Stochastic gene expression conditioned on large deviations
Horowitz, Jordan M.; Kulkarni, Rahul V.
2017-06-01
The intrinsic stochasticity of gene expression can give rise to large fluctuations and rare events that drive phenotypic variation in a population of genetically identical cells. Characterizing the fluctuations that give rise to such rare events motivates the analysis of large deviations in stochastic models of gene expression. Recent developments in non-equilibrium statistical mechanics have led to a framework for analyzing Markovian processes conditioned on rare events and for representing such processes by conditioning-free driven Markovian processes. We use this framework, in combination with approaches based on queueing theory, to analyze a general class of stochastic models of gene expression. Modeling gene expression as a Batch Markovian Arrival Process (BMAP), we derive exact analytical results quantifying large deviations of time-integrated random variables such as promoter activity fluctuations. We find that the conditioning-free driven process can also be represented by a BMAP that has the same form as the original process, but with renormalized parameters. The results obtained can be used to quantify the likelihood of large deviations, to characterize system fluctuations conditional on rare events and to identify combinations of model parameters that can give rise to dynamical phase transitions in system dynamics.
Expressing stochastic filters via number sequences
Capponi, A.; Farina, A; Pilotto, C.
2010-01-01
We generalize the results presented in [1] regarding the relation between the Kalman filter and the Fibonacci sequence. We consider more general filtering models and relate the finite dimensional Kalman and Benes filters to the Fibonacci sequence and to the Golden Section. We also prove that Fibonacci numbers may be expressed as the convolution of the Fibonacci and Padovan sequence, thus extending the connection between stochastic filtering and Fibonacci sequence to the Padovan sequence.
Applications of Little's Law to stochastic models of gene expression
Elgart, Vlad; Kulkarni, Rahul V
2010-01-01
The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of mRNA fluctuations ('Poisson' and 'Telegraph' processes) have been proposed in stochastic models of gene expression. Both Poisson and Telegraph scenario models explain experimental observations of noise in protein levels in terms of 'bursts' of protein expression. Correspondingly, there is considerable interest in establishing relations between burst and steady-state protein distributions for general stochastic models of gene expression. In this work, we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory. By applying a general theorem from queueing theory, Little's Law, we derive exact relations which connect burst and steady-state distribution means for models with arbitrary waiting-time distributions for arrival and degradation of mRNAs and proteins. The de...
Distribution of population-averaged observables in stochastic gene expression
Bhattacharyya, Bhaswati; Kalay, Ziya
2014-01-01
Observation of phenotypic diversity in a population of genetically identical cells is often linked to the stochastic nature of chemical reactions involved in gene regulatory networks. We investigate the distribution of population-averaged gene expression levels as a function of population, or sample, size for several stochastic gene expression models to find out to what extent population-averaged quantities reflect the underlying mechanism of gene expression. We consider three basic gene regulation networks corresponding to transcription with and without gene state switching and translation. Using analytical expressions for the probability generating function of observables and large deviation theory, we calculate the distribution and first two moments of the population-averaged mRNA and protein levels as a function of model parameters, population size, and number of measurements contained in a data set. We validate our results using stochastic simulations also report exact results on the asymptotic properties of population averages which show qualitative differences among different models.
Noise and Stochasticity in Gene Expression : A Pathogenic Fate Determinant
Jørgensen, Mikkel Girke; Raaphorst, Renske van; Veening, Jan-Willem; Harwood, Colin; Wipat, Anil
2013-01-01
Not all cells in a bacterial population exhibit exactly the same phenotype, even though they grow in the same environment and are genetically identical. This phenomenon is known as phenotypic variation. The major source of phenotypic variation is noise or stochasticity in gene expression networks,
Intrinsic and extrinsic contributions to stochasticity in gene expression
Swain, Peter S.; Elowitz, Michael B.; Siggia, Eric D.
2002-10-01
Gene expression is a stochastic, or "noisy," process. This noise comes about in two ways. The inherent stochasticity of biochemical processes such as transcription and translation generates "intrinsic" noise. In addition, fluctuations in the amounts or states of other cellular components lead indirectly to variation in the expression of a particular gene and thus represent "extrinsic" noise. Here, we show how the total variation in the level of expression of a given gene can be decomposed into its intrinsic and extrinsic components. We demonstrate theoretically that simultaneous measurement of two identical genes per cell enables discrimination of these two types of noise. Analytic expressions for intrinsic noise are given for a model that involves all the major steps in transcription and translation. These expressions give the sensitivity to various parameters, quantify the deviation from Poisson statistics, and provide a way of fitting experiment. Transcription dominates the intrinsic noise when the average number of proteins made per mRNA transcript is greater than 2. Below this number, translational effects also become important. Gene replication and cell division, included in the model, cause protein numbers to tend to a limit cycle. We calculate a general form for the extrinsic noise and illustrate it with the particular case of a single fluctuating extrinsic variablea repressor protein, which acts on the gene of interest. All results are confirmed by stochastic simulation using plausible parameters for Escherichia coli.
Distribution of population averaged observables in stochastic gene expression
Bhattacharyya, Bhaswati; Kalay, Ziya
2014-03-01
Observation of phenotypic diversity in a population of genetically identical cells is often linked to the stochastic nature of chemical reactions involved in gene regulatory networks. We investigate the distribution of population averaged gene expression levels as a function of population, or sample size for several stochastic gene expression models to find out to what extent population averaged quantities reflect the underlying mechanism of gene expression. We consider three basic gene regulation networks corresponding to transcription with and without gene state switching and translation. Using analytical expressions for the probability generating function (pgf) of observables and Large Deviation Theory, we calculate the distribution of population averaged mRNA and protein levels as a function of model parameters and population size. We validate our results using stochastic simulations also report exact results on the asymptotic properties of population averages which show qualitative differences for different models. We calculate the skewness and coefficient of variance for pgfs to estimate the sample size required for population average that contains information about gene expression models. This is relevant to experiments where a large number of data points are unavailable.
Linking stochastic fluctuations in chromatin structure and gene expression.
Directory of Open Access Journals (Sweden)
Christopher R Brown
Full Text Available The number of mRNA and protein molecules expressed from a single gene molecule fluctuates over time. These fluctuations have been attributed, in part, to the random transitioning of promoters between transcriptionally active and inactive states, causing transcription to occur in bursts. However, the molecular basis of transcriptional bursting remains poorly understood. By electron microscopy of single PHO5 gene molecules from yeast, we show that the "activated" promoter assumes alternative nucleosome configurations at steady state, including the maximally repressive, fully nucleosomal, and the maximally non-repressive, nucleosome-free, configuration. We demonstrate that the observed probabilities of promoter nucleosome configurations are obtained from a simple, intrinsically stochastic process of nucleosome assembly, disassembly, and position-specific sliding; and we show that gene expression and promoter nucleosome configuration can be mechanistically coupled, relating promoter nucleosome dynamics and gene expression fluctuations. Together, our findings suggest a structural basis for transcriptional bursting, and offer new insights into the mechanism of transcriptional regulation and the kinetics of promoter nucleosome transitions.
Analytical approximations for spatial stochastic gene expression in single cells and tissues.
Smith, Stephen; Cianci, Claudia; Grima, Ramon
2016-05-01
Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction-diffusion master equation (RDME) describing stochastic reaction-diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction-diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues.
Inferring single-cell gene expression mechanisms using stochastic simulation
Daigle, Bernie J.; Soltani, Mohammad; Petzold, Linda R.; Singh, Abhyudai
2015-01-01
Motivation: Stochastic promoter switching between transcriptionally active (ON) and inactive (OFF) states is a major source of noise in gene expression. It is often implicitly assumed that transitions between promoter states are memoryless, i.e. promoters spend an exponentially distributed time interval in each of the two states. However, increasing evidence suggests that promoter ON/OFF times can be non-exponential, hinting at more complex transcriptional regulatory architectures. Given the essential role of gene expression in all cellular functions, efficient computational techniques for characterizing promoter architectures are critically needed. Results: We have developed a novel model reduction for promoters with arbitrary numbers of ON and OFF states, allowing us to approximate complex promoter switching behavior with Weibull-distributed ON/OFF times. Using this model reduction, we created bursty Monte Carlo expectation-maximization with modified cross-entropy method (‘bursty MCEM2’), an efficient parameter estimation and model selection technique for inferring the number and configuration of promoter states from single-cell gene expression data. Application of bursty MCEM2 to data from the endogenous mouse glutaminase promoter reveals nearly deterministic promoter OFF times, consistent with a multi-step activation mechanism consisting of 10 or more inactive states. Our novel approach to modeling promoter fluctuations together with bursty MCEM2 provides powerful tools for characterizing transcriptional bursting across genes under different environmental conditions. Availability and implementation: R source code implementing bursty MCEM2 is available upon request. Contact: absingh@udel.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:25573914
Stochastic models for inferring genetic regulation from microarray gene expression data.
Tian, Tianhai
2010-03-01
Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information.
Shearer, Joseph; Boone, Deborah; Weisz, Harris; Jennings, Kristofer; Uchida, Tatsuo; Parsley, Margaret; DeWitt, Douglas; Prough, Donald; Hellmich, Helen
2016-04-01
Traumatic brain injury (TBI) is a risk factor for age-related dementia and development of neurodegenerative disorders such as Alzheimer's disease that are associated with cognitive decline. The exact mechanism for this risk is unknown but we hypothesized that TBI is exacerbating age-related changes in gene expression. Here, we present evidence in an animal model that experimental TBI increases age-related stochastic gene expression. We compared the variability in expression of several genes associated with cell survival or death, among three groups of laser capture microdissected hippocampal neurons from aging rat brains. TBI increased stochastic fluctuations in gene expression in both dying and surviving neurons compared to the naïve neurons. Increases in random, stochastic fluctuations in prosurvival or prodeath gene expression could potentially alter cell survival or cell death pathways in aging neurons after TBI which may lead to age-related cognitive decline.
Models of stochastic gene expression and Weyl algebra
Vidal, Samuel,; Petitot, Michel; Boulier, François; Lemaire, François; Kuttler, Celine
2010-01-01
International audience; This paper presents a symbolic algorithm for computing the ODE systems which describe the evolution of the moments associated to a chemical reaction system, considered from a stochastic point of view. The algorithm, which is formulated in the Weyl algebra, seems more efficient than the corresponding method, based on partial derivatives. In particular, an efficient method for handling conservation laws is presented. The output of the algorithm can be used for a further ...
Stochastic simulation of fluid flow in porous media by the complex variable expression method
Institute of Scientific and Technical Information of China (English)
SONG Hui-bin; ZHAN Mei-li; SHENG Jin-chang; LUO Yu-long
2013-01-01
A stochastic simulation of fluid flow in porous media using a complex variable expression method (SFCM) is presented in this paper.Hydraulic conductivity is considered as a random variable and is then expressed in complex variable form,the real part of which is a deterministic value and the imaginary part is a variable value.The stochastic seepage flow is simulated with the SFCM and is compared with the results calculated with the Monte Carlo stochastic finite element method.In using the Monte Carlo method to simulate the stochastic seepage flow field,the hydraulic conductivity is assumed in three different probability distributions using random sampling method.The obtained seepage flow field is examined through skewness analysis,and the skewed distribution probability density function is given.The head mode value and the head comprehensive standard deviation are used to represent the sta-tistics of calculation results obtained by the Monte Carlo method.The stochastic seepage flow field simulated by the SFCM is confirmed to be similar to that given by the Monte Carlo method from numerical aspects.The range of coefficient of variation of hydraulic conductivity in SFCM is larger than used previously in stochastic seepage flow field simulations,and the computation time is short.The results proved that the SFCM is a convenient calculating method for solving the complex problems.
