanism 2004 , کتابخانه دیجیتالی دانشگاه علوم پزشکی و خدمات درمانی شهید بهشتی
One of the functions of the cell nucleus is to help regulate gene expression by controlling molecular traffic across the nuclear envelope. Here we investigate, via stochastic simulation, what effects, if any, does segregation of a system into the nuclear and cytoplasmic compartments have on the stochastic properties of a motif with a negative feedback. One of the effects of the nuclear barrier is to delay the nuclear protein concentration, allowing it to behave in a switch-like manner. We found that this delay, defined as the time for the nuclear protein concentration to reach a certain threshold, has an extremely narrow distribution. To show this, we considered two models. In the first one, the proteins could diffuse freely from cytoplasm to nucleus (simple model); and in the second one,... the proteins required assistance from a special class of proteins called importins. For each model, we generated fifty parameter sets, chosen such that the temporal profiles they effectuated were very ...
This help file provides more information regarding the implementation of the stochastic search variable selection (SSVS, George and McCulloch, 1993) as implemented in the boral package.
Cancer cells that originate from a single cell acquire phenotypic heterogeneity because of genomic instability or heritable epigenetic changes (Lengauer et al., 1998; Shackleton et al., 2009). This heterogeneity is advantageous for the progression of cancer and promotes its highly invasive nature in tissues (Heppner, 1984; Rubin, 1990; Shackleton et al., 2009). Recently, however, it has been reported that the fate and behavior of mammalian cells, including cancer cells, can be determined by stochastic variation in gene expression (Brock et al., 2009). For example, heterogenous signaling patterns in monoclonal cancer cells can generate cells with diverse phenotypes, which have different drug sensitivities (Singh et al., 2010).. A typical example of a cancer that exhibits extensive heterogeneity is glioblastoma, which was previously termed glioblastoma multiforme, reflecting its histopathological divergence in size, shape, karyotype, etc. (Louis, 2006). Among the many experimental models of ...
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Published Article: Transcriptional Bursting from the HIV-1 Promoter Is a Significant Source of Stochastic Noise in HIV-1 Gene Expression ...
The team also looked at how the system responds to various perturbations, so as to ensure that the position of such boundaries remain more or less fixed.. Extrinsic factors, such as changes in ambient temperature, can lead to shifts in the relative position of the boundaries between two cell types. In addition, random internal fluctuations, conventionally referred to as noise, must be taken into account.. A cell is a small unit which contains only a relatively limited number of protein molecules. Therefore, small stochastic variations can affect the response of the whole system.. The calculations carried out by the Munich researchers indicate that the organism must choose whether to minimize intrinsic or extrinsic perturbations. It must then put up with the effects of the "uncontrolled" source, or devote minimal amounts of energy to reducing its effects. Thus, to dampen the effects of noise, the organism could increase the total number of proteins in the system, whereas the influence of ...
To test the software, we designed a genotype simulation program so that the true lengths of the alleles could be controlled. Our simulations suggested that the accuracy (the fraction of correct calls compared to the known lengths of the simulated alleles) of the PeakSeeker program was proportional to the number of replicate genotypes provided for each locus (Figure 4A), with notable increases in accuracy not occurring after 3 replicates. This finding was expected, as the effects of stochastic variation from any single genotype become less pronounced as more independent replicates are incorporated into the analysis. The algorithm was most accurate in calling genotypes for locus 1292, a marker with an asymmetric distribution of stutter peaks. We find that PeakSeeker tends to work best for such markers, since the additive product of asymmetrical stutter patterns tends to give heterozygous genotypes that look vastly different from homozytgotes, whereas symmetrical alleles often yield heterozygous ...
Compare cheapest textbook prices for Probability, Statistics, and Random Processes for Engineers (4th Edition), Stark, Henry - 9780132311236. Find the lowest prices on SlugBooks
Motivation: Stress response in cells is often mediated by quick activation of transcription factors (TFs). Given the difficulty in experimentally assaying TF activities, several statistical approaches have been proposed to infer them from microarray time courses. However, these approaches often rely on prior assumptions which rule out the rapid responses observed during stress response.. Results: We present a novel statistical model to infer how TFs mediate stress response in cells. The model is based on the assumption that sensory TFs quickly transit between active and inactive states. We therefore model mRNA production using a bistable dynamical systems whose behaviour is described by a system of differential equations driven by a latent stochastic process. We assume the stochastic process to be a two-state continuous time jump process, and devise both an exact solution for the inference problem as well as an efficient approximate algorithm. We evaluate the method on both simulated data and ...
View Notes - Chapter02 from STAT 211 at Texas A&M. Probability definitions Random process: a process whose outcome can not be predicted with certainty Sample space (S): the collection of all
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Once a potential network structure is created, a mathematical framework has to be chosen to develop a kinetic version. As different frameworks allow for complementary analysis and interpretation, it is often useful to keep the model interpretable by more than one formalism. The simultaneous use of alternative frameworks has proved beneficial, especially for gene regulatory networks. This can be seen in one of the landmark papers of synthetic biology describing the repressilator (Elowitz & Leibler 2000). A deterministic approach was used to analyse the qualitative behaviour in dependence of key parameters, while a stochastic version permitted testing of the robustness of the design to transcriptional noise. In this section, we will concentrate on these two frameworks.. As chemical and biological processes are inherently stochastic, it seems natural to take this into account for modelling. However, stochastic simulations are generally computationally much more intensive, and for bigger models or ...