Doubly stochastic (pseudo)gene expression in the regulation of cancer
Petrosyan, K. G.; Hu, Chin-Kun
2017-08-01
We extend a model of the regulation of cancer by gene and pseudogene messenger RNAs to take into account cell-to-cell variability. This introduces an additional randomness to the intensity of the intracellular noise. The intracellular stochasticity is modelled via an additive white noise source and the intercellular stochasticity, or randomness, is modelled via a steady-state Γ -distribution for the intracellular noise intensity. The doubly stochastic process is treated numerically and displays a difference compared with the single stochastic (pseudo)gene expression process, which is the randomness-induced shift of the onset of even-odd oscillations in the number of molecules. Similarities to experimental outcomes in the related literature are pointed out.
Connecting protein and mRNA burst distributions for stochastic models of gene expression
Elgart, Vlad; Fenley, Andrew T; Kulkarni, Rahul V
2011-01-01
The intrinsic stochasticity of gene expression can lead to large variability in protein levels for genetically identical cells. Such variability in protein levels can arise from infrequent synthesis of mRNAs which in turn give rise to bursts of protein expression. Protein expression occurring in bursts has indeed been observed experimentally and recent studies have also found evidence for transcriptional bursting, i.e. production of mRNAs in bursts. Given that there are distinct experimental techniques for quantifying the noise at different stages of gene expression, it is of interest to derive analytical results connecting experimental observations at different levels. In this work, we consider stochastic models of gene expression for which mRNA and protein production occurs in independent bursts. For such models, we derive analytical expressions connecting protein and mRNA burst distributions which show how the functional form of the mRNA burst distribution can be inferred from the protein burst distributio...
Stochastic modeling for the expression of a gene regulated by competing transcription factors.
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Hsih-Te Yang
Full Text Available It is widely accepted that gene expression regulation is a stochastic event. The common approach for its computer simulation requires detailed information on the interactions of individual molecules, which is often not available for the analyses of biological experiments. As an alternative approach, we employed a more intuitive model to simulate the experimental result, the Markov-chain model, in which a gene is regulated by activators and repressors, which bind the same site in a mutually exclusive manner. Our stochastic simulation in the presence of both activators and repressors predicted a Hill-coefficient of the dose-response curve closer to the experimentally observed value than the calculated value based on the simple additive effects of activators alone and repressors alone. The simulation also reproduced the heterogeneity of gene expression levels among individual cells observed by Fluorescence Activated Cell Sorting analysis. Therefore, our approach may help to apply stochastic simulations to broader experimental data.
Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.
2013-04-01
Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.
Roussel, Marc R; Zhu, Rui
2006-12-08
The quantitative modeling of gene transcription and translation requires a treatment of two key features: stochastic fluctuations due to the limited copy numbers of key molecules (genes, RNA polymerases, ribosomes), and delayed output due to the time required for biopolymer synthesis. Recently proposed algorithms allow for efficient simulations of such systems. However, it is critical to know whether the results of delay stochastic simulations agree with those from more detailed models of the transcription and translation processes. We present a generalization of previous delay stochastic simulation algorithms which allows both for multiple delays and for distributions of delay times. We show that delay stochastic simulations closely approximate simulations of a detailed transcription model except when two-body effects (e.g. collisions between polymerases on a template strand) are important. Finally, we study a delay stochastic model of prokaryotic transcription and translation which reproduces observations from a recent experimental study in which a single gene was expressed under the control of a repressed lac promoter in E. coli cells. This demonstrates our ability to quantitatively model gene expression using these new methods.
Roussel, Marc R.; Zhu, Rui
2006-12-01
The quantitative modeling of gene transcription and translation requires a treatment of two key features: stochastic fluctuations due to the limited copy numbers of key molecules (genes, RNA polymerases, ribosomes), and delayed output due to the time required for biopolymer synthesis. Recently proposed algorithms allow for efficient simulations of such systems. However, it is critical to know whether the results of delay stochastic simulations agree with those from more detailed models of the transcription and translation processes. We present a generalization of previous delay stochastic simulation algorithms which allows both for multiple delays and for distributions of delay times. We show that delay stochastic simulations closely approximate simulations of a detailed transcription model except when two-body effects (e.g. collisions between polymerases on a template strand) are important. Finally, we study a delay stochastic model of prokaryotic transcription and translation which reproduces observations from a recent experimental study in which a single gene was expressed under the control of a repressed lac promoter in E. coli cells. This demonstrates our ability to quantitatively model gene expression using these new methods.
Decreasing the stochasticity of mammalian gene expression by a synthetic gene circuit
Nevozhay, Dmitry; Zal, Tomasz; Balazsi, Gabor
2012-02-01
Gene therapy and functional genetic studies usually require precisely controlled and uniform gene expression in a population of cells for reliable level of protein production. Due to this requirement, stochastic gene expression is perceived as undesirable in these fields and ideally has to be minimized. The number of approaches for decreasing gene expression stochasticity in mammalian cells is limited. This creates an unmet need to develop new gene expression systems for this purpose. Based on earlier synthetic constructs in yeast, we developed and assessed a negative feedback-based mammalian gene circuit, with uniform and low level of stochasticity in gene expression at different levels of induction. In addition, this new synthetic construct enables highly precise gene expression control in mammalian cells, due to the linear dependence of gene expression on the inducer concentration applied to the system. This mammalian gene expression circuit has potential applicability for the development of new treatment modalities in gene therapy and research tools in functional genetics. In addition, this work creates a roadmap for moving synthetic gene circuits from microbes into mammalian cells.
Soltani, Mohammad; Vargas-Garcia, Cesar A; Antunes, Duarte; Singh, Abhyudai
2016-08-01
Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in cell-division times generates additional intercellular variability in protein levels. Moreover, as many mRNA/protein species are expressed at low-copy numbers, errors incurred in partitioning of molecules between two daughter cells are significant. We derive analytical formulas for the total noise in protein levels when the cell-cycle duration follows a general class of probability distributions. Using a novel hybrid approach the total noise is decomposed into components arising from i) stochastic expression; ii) partitioning errors at the time of cell division and iii) random cell-division events. These formulas reveal that random cell-division times not only generate additional extrinsic noise, but also critically affect the mean protein copy numbers and intrinsic noise components. Counter intuitively, in some parameter regimes, noise in protein levels can decrease as cell-division times become more stochastic. Computations are extended to consider genome duplication, where transcription rate is increased at a random point in the cell cycle. We systematically investigate how the timing of genome duplication influences different protein noise components. Intriguingly, results show that noise contribution from stochastic expression is minimized at an optimal genome-duplication time. Our theoretical results motivate new experimental methods for decomposing protein noise levels from synchronized and asynchronized single-cell expression data. Characterizing the contributions of individual noise mechanisms will lead to precise estimates of gene expression parameters and techniques for altering stochasticity to change phenotype of individual cells.
Stochastic holin expression can account for lysis time variation in the bacteriophage λ.
Singh, Abhyudai; Dennehy, John J
2014-06-06
The inherent stochastic nature of biochemical processes can drive differences in gene expression between otherwise identical cells. While cell-to-cell variability in gene expression has received much attention, randomness in timing of events has been less studied. We investigate event timing at the single-cell level in a simple system, the lytic pathway of the bacterial virus phage λ. In individual cells, lysis occurs on average at 65 min, with an s.d. of 3.5 min. Interestingly, mutations in the lysis protein, holin, alter both the lysis time (LT) mean and variance. In our analysis, LT is formulated as the first-passage time (FPT) for cellular holin levels to cross a critical threshold. Exact analytical formulae for the FPT moments are derived for stochastic gene expression models. These formulae reveal how holin transcription and translation efficiencies independently modulate the LT mean and variation. Analytical expressions for the LT moments are used to evaluate previously published single-cell LT data for λ phages with mutations in the holin sequence or its promoter. Our results show that stochastic holin expression is sufficient to account for the intercellular LT differences in both wild-type phages, and phage variants where holin transcription and the threshold for lysis have been experimentally altered. Finally, our analysis reveals regulatory motifs that enhance the robustness of lysis timing to cellular noise.
Adiabatic reduction of a model of stochastic gene expression with jump Markov process.
Yvinec, Romain; Zhuge, Changjing; Lei, Jinzhi; Mackey, Michael C
2014-04-01
This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.
Frequency modulation of stochastic gene expression bursts by strongly interacting small RNAs
Kumar, Niraj; Jia, Tao; Zarringhalam, Kourosh; Kulkarni, Rahul V.
2016-10-01
The sporadic nature of gene expression at the single-cell level—long periods of inactivity punctuated by bursts of mRNA or protein production—plays a critical role in diverse cellular processes. To elucidate the cellular role of bursting in gene expression, synthetic biology approaches have been used to design simple genetic circuits with bursty mRNA or protein production. Understanding how such genetic circuits can be designed with the ability to control burst-related parameters requires the development of quantitative stochastic models of gene expression. In this work, we analyze stochastic models for the regulation of gene expression bursts by strongly interacting small RNAs. For the parameter range considered, results based on mean-field approaches are significantly inaccurate and alternative analytical approaches are needed. Using simplifying approximations, we obtain analytical results for the corresponding steady-state distributions that are in agreement with results from stochastic simulations. These results indicate that regulation by small RNAs, in the strong interaction limit, can be used to effectively modulate the frequency of bursting. We explore the consequences of such regulation for simple genetic circuits involving feedback effects and switching between promoter states.
Frequency modulation of stochastic gene expression bursts by strongly interacting small RNAs.
Kumar, Niraj; Jia, Tao; Zarringhalam, Kourosh; Kulkarni, Rahul V
2016-10-01
The sporadic nature of gene expression at the single-cell level-long periods of inactivity punctuated by bursts of mRNA or protein production-plays a critical role in diverse cellular processes. To elucidate the cellular role of bursting in gene expression, synthetic biology approaches have been used to design simple genetic circuits with bursty mRNA or protein production. Understanding how such genetic circuits can be designed with the ability to control burst-related parameters requires the development of quantitative stochastic models of gene expression. In this work, we analyze stochastic models for the regulation of gene expression bursts by strongly interacting small RNAs. For the parameter range considered, results based on mean-field approaches are significantly inaccurate and alternative analytical approaches are needed. Using simplifying approximations, we obtain analytical results for the corresponding steady-state distributions that are in agreement with results from stochastic simulations. These results indicate that regulation by small RNAs, in the strong interaction limit, can be used to effectively modulate the frequency of bursting. We explore the consequences of such regulation for simple genetic circuits involving feedback effects and switching between promoter states.
Stochastic protein expression in individual cells at the single molecule level
Cai, Long; Friedman, Nir; Xie, X. Sunney
2006-03-01
In a living cell, gene expression-the transcription of DNA to messenger RNA followed by translation to protein-occurs stochastically, as a consequence of the low copy number of DNA and mRNA molecules involved. These stochastic events of protein production are difficult to observe directly with measurements on large ensembles of cells owing to lack of synchronization among cells. Measurements so far on single cells lack the sensitivity to resolve individual events of protein production. Here we demonstrate a microfluidic-based assay that allows real-time observation of the expression of β-galactosidase in living Escherichia coli cells with single molecule sensitivity. We observe that protein production occurs in bursts, with the number of molecules per burst following an exponential distribution. We show that the two key parameters of protein expression-the burst size and frequency-can be either determined directly from real-time monitoring of protein production or extracted from a measurement of the steady-state copy number distribution in a population of cells. Application of this assay to probe gene expression in individual budding yeast and mouse embryonic stem cells demonstrates its generality. Many important proteins are expressed at low levels, and are thus inaccessible by current genomic and proteomic techniques. This microfluidic single cell assay opens up possibilities for system-wide characterization of the expression of these low copy number proteins.
Lei, Jinzhi; Yvinec, Romain; Zhuge, Changjing
2012-01-01
This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription. We prove that an adiabatic reduction can be performed in a stochastic slow/fast system with a jump Markov process. In the gene expression model, the production of mRNA (the fast variable) is assumed to follow a compound Poisson process (the phenomena called bursting in molecular biology) and the production of protein (the slow variable) is linear as a function of mRNA. When the dynamics of mRNA is assumed to be faster than the protein dynamics (due to a mRNA degradation rate larger than for the protein) we prove that, with the appropriate scaling, the bursting phenomena can be transmitted to the slow variable. We show that the reduced equation is either a stochastic differential equation with a jump Markov process or a deterministic ordinary differential equation depending on the scaling that is appropriate. These results are significant because adiabatic reduction techniques seem to have not been de...
Population genetics of non-genetic traits: Evolutionary roles of stochasticity in gene expression
Mineta, Katsuhiko
2015-05-01
The role of stochasticity in evolutionary genetics has long been debated. To date, however, the potential roles of non-genetic traits in evolutionary processes have been largely neglected. In molecular biology, growing evidence suggests that stochasticity in gene expression (SGE) is common and that SGE has major impacts on phenotypes and fitness. Here, we provide a general overview of the potential effects of SGE on population genetic parameters, arguing that SGE can indeed have a profound effect on evolutionary processes. Our analyses suggest that SGE potentially alters the fate of mutations by influencing effective population size and fixation probability. In addition, a genetic control of SGE magnitude could evolve under certain conditions, if the fitness of the less-fit individual increases due to SGE and environmental fluctuation. Although empirical evidence for our arguments is yet to come, methodological developments for precisely measuring SGE in living organisms will further advance our understanding of SGE-driven evolution.
An Algorithm for the Stochastic Simulation of Gene Expression and Heterogeneous Population Dynamics
Charlebois, Daniel A; Fraser, Dawn; Kaern, Mads
2011-01-01
We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations. To benchmark performance, we compare simulation results with steadystate and time-dependent analytical solutions for several scenarios, including steadystate and time-dependent gene expression, and the effects on population heterogeneity of cell growth, division, and DNA replication. This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression. We also use the algorithm to model gene expression dynamics within "bet-hedging" cell populations during their adaption to environmental stress. These simulations indicate that the algorithm provides a framework suitable for simulating and ana...
Blankenship, Whitney G.
2015-01-01
From the moment the United States entered World War II, public schools across the nation bombarded the Office of Education Wartime Commission requesting advice on how to mobilize schools for the war effort. American schools would rise to the occasion, implementing numerous programs including pre-induction training and the Victory Corps. The…
Stochastic fluctuations and distributed control of gene expression impact cellular memory.
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Guillaume Corre
Full Text Available Despite the stochastic noise that characterizes all cellular processes the cells are able to maintain and transmit to their daughter cells the stable level of gene expression. In order to better understand this phenomenon, we investigated the temporal dynamics of gene expression variation using a double reporter gene model. We compared cell clones with transgenes coding for highly stable mRNA and fluorescent proteins with clones expressing destabilized mRNA-s and proteins. Both types of clones displayed strong heterogeneity of reporter gene expression levels. However, cells expressing stable gene products produced daughter cells with similar level of reporter proteins, while in cell clones with short mRNA and protein half-lives the epigenetic memory of the gene expression level was completely suppressed. Computer simulations also confirmed the role of mRNA and protein stability in the conservation of constant gene expression levels over several cell generations. These data indicate that the conservation of a stable phenotype in a cellular lineage may largely depend on the slow turnover of mRNA-s and proteins.
Zhang, Xinmin; Wu, Bin; Liu, Xiaoyu; Shen, Ziyin
2011-01-01
For multicellular organisms, different tissues coordinate to integrate physiological functions, although this systematically and gradually declines in the aging process. Therefore, an association exists between tissue coordination and aging, and investigating the evolution of tissue coordination with age is of interest. In the past decade, both common and heterogeneous aging processes among tissues were extensively investigated. The results on spatial association of gene changes that determine lifespan appear complex and paradoxical. To reconcile observed commonality and heterogeneity of gene changes among tissues and to address evolution feature of tissue coordination with age, we introduced a new analytical strategy to systematically analyze genome-wide spatio-temporal gene expression profiles. We first applied the approach to natural aging process in three species (Rat, Mouse and Drosophila) and then to anti-aging process in Mouse. The results demonstrated that temporal gene expression alteration in different tissues experiences a progressive association evolution from spatial synchrony to asynchrony and stochasticity with age. This implies that tissue coordination gradually declines with age. Male mice showed earlier spatial asynchrony in gene expression than females, suggesting that male animals are more prone to aging than females. The confirmed anti-aging interventions (resveratrol and caloric restriction) enhanced tissue coordination, indicating their underlying anti-aging mechanism on multiple tissue levels. Further, functional analysis suggested asynchronous DNA/protein damage accumulation as well as asynchronous repair, modification and degradation of DNA/protein in tissues possibly contributes to asynchronous and stochastic changes of tissue microenvironment. This increased risk for a variety of age-related diseases such as neurodegeneration and cancer that eventually accelerate organismal aging and death. Our study suggests a novel molecular event
CTCF Is Required for Neural Development and Stochastic Expression of Clustered Pcdh Genes in Neurons
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Teruyoshi Hirayama
2012-08-01
Full Text Available The CCCTC-binding factor (CTCF is a key molecule for chromatin conformational changes that promote cellular diversity, but nothing is known about its role in neurons. Here, we produced mice with a conditional knockout (cKO of CTCF in postmitotic projection neurons, mostly in the dorsal telencephalon. The CTCF-cKO mice exhibited postnatal growth retardation and abnormal behavior and had defects in functional somatosensory mapping in the brain. In terms of gene expression, 390 transcripts were expressed at significantly different levels between CTCF-deficient and control cortex and hippocampus. In particular, the levels of 53 isoforms of the clustered protocadherin (Pcdh genes, which are stochastically expressed in each neuron, declined markedly. Each CTCF-deficient neuron showed defects in dendritic arborization and spine density during brain development. Their excitatory postsynaptic currents showed normal amplitude but occurred with low frequency. Our results indicate that CTCF regulates functional neural development and neuronal diversity by controlling clustered Pcdh expression.
From single-cell to cell-pool transcriptomes: stochasticity in gene expression and RNA splicing.
Marinov, Georgi K; Williams, Brian A; McCue, Ken; Schroth, Gary P; Gertz, Jason; Myers, Richard M; Wold, Barbara J
2014-03-01
Single-cell RNA-seq mammalian transcriptome studies are at an early stage in uncovering cell-to-cell variation in gene expression, transcript processing and editing, and regulatory module activity. Despite great progress recently, substantial challenges remain, including discriminating biological variation from technical noise. Here we apply the SMART-seq single-cell RNA-seq protocol to study the reference lymphoblastoid cell line GM12878. By using spike-in quantification standards, we estimate the absolute number of RNA molecules per cell for each gene and find significant variation in total mRNA content: between 50,000 and 300,000 transcripts per cell. We directly measure technical stochasticity by a pool/split design and find that there are significant differences in expression between individual cells, over and above technical variation. Specific gene coexpression modules were preferentially expressed in subsets of individual cells, including one enriched for mRNA processing and splicing factors. We assess cell-to-cell variation in alternative splicing and allelic bias and report evidence of significant differences in splice site usage that exceed splice variation in the pool/split comparison. Finally, we show that transcriptomes from small pools of 30-100 cells approach the information content and reproducibility of contemporary RNA-seq from large amounts of input material. Together, our results define an experimental and computational path forward for analyzing gene expression in rare cell types and cell states.
Aire controls gene expression in the thymic epithelium with ordered stochasticity
Meredith, Matthew; Zemmour, David; Mathis, Diane; Benoist, Christophe
2015-01-01
Aire controls immunologic tolerance by inducing the ectopic thymic expression of many tissue-specific genes, acting broadly by removing stops on the transcriptional machinery. To better understand Aire’s specificity, we performed single-cell RNAseq and DNA methylation analysis in Aire-sufficient and -deficient medullary epithelial cells (mTECs). Each of Aire’s target genes was induced in only a minority of mTECs, independently of DNA methylation patterns, as small inter-chromosomal gene clusters activated in concert in a proportion of mTECs. These microclusters differed between individual mice, and thus suggest an organization of the DNA or of the epigenome that results from stochastic determinism, but is bookmarked and stable through mTEC divisions, ensuring more effective presentation of self-antigens, and favoring diversity of self-tolerance between individuals. PMID:26237550
Directory of Open Access Journals (Sweden)
Mao Yu
2009-07-01
Full Text Available Abstract Background The identification of gene differential co-expression patterns between cancer stages is a newly developing method to reveal the underlying molecular mechanisms of carcinogenesis. Most researches of this subject lack an algorithm useful for performing a statistical significance assessment involving cancer progression. Lacking this specific algorithm is apparently absent in identifying precise gene pairs correlating to cancer progression. Results In this investigation we studied gene pair co-expression change by using a stochastic process model for approximating the underlying dynamic procedure of the co-expression change during cancer progression. Also, we presented a novel analytical method named 'Stochastic process model for Identifying differentially co-expressed Gene pair' (SIG method. This method has been applied to two well known prostate cancer data sets: hormone sensitive versus hormone resistant, and healthy versus cancerous. From these data sets, 428,582 gene pairs and 303,992 gene pairs were identified respectively. Afterwards, we used two different current statistical methods to the same data sets, which were developed to identify gene pair differential co-expression and did not consider cancer progression in algorithm. We then compared these results from three different perspectives: progression analysis, gene pair identification effectiveness analysis, and pathway enrichment analysis. Statistical methods were used to quantify the quality and performance of these different perspectives. They included: Re-identification Scale (RS and Progression Score (PS in progression analysis, True Positive Rate (TPR in gene pair analysis, and Pathway Enrichment Score (PES in pathway analysis. Our results show small values of RS and large values of PS, TPR, and PES; thus, suggesting that gene pairs identified by the SIG method are highly correlated with cancer progression, and highly enriched in disease-specific pathways. From
Shepherd, Douglas; Shapiro, Evan; Perillo, Evan; Werner, James
2014-03-01
Biological processes at the microscopic level appear stochastic, requiring precise measurement and analytical techniques to determine the nature of the underlying regulatory networks. Single-molecule, single-cell studies of gene expression have provided insights into how cells respond to external stimuli. Recent work has suggested that macroscopic cell properties, such as cell morphology, are correlated with gene expression. Here we present single-cell studies of a signal-activated gene network: Interleukin 4 (IL4) RNA production in rat basophil leukemia (RBL) cells during the allergic response. We fluorescently label individual IL4 RNA transcripts in populations of RBL cells, subject to varying external stimuli. A custom super-resolution microscope is used to measure the number of fluorescent labeled IL4 transcripts in populations of RBL cells on a cell-by-cell basis. To test the hypothesis that cell morphology is connected genotype, we analyze white light images of RBL cells and cross-reference cell morphology with IL4 RNA levels. We find that the activation of RBL cells, determined by white-light imaging, is well correlated with IL4 mRNA expression.
Matsumoto, Tomotaka
2015-11-24
Recent studies suggest the existence of a stochasticity in gene expression (SGE) in many organisms, and its non-negligible effect on their phenotype and fitness. To date, however, how SGE affects the key parameters of population genetics are not well understood. SGE can increase the phenotypic variation and act as a load for individuals, if they are at the adaptive optimum in a stable environment. On the other hand, part of the phenotypic variation caused by SGE might become advantageous if individuals at the adaptive optimum become genetically less-adaptive, for example due to an environmental change. Furthermore, SGE of unimportant genes might have little or no fitness consequences. Thus, SGE can be advantageous, disadvantageous, or selectively neutral depending on its context. In addition, there might be a genetic basis that regulates magnitude of SGE, which is often referred to as “modifier genes,” but little is known about the conditions under which such an SGE-modifier gene evolves. In the present study, we conducted individual-based computer simulations to examine these conditions in a diploid model. In the simulations, we considered a single locus that determines organismal fitness for simplicity, and that SGE on the locus creates fitness variation in a stochastic manner. We also considered another locus that modifies the magnitude of SGE. Our results suggested that SGE was always deleterious in stable environments and increased the fixation probability of deleterious mutations in this model. Even under frequently changing environmental conditions, only very strong natural selection made SGE adaptive. These results suggest that the evolution of SGE-modifier genes requires strict balance among the strength of natural selection, magnitude of SGE, and frequency of environmental changes. However, the degree of dominance affected the condition under which SGE becomes advantageous, indicating a better opportunity for the evolution of SGE in different genetic
Gualdrini, G; Tanner, R J; Agosteo, S; Pola, A; Bedogni, R; Ferrari, P; Lacoste, V; Bordy, J-M; Chartier, J-L; de Carlan, L; Gomez Ros, J-M; Grosswendt, B; Kodeli, I; Price, R A; Rollet, S; Schultz, F; Siebert, B; Terrissol, M; Zankl, M
2008-01-01
Within the scope of CONRAD (A Coordinated Action for Radiation Dosimetry) Work Package 4 on Computational Dosimetry jointly collaborated with the other research actions on internal dosimetry, complex mixed radiation fields at workplaces and medical staff dosimetry. Besides these collaborative actions, WP4 promoted an international comparison on eight problems with their associated experimental data. A first set of three problems, the results of which are herewith summarised, dealt only with the expression of the stochastic uncertainties of the results: the analysis of the response function of a proton recoil telescope detector, the study of a Bonner sphere neutron spectrometer and the analysis of the neutron spectrum and dosimetric quantity H(p)(10) in a thermal neutron facility operated by IRSN Cadarache (the SIGMA facility). A second paper will summarise the results of the other five problems which dealt with the full uncertainty budget estimate. A third paper will present the results of a comparison on in vivo measurements of the (241)Am bone-seeker nuclide distributed in the knee. All the detailed papers will be presented in the WP4 Final Workshop Proceedings.
A geometric analysis of fast-slow models for stochastic gene expression.
Popović, Nikola; Marr, Carsten; Swain, Peter S
2016-01-01
Stochastic models for gene expression frequently exhibit dynamics on several different scales. One potential time-scale separation is caused by significant differences in the lifetimes of mRNA and protein; the ratio of the two degradation rates gives a natural small parameter in the resulting chemical master equation, allowing for the application of perturbation techniques. Here, we develop a framework for the analysis of a family of 'fast-slow' models for gene expression that is based on geometric singular perturbation theory. We illustrate our approach by giving a complete characterisation of a standard two-stage model which assumes transcription, translation, and degradation to be first-order reactions. In particular, we present a systematic expansion procedure for the probability-generating function that can in principle be taken to any order in the perturbation parameter, allowing for an approximation of the corresponding propagator probabilities to that same order. For illustrative purposes, we perform this expansion explicitly to first order, both on the fast and the slow time-scales; then, we combine the resulting asymptotics into a composite fast-slow expansion that is uniformly valid in time. In the process, we extend, and prove rigorously, results previously obtained by Shahrezaei and Swain (Proc Natl Acad Sci USA 105(45):17256-17261, 2008) and Bokes et al. (J Math Biol 64(5):829-854, 2012; J Math Biol 65(3):493-520, 2012). We verify our asymptotics by numerical simulation, and we explore its practical applicability and the effects of a variation in the system parameters and the time-scale separation. Focussing on biologically relevant parameter regimes that induce translational bursting, as well as those in which mRNA is frequently transcribed, we find that the first-order correction can significantly improve the steady-state probability distribution. Similarly, in the time-dependent scenario, inclusion of the first-order fast asymptotics results in a
Cheng, Yang; Wong, Michael T; van der Maaten, Laurens; Newell, Evan W
2016-01-15
Rapid progress in single-cell analysis methods allow for exploration of cellular diversity at unprecedented depth and throughput. Visualizing and understanding these large, high-dimensional datasets poses a major analytical challenge. Mass cytometry allows for simultaneous measurement of >40 different proteins, permitting in-depth analysis of multiple aspects of cellular diversity. In this article, we present one-dimensional soli-expression by nonlinear stochastic embedding (One-SENSE), a dimensionality reduction method based on the t-distributed stochastic neighbor embedding (t-SNE) algorithm, for categorical analysis of mass cytometry data. With One-SENSE, measured parameters are grouped into predefined categories, and cells are projected onto a space composed of one dimension for each category. In contrast with higher-dimensional t-SNE, each dimension (plot axis) in One-SENSE has biological meaning that can be easily annotated with binned heat plots. We applied One-SENSE to probe relationships between categories of human T cell phenotypes and observed previously unappreciated cellular populations within an orchestrated view of immune cell diversity. The presentation of high-dimensional cytometric data using One-SENSE showed a significant improvement in distinguished T cell diversity compared with the original t-SNE algorithm and could be useful for any high-dimensional dataset.
Stochastic volatility and stochastic leverage
DEFF Research Database (Denmark)
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
A stochastic model for optimizing composite predictors based on gene expression profiles.
Ramanathan, Murali
2003-07-01
This project was done to develop a mathematical model for optimizing composite predictors based on gene expression profiles from DNA arrays and proteomics. The problem was amenable to a formulation and solution analogous to the portfolio optimization problem in mathematical finance: it requires the optimization of a quadratic function subject to linear constraints. The performance of the approach was compared to that of neighborhood analysis using a data set containing cDNA array-derived gene expression profiles from 14 multiple sclerosis patients receiving intramuscular inteferon-beta1a. The Markowitz portfolio model predicts that the covariance between genes can be exploited to construct an efficient composite. The model predicts that a composite is not needed for maximizing the mean value of a treatment effect: only a single gene is needed, but the usefulness of the effect measure may be compromised by high variability. The model optimized the composite to yield the highest mean for a given level of variability or the least variability for a given mean level. The choices that meet this optimization criteria lie on a curve of composite mean vs. composite variability plot referred to as the "efficient frontier." When a composite is constructed using the model, it outperforms the composite constructed using the neighborhood analysis method. The Markowitz portfolio model may find potential applications in constructing composite biomarkers and in the pharmacogenomic modeling of treatment effects derived from gene expression endpoints.
Frédéric, Pierret
2014-01-01
The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.
Stochastic Shadowing and Stochastic Stability
Todorov, Dmitry
2014-01-01
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are significantly non-uniformly hyperbolic systems that satisfy stochastic shadowing property.
Stochastic gene expression in single cells: exploring the importance of noise in genetic networks
van Oudenaarden, Alexander
2003-03-01
Cells are intrinsically noisy biochemical reactors. This leads to random cell to cell variation (noise) in gene expression levels. First, I will address the source of this noise at the level of transcription and translation of a single gene. Our experimental results demonstrate that the intrinsic noise of a single gene is predominantly controlled at the translational level, and that increased translational efficiency leads to increased noise strength. This observation is consistent with a theoretical model in which proteins are randomly produced in sharp bursts followed by periods of slow decay. Second, I will explore the importance of genetic noise for a naturally occuring network: the lac operon. The classic lactose utilization network of E. coli has been under investigation for several decades and, in its simplest form the network may be modeled as a single positive feedback module. However, this simplicity is deceptive, as even this basic network is capable of complex metabolic behavior, including adaptation, amplification, and graded-to-binary response conversion. I will present single cell measurements on the expression of key genes in lactose uptake network and explore the importance of genetic noise on the regulation of these genes.
Stochastic Nature in Cellular Processes
Institute of Scientific and Technical Information of China (English)
刘波; 刘圣君; 王祺; 晏世伟; 耿轶钊; SAKATA Fumihiko; GAO Xing-Fa
2011-01-01
The importance of stochasticity in cellular processes is increasingly recognized in both theoretical and experimental studies. General features of stochasticity in gene regulation and expression are briefly reviewed in this article, which include the main experimental phenomena, classification, quantization and regulation of noises. The correlation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methods that can capture effects of intrinsic and extrinsic noise are described.
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
This thesis addresses stochastic modelling of turbulence with applications to wind energy in mind. The primary tool is ambit processes, a recently developed class of computationally tractable stochastic processes based on integration with respect to Lévy bases. The subject of ambit processes...... stochastic turbulence model based on ambit processes is proposed. It is shown how a prescribed isotropic covariance structure can be reproduced. Non-Gaussian turbulence models are obtained through non-Gaussian Lévy bases or through volatility modulation of Lévy bases. As opposed to spectral models operating...... is dissipated into heat due to the internal friction caused by viscosity. An existing stochastic model, also expressed in terms of ambit processes, is extended and shown to give a universal and parsimonious description of the turbulent energy dissipation. The volatility modulation, referred to above, has...
Mesoscopic Fluctuations in Stochastic Spacetime
Shiokawa, K
2000-01-01
Mesoscopic effects associated with wave propagation in spacetime with metric stochasticity are studied. We show that the scalar and spinor waves in a stochastic spacetime behave similarly to the electrons in a disordered system. Viewing this as the quantum transport problem, mesoscopic fluctuations in such a spacetime are discussed. The conductance and its fluctuations are expressed in terms of a nonlinear sigma model in the closed time path formalism. We show that the conductance fluctuations are universal, independent of the volume of the stochastic region and the amount of stochasticity.
Directory of Open Access Journals (Sweden)
Robert P Jenkins
2015-11-01
Full Text Available The somite segmentation clock is a robust oscillator used to generate regularly-sized segments during early vertebrate embryogenesis. It has been proposed that the clocks of neighbouring cells are synchronised via inter-cellular Notch signalling, in order to overcome the effects of noisy gene expression. When Notch-dependent communication between cells fails, the clocks of individual cells operate erratically and lose synchrony over a period of about 5 to 8 segmentation clock cycles (2-3 hours in the zebrafish. Here, we quantitatively investigate the effects of stochasticity on cell synchrony, using mathematical modelling, to investigate the likely source of such noise. We find that variations in the transcription, translation and degradation rate of key Notch signalling regulators do not explain the in vivo kinetics of desynchronisation. Rather, the analysis predicts that clock desynchronisation, in the absence of Notch signalling, is due to the stochastic dissociation of Her1/7 repressor proteins from the oscillating her1/7 autorepressed target genes. Using in situ hybridisation to visualise sites of active her1 transcription, we measure an average delay of approximately three minutes between the times of activation of the two her1 alleles in a cell. Our model shows that such a delay is sufficient to explain the in vivo rate of clock desynchronisation in Notch pathway mutant embryos and also that Notch-mediated synchronisation is sufficient to overcome this stochastic variation. This suggests that the stochastic nature of repressor/DNA dissociation is the major source of noise in the segmentation clock.
Directory of Open Access Journals (Sweden)
Kathryn Miller-Jensen
Full Text Available The sequence of a promoter within a genome does not uniquely determine gene expression levels and their variability; rather, promoter sequence can additionally interact with its location in the genome, or genomic context, to shape eukaryotic gene expression. Retroviruses, such as human immunodeficiency virus-1 (HIV, integrate their genomes into those of their host and thereby provide a biomedically-relevant model system to quantitatively explore the relationship between promoter sequence, genomic context, and noise-driven variability on viral gene expression. Using an in vitro model of the HIV Tat-mediated positive-feedback loop, we previously demonstrated that fluctuations in viral Tat-transactivating protein levels generate integration-site-dependent, stochastically-driven phenotypes, in which infected cells randomly 'switch' between high and low expressing states in a manner that may be related to viral latency. Here we extended this model and designed a forward genetic screen to systematically identify genetic elements in the HIV LTR promoter that modulate the fraction of genomic integrations that specify 'Switching' phenotypes. Our screen identified mutations in core promoter regions, including Sp1 and TATA transcription factor binding sites, which increased the Switching fraction several fold. By integrating single-cell experiments with computational modeling, we further investigated the mechanism of Switching-fraction enhancement for a selected Sp1 mutation. Our experimental observations demonstrated that the Sp1 mutation both impaired Tat-transactivated expression and also altered basal expression in the absence of Tat. Computational analysis demonstrated that the observed change in basal expression could contribute significantly to the observed increase in viral integrations that specify a Switching phenotype, provided that the selected mutation affected Tat-mediated noise amplification differentially across genomic contexts. Our study
McKean, Henry P
2005-01-01
This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. -E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplemen
Parzen, Emanuel
2015-01-01
Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine
Schneider, Johannes J
2007-01-01
This book addresses stochastic optimization procedures in a broad manner. The first part offers an overview of relevant optimization philosophies; the second deals with benchmark problems in depth, by applying a selection of optimization procedures. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them.
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Stochastic Constraint Programming
Walsh, Toby
2009-01-01
To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number...
Energy Technology Data Exchange (ETDEWEB)
Bisognano, J.; Leemann, C.
1982-03-01
Stochastic cooling is the damping of betatron oscillations and momentum spread of a particle beam by a feedback system. In its simplest form, a pickup electrode detects the transverse positions or momenta of particles in a storage ring, and the signal produced is amplified and applied downstream to a kicker. The time delay of the cable and electronics is designed to match the transit time of particles along the arc of the storage ring between the pickup and kicker so that an individual particle receives the amplified version of the signal it produced at the pick-up. If there were only a single particle in the ring, it is obvious that betatron oscillations and momentum offset could be damped. However, in addition to its own signal, a particle receives signals from other beam particles. In the limit of an infinite number of particles, no damping could be achieved; we have Liouville's theorem with constant density of the phase space fluid. For a finite, albeit large number of particles, there remains a residue of the single particle damping which is of practical use in accumulating low phase space density beams of particles such as antiprotons. It was the realization of this fact that led to the invention of stochastic cooling by S. van der Meer in 1968. Since its conception, stochastic cooling has been the subject of much theoretical and experimental work. The earliest experiments were performed at the ISR in 1974, with the subsequent ICE studies firmly establishing the stochastic cooling technique. This work directly led to the design and construction of the Antiproton Accumulator at CERN and the beginnings of p anti p colliding beam physics at the SPS. Experiments in stochastic cooling have been performed at Fermilab in collaboration with LBL, and a design is currently under development for a anti p accumulator for the Tevatron.
Eichhorn, Ralf; Aurell, Erik
2014-04-01
'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response
Crisan, Dan
2011-01-01
"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa
Jędrak, Jakub
2016-01-01
We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability distribution and the model parameters depend on time in an arbitrary (e.g. oscillatory) manner, and for arbitrary initial conditions. We show that in the case of periodic external activation and constant protein degradation rate, the response of the gene is analogous to the RC low-pass filter, where slow oscillations of the external driving have a greater effect on gene expression than the fast ones. We also demonstrate that the $n$-th cumulant of the protein number distribution depends on the $n$-th moment of the burst size distribution. We use these results to show that different measures of noise (coefficient of variation, Fano factor, fractional change of varian...
A Note on the Stochastic Nature of Feynman Quantum Paths
L. Botelho, Luiz C.
2016-06-01
We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.
A Note on the Stochastic Nature of Feynman Quantum Paths
Botelho, Luiz C. L.
2016-11-01
We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.
Dynamics of stochastic systems
Klyatskin, Valery I
2005-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...
Jedrak, Jakub; Ochab-Marcinek, Anna
2016-09-01
We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability distribution and the model parameters depend on time in an arbitrary (e.g., oscillatory) manner, and for arbitrary initial conditions. We show that in the case of periodic external activation and constant protein degradation rate, the response of the gene is analogous to the resistor-capacitor low-pass filter, where slow oscillations of the external driving have a greater effect on gene expression than the fast ones. We also demonstrate that the n th cumulant of the protein number distribution depends on the n th moment of the burst size distribution. We use these results to show that different measures of noise (coefficient of variation, Fano factor, fractional change of variance) may vary in time in a different manner. Therefore, any biological hypothesis of evolutionary optimization based on the nonmonotonic dependence of a chosen measure of noise on time must justify why it assumes that biological evolution quantifies noise in that particular way. Finally, we show that not only for exponentially distributed burst sizes but also for a wider class of burst size distributions (e.g., Dirac delta and gamma) the control of gene expression level by burst frequency modulation gives rise to proportional scaling of variance of the protein number distribution to its mean, whereas the control by amplitude modulation implies proportionality of protein number variance to the mean squared.
Directory of Open Access Journals (Sweden)
Romanu Ekaterini
2006-01-01
Full Text Available This article shows the similarities between Claude Debussy’s and Iannis Xenakis’ philosophy of music and work, in particular the formers Jeux and the latter’s Metastasis and the stochastic works succeeding it, which seem to proceed parallel (with no personal contact to what is perceived as the evolution of 20th century Western music. Those two composers observed the dominant (German tradition as outsiders, and negated some of its elements considered as constant or natural by "traditional" innovators (i.e. serialists: the linearity of musical texture, its form and rhythm.
Buganim, Y.; Faddah, D.A.; Cheng, A.W.; Itskovich, E.; Markoulaki, S.; Ganz, K.; Klemm, S.L.; van Oudenaarden, A.; Jaenisch, R.
2012-01-01
During cellular reprogramming, only a small fraction of cells become induced pluripotent stem cells (iPSCs). Previous analyses of gene expression during reprogramming were based on populations of cells, impeding single-cell level identification of reprogramming events. We utilized two gene
DEFF Research Database (Denmark)
Optical Density bioscreen measurements of P. aeruginosa to perform a Maximum Likelihood estimation of the model parameters and subsequently obtain a smoothing estimate for the model state variables by means of a nonlinear smoothing algorithm based on the extended Kalman filter, using an implementation....... aeruginosa we observe a growth pattern far from Monod growth. Therefore a reformulation of the growth expression is necessary. Without any pre-knowledge about the functional dependence between the growth rate and the substrate content and with only limited experimental resources necessary, the proposed...... described by Kristensen et. al [2]. The resulting time series allows us graphically to inspect the functional dependence of the growth rate on the substrate content. From the method described above we find three new plausible expressions for μ(S). Therefore we apply the likelihood-ratio test to compare...
Stochastic Model Checking of the Stochastic Quality Calculus
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin
2015-01-01
The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input...
Lanchier, Nicolas
2017-01-01
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...
Energy Technology Data Exchange (ETDEWEB)
Blaskiewicz, M.
2011-01-01
Stochastic Cooling was invented by Simon van der Meer and was demonstrated at the CERN ISR and ICE (Initial Cooling Experiment). Operational systems were developed at Fermilab and CERN. A complete theory of cooling of unbunched beams was developed, and was applied at CERN and Fermilab. Several new and existing rings employ coasting beam cooling. Bunched beam cooling was demonstrated in ICE and has been observed in several rings designed for coasting beam cooling. High energy bunched beams have proven more difficult. Signal suppression was achieved in the Tevatron, though operational cooling was not pursued at Fermilab. Longitudinal cooling was achieved in the RHIC collider. More recently a vertical cooling system in RHIC cooled both transverse dimensions via betatron coupling.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.
Stochastic Averaging and Stochastic Extremum Seeking
Liu, Shu-Jun
2012-01-01
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...
Stochastic Modelling of Energy Systems
DEFF Research Database (Denmark)
Andersen, Klaus Kaae
2001-01-01
equations are expressed in terms of stochastic differential equations. From a theoretical viewpoint the techniques for experimental design, parameter estimation and model validation are considered. From the practical viewpoint emphasis is put on how this methods can be used to construct models adequate...
Directory of Open Access Journals (Sweden)
Asha Jenkins
2016-11-01
Conclusions: PGE2 gel is an efficient agent for pre induction cervical ripening when compared to Foley catheter and misoprostol tablet though it is expensive, unstable and requires refrigeration. Tablet misoprostol significantly reduces the ripening duration, ripening delivery interval and the total duration to delivery. Misoprostol tablet is inexpensive, stable at room temperature and easy to administer. It also reduces the need for oxytocin augmentation. However the safety of misoprostol is still a concern due to increased maternal and neonatal complications. Foley catheter alone is not a good cervical ripening agent. [Int J Reprod Contracept Obstet Gynecol 2016; 5(11.000: 3902-3908
Sobczyk, K
1985-01-01
This is a concise, unified exposition of the existing methods of analysis of linear stochastic waves with particular reference to the most recent results. Both scalar and vector waves are considered. Principal attention is concentrated on wave propagation in stochastic media and wave scattering at stochastic surfaces. However, discussion extends also to various mathematical aspects of stochastic wave equations and problems of modelling stochastic media.
Stochastic homothetically revealed preference for tight stochastic demand functions
Jan Heufer
2009-01-01
This paper strengthens the framework of stochastic revealed preferences introduced by Bandyopadhyay et al. (1999, 2004) for stochastic homothetically revealed preferences for tight stochastic demand functions.
Strasser, Michael; Theis, Fabian J; Marr, Carsten
2012-01-04
A toggle switch consists of two genes that mutually repress each other. This regulatory motif is active during cell differentiation and is thought to act as a memory device, being able to choose and maintain cell fate decisions. Commonly, this switch has been modeled in a deterministic framework where transcription and translation are lumped together. In this description, bistability occurs for transcription factor cooperativity, whereas autoactivation leads to a tristable system with an additional undecided state. In this contribution, we study the stability and dynamics of a two-stage gene expression switch within a probabilistic framework inspired by the properties of the Pu/Gata toggle switch in myeloid progenitor cells. We focus on low mRNA numbers, high protein abundance, and monomeric transcription-factor binding. Contrary to the expectation from a deterministic description, this switch shows complex multiattractor dynamics without autoactivation and cooperativity. Most importantly, the four attractors of the system, which only emerge in a probabilistic two-stage description, can be identified with committed and primed states in cell differentiation. To begin, we study the dynamics of the system and infer the mechanisms that move the system between attractors using both the quasipotential and the probability flux of the system. Next, we show that the residence times of the system in one of the committed attractors are geometrically distributed. We derive an analytical expression for the parameter of the geometric distribution, therefore completely describing the statistics of the switching process and elucidate the influence of the system parameters on the residence time. Moreover, we find that the mean residence time increases linearly with the mean protein level. This scaling also holds for a one-stage scenario and for autoactivation. Finally, we study the implications of this distribution for the stability of a switch and discuss the influence of the
Correlation functions in stochastic inflation
Energy Technology Data Exchange (ETDEWEB)
Vennin, Vincent [University of Portsmouth, Institute of Cosmology and Gravitation, Portsmouth (United Kingdom); Starobinsky, Alexei A. [L.D. Landau Institute for Theoretical Physics RAS, Moscow (Russian Federation); Utrecht University, Department of Physics and Astronomy, Institute for Theoretical Physics, Utrecht (Netherlands)
2015-09-15
Combining the stochastic and δ N formalisms, we derive non-perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered as saddle-point limits of the full results. This yields a classicality criterion that shows that stochastic effects are small only if the potential is sub-Planckian and not too flat. The saddle-point approximation also provides an expansion scheme for calculating stochastic corrections to observable quantities perturbatively in this regime. In the opposite regime, we show that a strong suppression in the power spectrum is generically obtained, and we comment on the physical implications of this effect. (orig.)
Stochastic Physicochemical Dynamics
Tsekov, R.
2001-02-01
fluctuations. The range of validity of the Boltzmann-Einstein principle is also discussed and a generalized alternative is proposed. Both expressions coincide in the small fluctuation limit, providing a normal distribution density. Fluctuation Stability of Thin Liquid Films: Memory effect of Brownian motion in an incompressible fluid is studied. The reasoning is based on the Mori-Zwanzig formalism and a new formulation of the Langevin force as a result of collisions between an effective and the Brownian particles. Thus, the stochastic force autocorrelation function with finite dispersion and the corresponding Brownian particle velocity autocorrelation function are obtained. It is demonstrated that the dynamic structure is very important for the rate of drainage of a thin liquid film and it can be effectively taken into account by a dynamic fractal dimension. It is shown that the latter is a powerful tool for description of the film drainage and classifies all the known results from the literature. The obtained general expression for the thinning rate is a heuristic one and predicts variety of drainage models, which are even difficult to simulate in practice. It is a typical example of a scaling law, which explains the origin of the complicate dependence of the thinning rate on the film radius. On the basis of the theory of stochastic processes the evolution of the spatial correlation function of the surface waves on a thin liquid film as well as the corresponding root mean square amplitude A(t) and number of uncorrelated subdomains N(t) are obtained. A formulation of the life time of unstable nonthinning films is proposed, based on the evolution of A and N. It is shown that the presence of uncorrelated subdomains shortens the life time of the film. Some numerical results for A(t) and N(t) at different film thicknesses h and areas S, are demonstrated, taking into account only van der Waals and capillary forces. Resonant Diffusion in Molecular Solid Structures: A new approach to
The stochastic integrable AKNS hierarchy
Arnaudon, Alexis
2015-01-01
We derive a stochastic AKNS hierarchy using geometrical methods. The integrability is shown via a stochastic zero curvature relation associated with a stochastic isospectral problem. We expose some of the stochastic integrable partial differential equations which extend the stochastic KdV equation discovered by M. Wadati in 1983 for all the AKNS flows. We also show how to find stochastic solitons from the stochastic evolution of the scattering data of the stochastic IST. We finally expose som...
Moawia Alghalith
2012-01-01
We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
Stochastic processes - quantum physics
Energy Technology Data Exchange (ETDEWEB)
Streit, L. (Bielefeld Univ. (Germany, F.R.))
1984-01-01
The author presents an elementary introduction to stochastic processes. He starts from simple quantum mechanics and considers problems in probability, finally presenting quantum dynamics in terms of stochastic processes.
Losslessness of Nonlinear Stochastic Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Xikui Liu
2015-01-01
Full Text Available This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree 0,…,0 and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.
Stochastic tools in turbulence
Lumey, John L
2012-01-01
Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the
Energy Technology Data Exchange (ETDEWEB)
Brennan,J.M.; Blaskiewicz, M. M.; Severino, F.
2009-05-04
After the success of longitudinal stochastic cooling of bunched heavy ion beam in RHIC, transverse stochastic cooling in the vertical plane of Yellow ring was installed and is being commissioned with proton beam. This report presents the status of the effort and gives an estimate, based on simulation, of the RHIC luminosity with stochastic cooling in all planes.
Stochastic string models with continuous semimartingales
Bueno-Guerrero, Alberto; Moreno, Manuel; Navas, Javier F.
2015-09-01
This paper reformulates the stochastic string model of Santa-Clara and Sornette using stochastic calculus with continuous semimartingales. We present some new results, such as: (a) the dynamics of the short-term interest rate, (b) the PDE that must be satisfied by the bond price, and (c) an analytic expression for the price of a European bond call option. Additionally, we clarify some important features of the stochastic string model and show its relevance to price derivatives and the equivalence with an infinite dimensional HJM model to price European options.
A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES
Institute of Scientific and Technical Information of China (English)
Qi-Ming HE; Eldon GUNN
2003-01-01
In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2×2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3×3 matrix, including all possible (function) stochastic root matrices. In addition, we comment on some numerical methods for computing stochastic root matrices of stochastic matrices.
Ogawa, Shigeyoshi
2017-01-01
This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...
Stochastic Lie group integrators
Malham, Simon J A
2007-01-01
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie algebra via the exponential map. We construct an approximation to the stochastic flow in the Lie algebra via closed operations and then push back to the Lie group and then to the manifold, thus ensuring our approximation lies in the manifold. We call such schemes stochastic Munthe-Kaas methods after their deterministic counterparts. We also present stochastic Lie group integration schemes based on Castell--Gaines methods. These involve using an underlying ordinary differential integrator to approximate the flow generated by a truncated stochastic exponential Lie series. They become stochastic Lie group integrator schemes if...
Ruin problems with stochastic premium stochastic return on investments
Institute of Scientific and Technical Information of China (English)
WANG Rongming; XU Lin; YAO Dingjun
2007-01-01
In this paper, ruin problems in the risk model with stochastic premium incomes and stochastic return on investments are studied. The logarithm of the asset price process is assumed to be a Lévy process. An exact expression for expected discounted penalty function is established. Lower bounds and two kinds of upper bounds for expected discounted penalty function are obtained by inductive method and martingale approach. Integro- differential equations for the expected discounted penalty function are ob- tained when the Lévy process is a Brownian motion with positive drift and a compound Poisson process, respectively. Some analytical examples and numerical examples are given to illustrate the upper bounds and the applications of the integro-differential equations in this paper.
Fundamentals of Stochastic Networks
Ibe, Oliver C
2011-01-01
An interdisciplinary approach to understanding queueing and graphical networks In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physi
Fluctuations as stochastic deformation
Kazinski, P. O.
2008-04-01
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Stochastic problems in population genetics
Maruyama, Takeo
1977-01-01
These are" notes based on courses in Theoretical Population Genetics given at the University of Texas at Houston during the winter quarter, 1974, and at the University of Wisconsin during the fall semester, 1976. These notes explore problems of population genetics and evolution involving stochastic processes. Biological models and various mathematical techniques are discussed. Special emphasis is given to the diffusion method and an attempt is made to emphasize the underlying unity of various problems based on the Kolmogorov backward equation. A particular effort was made to make the subject accessible to biology students who are not familiar with stochastic processes. The references are not exhaustive but were chosen to provide a starting point for the reader interested in pursuing the subject further. Acknowledgement I would like to use this opportunity to express my thanks to Drs. J. F. Crow, M. Nei and W. J. Schull for their hospitality during my stays at their universities. I am indebted to Dr. M. Kimura...
Stochastic longshore current dynamics
Restrepo, Juan M.; Venkataramani, Shankar
2016-12-01
We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.
Master-equation approach to stochastic neurodynamics
Ohira, Toru; Cowan, Jack D.
1993-09-01
A master-equation approach to the stochastic neurodynamics proposed by Cowan [in Advances in Neural Information Processing Systems 3, edited by R. P. Lippman, J. E. Moody, and D. S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p. 62] is investigated in this paper. We deal with a model neural network that is composed of two-state neurons obeying elementary stochastic transition rates. We show that such an approach yields concise expressions for multipoint moments and an equation of motion. We apply the formalism to a (1+1)-dimensional system. Exact and approximate expressions for various statistical parameters are obtained and compared with Monte Carlo simulations.
A Stochastic Employment Problem
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Stochastic Convection Parameterizations
Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios
2012-01-01
computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts
Instantaneous stochastic perturbation theory
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Verhoosel, C.V.; Gutiérrez, M.A.; Hulshoff, S.J.
2006-01-01
The field of fluid-structure interaction is combined with the field of stochastics to perform a stochastic flutter analysis. Various methods to directly incorporate the effects of uncertainties in the flutter analysis are investigated. The panel problem with a supersonic fluid flowing over it is con
Greenwood, Priscilla E
2016-01-01
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...
Stochastic volatility selected readings
Shephard, Neil
2005-01-01
Neil Shephard has brought together a set of classic and central papers that have contributed to our understanding of financial volatility. They cover stocks, bonds and currencies and range from 1973 up to 2001. Shephard, a leading researcher in the field, provides a substantial introduction in which he discusses all major issues involved. General Introduction N. Shephard. Part I: Model Building. 1. A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices, (P. K. Clark). 2. Financial Returns Modelled by the Product of Two Stochastic Processes: A Study of Daily Sugar Prices, 1961-7, S. J. Taylor. 3. The Behavior of Random Variables with Nonstationary Variance and the Distribution of Security Prices, B. Rosenberg. 4. The Pricing of Options on Assets with Stochastic Volatilities, J. Hull and A. White. 5. The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model, F. X. Diebold and M. Nerlove. 6. Multivariate Stochastic Variance Models. 7. Stochastic Autoregressive...
Information Anatomy of Stochastic Equilibria
Directory of Open Access Journals (Sweden)
Sarah Marzen
2014-08-01
Full Text Available A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some—the ephemeral information—is dissipated and some—the bound information—is actively stored and so affects future behavior. We derive analytic expressions for the ephemeral and bound information in the limit of infinitesimal time discretization for two classical systems that exhibit dynamical equilibria: first-order Langevin equations (i where the drift is the gradient of an analytic potential function and the diffusion matrix is invertible and (ii with a linear drift term (Ornstein–Uhlenbeck, but a noninvertible diffusion matrix. In both cases, the bound information is sensitive to the drift and diffusion, while the ephemeral information is sensitive only to the diffusion matrix and not to the drift. Notably, this information anatomy changes discontinuously as any of the diffusion coefficients vanishes, indicating that it is very sensitive to the noise structure. We then calculate the information anatomy of the stochastic cusp catastrophe and of particles diffusing in a heat bath in the overdamped limit, both examples of stochastic gradient descent on a potential landscape. Finally, we use our methods to calculate and compare approximations for the time-local predictive information for adaptive agents.
Stochastic Calculus of Wrapped Compartments
Coppo, Mario; Drocco, Maurizio; Grassi, Elena; Troina, Angelo; 10.4204/EPTCS.28.6
2010-01-01
The Calculus of Wrapped Compartments (CWC) is a variant of the Calculus of Looping Sequences (CLS). While keeping the same expressiveness, CWC strongly simplifies the development of automatic tools for the analysis of biological systems. The main simplification consists in the removal of the sequencing operator, thus lightening the formal treatment of the patterns to be matched in a term (whose complexity in CLS is strongly affected by the variables matching in the sequences). We define a stochastic semantics for this new calculus. As an application we model the interaction between macrophages and apoptotic neutrophils and a mechanism of gene regulation in E.Coli.
Sequential stochastic optimization
Cairoli, Renzo
1996-01-01
Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet
Kraenkel, R. A.; da Silva, D. J. Pamplona
2010-01-01
We consider the dynamics of a biological population described by the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the case where the spatial domain consists of alternating favorable and adverse patches whose sizes are distributed randomly. For the one-dimensional case we define a stochastic analogue of the classical critical patch size. We address the issue of persistence of a population and we show that the minimum fraction of the length of favorable segments to the total length is always smaller in the stochastic case than in a periodic arrangement. In this sense, spatial stochasticity favors viability of a population.
Fundamentals of Stochastic Filtering
Crisan, Dan
2008-01-01
The objective of stochastic filtering is to determine the best estimate for the state of a stochastic dynamical system from partial observations. The solution of this problem in the linear case is the well known Kalman-Bucy filter which has found widespread practical application. The purpose of this book is to provide a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient
Overwinding in a stochastic model of an extended polymer
Energy Technology Data Exchange (ETDEWEB)
Bernido, Christopher C. [Research Center for Theoretical Physics, Central Visayan Institute Foundation, Jagna, Bohol 6308 (Philippines)], E-mail: cbernido@mozcom.com; Carpio-Bernido, M. Victoria [Research Center for Theoretical Physics, Central Visayan Institute Foundation, Jagna, Bohol 6308 (Philippines)
2007-09-10
We evaluate explicit expressions of length-dependent winding configuration probabilities for a biopolymer. The stochastic model incorporates several experimentally observed features. In particular, it exhibits overwinding under stretching forces until a critical length of the polymer is reached.
Stochastic differential equations and applications
Friedman, Avner
2006-01-01
This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es
Doberkat, Ernst-Erich
2009-01-01
Combining coalgebraic reasoning, stochastic systems and logic, this volume presents the principles of coalgebraic logic from a categorical perspective. Modal logics are also discussed, including probabilistic interpretations and an analysis of Kripke models.
Stochastic calculus with infinitesimals
Herzberg, Frederik
2013-01-01
Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
Stochastic processes inference theory
Rao, Malempati M
2014-01-01
This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
Notes on the Stochastic Exponential and Logarithm
Larsson, Martin; Ruf, Johannes
2017-01-01
Stochastic exponentials are defined for semimartingales on stochastic intervals, and stochastic logarithms are defined for nonnegative semimartingales, up to the first time the semimartingale hits zero continuously. In the case of (nonnegative) local supermartingales, these two stochastic transformations are inverse to each other. The reciprocal of a stochastic exponential is again a stochastic exponential on a stochastic interval.
Geometric Stochastic Resonance
Ghosh, Pulak Kumar; Savel'ev, Sergey E; Nori, Franco
2015-01-01
A Brownian particle moving across a porous membrane subject to an oscillating force exhibits stochastic resonance with properties which strongly depend on the geometry of the confining cavities on the two sides of the membrane. Such a manifestation of stochastic resonance requires neither energetic nor entropic barriers, and can thus be regarded as a purely geometric effect. The magnitude of this effect is sensitive to the geometry of both the cavities and the pores, thus leading to distinctive optimal synchronization conditions.
Stochastic resonance in an intracellular genetic perceptron
Bates, Russell; Blyuss, Oleg; Zaikin, Alexey
2014-03-01
Intracellular genetic networks are more intelligent than was first assumed due to their ability to learn. One of the manifestations of this intelligence is the ability to learn associations of two stimuli within gene-regulating circuitry: Hebbian-type learning within the cellular life. However, gene expression is an intrinsically noisy process; hence, we investigate the effect of intrinsic and extrinsic noise on this kind of intracellular intelligence. We report a stochastic resonance in an intracellular associative genetic perceptron, a noise-induced phenomenon, which manifests itself in noise-induced increase of response in efficiency after the learning event under the conditions of optimal stochasticity.
Stochasticity in cell biology: Modeling across levels
Pedraza, Juan Manuel
2009-03-01
Effective modeling of biological processes requires focusing on a particular level of description, and this requires summarizing de details of lower levels into effective variables and properly accounting for the constrains that other levels impose. In the context of stochasticity in gene expression, I will show how the details of the stochastic process can be characterized by a few effective parameters, which facilitates modeling but complicates interpretation of current experiments. I will show how the resulting noise can provide advantageous or deleterious phenotypic fluctuation and how noise control in the copy number control system of plasmids can change the selective pressures. This system illustrates the direct connection between molecular dynamics and evolutionary dynamics.
Stochastic noise in splicing machinery.
Melamud, Eugene; Moult, John
2009-08-01
The number of known alternative human isoforms has been increasing steadily with the amount of available transcription data. To date, over 100 000 isoforms have been detected in EST libraries, and at least 75% of human genes have at least one alternative isoform. In this paper, we propose that most alternative splicing events are the result of noise in the splicing process. We show that the number of isoforms and their abundance can be predicted by a simple stochastic noise model that takes into account two factors: the number of introns in a gene and the expression level of a gene. The results strongly support the hypothesis that most alternative splicing is a consequence of stochastic noise in the splicing machinery, and has no functional significance. The results are also consistent with error rates tuned to ensure that an adequate level of functional product is produced and to reduce the toxic effect of accumulation of misfolding proteins. Based on simulation of sampling of virtual cDNA libraries, we estimate that error rates range from 1 to 10% depending on the number of introns and the expression level of a gene.
Institute of Scientific and Technical Information of China (English)
明锋; 杨元喜; 曾安敏
2015-01-01
The co-variance matrix of chosen noise model is required when using maximum likelihood estimation to analysis the station’s coordinate time series.The power law noise model is one of colored noise with different stochastic processes ran-ging from white to random walk,including flicker and fractional noise.However,in current research,the specific procedure to generate co-variance matrix of power law noise is often not prescribed in sufficient detail.In this paper,an analytical expres-sion is proposed for creating stochastic model of power law noise based on fractional differencing theory in time domain.With this expression,the element of co-variance matrix can be calculated in a recursive algorithm if the power law noise process is stationary.This analytical expression would be of help for investigating the characteristic of the noise process or for the simula-ting the desired colored noise.%利用最大似然估计法分析测站坐标时间序列时，需根据时间序列的噪声特性构造相应的协方差阵。由于幂律噪声除包含白噪声，闪烁噪声和随机漫步噪声等谱指数为整数的噪声外，还包含谱指数为实数的噪声，且其统计特性各不相同。除白噪声和随机漫步噪声外，已有研究并没有详细给出其它幂律噪声随机模型的构造方法。本文针对有色噪声中幂律噪声类型的时间相关特性，基于分数阶差分的理论和性质，详细给出了时间域上平稳和非平稳幂律噪声的随机模型的解析表达式，并给出了相应元素之间的递推关系。该解析表达式对于研究幂律噪声时间相关性或模拟相应特征的有色噪声有一定的参考价值。
StochPy: a comprehensive, user-friendly tool for simulating stochastic biological processes.
Directory of Open Access Journals (Sweden)
Timo R Maarleveld
Full Text Available Single-cell and single-molecule measurements indicate the importance of stochastic phenomena in cell biology. Stochasticity creates spontaneous differences in the copy numbers of key macromolecules and the timing of reaction events between genetically-identical cells. Mathematical models are indispensable for the study of phenotypic stochasticity in cellular decision-making and cell survival. There is a demand for versatile, stochastic modeling environments with extensive, preprogrammed statistics functions and plotting capabilities that hide the mathematics from the novice users and offers low-level programming access to the experienced user. Here we present StochPy (Stochastic modeling in Python, which is a flexible software tool for stochastic simulation in cell biology. It provides various stochastic simulation algorithms, SBML support, analyses of the probability distributions of molecule copy numbers and event waiting times, analyses of stochastic time series, and a range of additional statistical functions and plotting facilities for stochastic simulations. We illustrate the functionality of StochPy with stochastic models of gene expression, cell division, and single-molecule enzyme kinetics. StochPy has been successfully tested against the SBML stochastic test suite, passing all tests. StochPy is a comprehensive software package for stochastic simulation of the molecular control networks of living cells. It allows novice and experienced users to study stochastic phenomena in cell biology. The integration with other Python software makes StochPy both a user-friendly and easily extendible simulation tool.
Stochastic Samples versus Vacuum Expectation Values in Cosmology
Tsamis, N C; Woodard, R P
2010-01-01
Particle theorists typically use expectation values to study the quantum back-reaction on inflation, whereas many cosmologists stress the stochastic nature of the process. While expectation values certainly give misleading results for some things, such as the stress tensor, we argue that operators exist for which there is no essential problem. We quantify this by examining the stochastic properties of a noninteracting, massless, minimally coupled scalar on a locally de Sitter background. The square of the stochastic realization of this field seems to provide an example of great relevance for which expectation values are not misleading. We also examine the frequently expressed concern that significant back-reaction from expectation values necessarily implies large stochastic fluctuations between nearby spatial points. Rather than viewing the stochastic formalism in opposition to expectation values, we argue that it provides a marvelously simple way of capturing the leading infrared logarithm corrections to the...
Quantum Spontaneous Stochasticity
Eyink, Gregory L
2015-01-01
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions for given initial data are unique. In fluid turbulence non-uniqueness due to "roughness" of the advecting velocity field is known to lead to stochastic motion of classical particles. Vanishingly small random perturbations are magnified by Richardson diffusion in a "nearly rough" velocity field so that motion remains stochastic as the noise disappears, or classical spontaneous stochasticity, . Analogies between stochastic particle motion in turbulence and quantum evolution suggest that there should be quantum spontaneous stochasticity (QSS). We show this for 1D models of a particle in a repulsive potential that is "nearly rough" with $V(x) \\sim C|x|^{1+\\alpha}$ at distances $|x|\\gg \\ell$ , for some UV cut-off $\\ell$, and for initial Gaussian wave-packet centered at 0. We consi...
Stochastic optimization methods
Marti, Kurt
2005-01-01
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.
Stochastic dynamics and irreversibility
Tomé, Tânia
2015-01-01
This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
STOCHASTIC COOLING FOR BUNCHED BEAMS.
Energy Technology Data Exchange (ETDEWEB)
BLASKIEWICZ, M.
2005-05-16
Problems associated with bunched beam stochastic cooling are reviewed. A longitudinal stochastic cooling system for RHIC is under construction and has been partially commissioned. The state of the system and future plans are discussed.
Stochastic dynamics and control
Sun, Jian-Qiao; Zaslavsky, George
2006-01-01
This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress proc
Foundations of stochastic analysis
Rao, M M; Lukacs, E
1981-01-01
Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and mea
Stochastic Electrochemical Kinetics
Beruski, O
2016-01-01
A model enabling the extension of the Stochastic Simulation Algorithm to electrochemical systems is proposed. The physical justifications and constraints for the derivation of a chemical master equation are provided and discussed. The electrochemical driving forces are included in the mathematical framework, and equations are provided for the associated electric responses. The implementation for potentiostatic and galvanostatic systems is presented, with results pointing out the stochastic nature of the algorithm. The electric responses presented are in line with the expected results from the theory, providing a new tool for the modeling of electrochemical kinetics.
Markov stochasticity coordinates
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method-termed Markov Stochasticity Coordinates-is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Markov stochasticity coordinates
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: iddo.eliazar@intel.com
2017-01-15
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Stochastic Gravity: Theory and Applications
Directory of Open Access Journals (Sweden)
Hu Bei Lok
2004-01-01
Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction
Stochastic integrals: a combinatorial approach
Rota, Gian-Carlo; Wallstrom, Timothy C.
1997-01-01
A combinatorial definition of multiple stochastic integrals is given in the setting of random measures. It is shown that some properties of such stochastic integrals, formerly known to hold in special cases, are instances of combinatorial identities on the lattice of partitions of a set. The notion of stochastic sequences of binomial type is introduced as a generalization of special polynomial sequences occuring in stochastic integration, such as Hermite, Poisson–Charlier an...
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Stochastic integral equations without probability
Mikosch, T; Norvaisa, R
2000-01-01
A pathwise approach to stochastic integral equations is advocated. Linear extended Riemann-Stieltjes integral equations driven by certain stochastic processes are solved. Boundedness of the p-variation for some 0
stochastic process. Typical examples of such
Analysis of bilinear stochastic systems
Willsky, A. S.; Martin, D. N.; Marcus, S. I.
1975-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes. After defining the systems of interest, consideration is given to the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
Factors influencing lysis time stochasticity in bacteriophage λ
Directory of Open Access Journals (Sweden)
Dennehy John J
2011-08-01
Full Text Available Abstract Background Despite identical genotypes and seemingly uniform environments, stochastic gene expression and other dynamic intracellular processes can produce considerable phenotypic diversity within clonal microbes. One trait that provides a good model to explore the molecular basis of stochastic variation is the timing of host lysis by bacteriophage (phage. Results Individual lysis events of thermally-inducible λ lysogens were observed using a temperature-controlled perfusion chamber mounted on an inverted microscope. Both mean lysis time (MLT and its associated standard deviation (SD were estimated. Using the SD as a measure of lysis time stochasticity, we showed that lysogenic cells in controlled environments varied widely in lysis times, and that the level of lysis time stochasticity depended on allelic variation in the holin sequence, late promoter (pR' activity, and host growth rate. In general, the MLT was positively correlated with the SD. Both lower pR' activities and lower host growth rates resulted in larger SDs. Results from premature lysis, induced by adding KCN at different time points after lysogen induction, showed a negative correlation between the timing of KCN addition and lysis time stochasticity. Conclusions Taken together with results published by others, we conclude that a large fraction of λ lysis time stochasticity is the result of random events following the expression and diffusion of the holin protein. Consequently, factors influencing the timing of reaching critical holin concentrations in the cell membrane, such as holin production rate, strongly influence the mean lysis time and the lysis time stochasticity.
The stochastic quality calculus
DEFF Research Database (Denmark)
Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis
2014-01-01
We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated...
Stochastic Control - External Models
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
2005-01-01
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...
D.F. Schrager
2006-01-01
We propose a new model for stochastic mortality. The model is based on the literature on affine term structure models. It satisfies three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with financial option pricing m
Wheeler, Tim Allan; Holder, Martin; Winner, Hermann; Kochenderfer, Mykel
2017-01-01
Accurate simulation and validation of advanced driver assistance systems requires accurate sensor models. Modeling automotive radar is complicated by effects such as multipath reflections, interference, reflective surfaces, discrete cells, and attenuation. Detailed radar simulations based on physical principles exist but are computationally intractable for realistic automotive scenes. This paper describes a methodology for the construction of stochastic automotive radar models based on deep l...
Energy Technology Data Exchange (ETDEWEB)
Tollestrup, A.V.; Dugan, G
1983-12-01
Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)
Multistage quadratic stochastic programming
Lau, Karen K.; Womersley, Robert S.
2001-04-01
Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.
Stochasticity or the fatal `imperfection' of cloning
Indian Academy of Sciences (India)
Reiner A Veitia
2005-02-01
The concept of clone is analysed with the aim of exploring the limits to which a phenotype can be said to be determined geneticaly. First of all, mutations that result from the replication, topological manipulation or lesion of DNA introduce a source of heritable variation in an otherwise identical genetic background. But more important, stochastic effects in many biological processes may superimpose a phenotypic variation which is not encoded in the genome. The source of stochasticity ranges from the random selection of alleles or whole chromosomes to be expressed in small cell populations, to fluctuations in processes such as gene expression, due to limiting amounts of the players involved. The picture emerging is that the term clone is a statistical over-simplification representing a series of individuals having essentially the same genome but capable of exhibiting wide phenotypic variation. Finally, to what extent fluctuations in biological processes, usually thought of as noise, are in fact signal is also discussed.
Stochastic Simulation of Process Calculi for Biology
Phillips, Andrew; Paulevé, Loïc; 10.4204/EPTCS.40.1
2010-01-01
Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed, many of which are expressive enough to generate unbounded numbers of molecular species and reactions. As a result of this expressiveness, such calculi cannot rely on standard reaction-based simulation methods, which require fixed numbers of species and reactions. Rather than implementing custom stochastic simulation algorithms for each process calculus, we propose to use a generic abstract machine that can be instantiated to a range of process calculi and a range of reaction-based simulation algorithms. The abstract machine functions as a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. In this short paper we give a brief summary of the generic abstract machine, and show how it can be instant...
Limits for Stochastic Reaction Networks
DEFF Research Database (Denmark)
Cappelletti, Daniele
at a certain time are stochastically modelled by means of a continuous-time Markov chain. Our work concerns primarily stochastic reaction systems, and their asymptotic properties. In Paper I, we consider a reaction system with intermediate species, i.e. species that are produced and fast degraded along a path...... of the stochastic reaction systems. Specically, we build a theory for stochastic reaction systems that is parallel to the deciency zero theory for deterministic systems, which dates back to the 70s. A deciency theory for stochastic reaction systems was missing, and few results connecting deciency and stochastic....... Such species, in the deterministic modelling regime, assume always the same value at any positive steady state. In the stochastic setting, we prove that, if the initial condition is a point in the basin of attraction of a positive steady state of the corresponding deterministic model and tends to innity...
Stochastic processes in cell biology
Bressloff, Paul C
2014-01-01
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily...
Stochastic population growth in spatially heterogeneous environments.
Evans, Steven N; Ralph, Peter L; Schreiber, Sebastian J; Sen, Arnab
2013-02-01
stochastic growth rate, we derive an explicit expression for the stochastic growth rate for populations living in two patches, determine which choices of the dispersal matrix D produce the maximal stochastic growth rate for a freely dispersing population, derive an analytic approximation of the stochastic growth rate for dispersal limited populations, and use group theoretic techniques to approximate the stochastic growth rate for populations living in multi-scale landscapes (e.g. insects on plants in meadows on islands). Our results provide fundamental insights into "ideal free" movement in the face of uncertainty, the persistence of coupled sink populations, the evolution of dispersal rates, and the single large or several small (SLOSS) debate in conservation biology. For example, our analysis implies that even in the absence of density-dependent feedbacks, ideal-free dispersers occupy multiple patches in spatially heterogeneous environments provided environmental fluctuations are sufficiently strong and sufficiently weakly correlated across space. In contrast, for diffusively dispersing populations living in similar environments, intermediate dispersal rates maximize their stochastic growth rate.
Dynamic stochastic optimization
Ermoliev, Yuri; Pflug, Georg
2004-01-01
Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective an...
Directory of Open Access Journals (Sweden)
William Margulies
2004-11-01
Full Text Available In this paper, we study a specific stochastic differential equation depending on a parameter and obtain a representation of its probability density function in terms of Jacobi Functions. The equation arose in a control problem with a quadratic performance criteria. The quadratic performance is used to eliminate the control in the standard Hamilton-Jacobi variational technique. The resulting stochastic differential equation has a noise amplitude which complicates the solution. We then solve Kolmogorov's partial differential equation for the probability density function by using Jacobi Functions. A particular value of the parameter makes the solution a Martingale and in this case we prove that the solution goes to zero almost surely as time tends to infinity.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Multistage stochastic optimization
Pflug, Georg Ch
2014-01-01
Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book
Samuelson, Paul A.
1971-01-01
Because a commodity like wheat can be carried forward from one period to the next, speculative arbitrage serves to link its prices at different points of time. Since, however, the size of the harvest depends on complicated probability processes impossible to forecast with certainty, the minimal model for understanding market behavior must involve stochastic processes. The present study, on the basis of the axiom that it is the expected rather than the known-for-certain prices which enter into all arbitrage relations and carryover decisions, determines the behavior of price as the solution to a stochastic-dynamic-programming problem. The resulting stationary time series possesses an ergodic state and normative properties like those often observed for real-world bourses. PMID:16591903
Essentials of stochastic processes
Durrett, Richard
2016-01-01
Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...
Stochastic calculus and applications
Cohen, Samuel N
2015-01-01
Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to wo...
Stochastic gravitoelectromagnetic inflation
Aguilar, J E M; Bellini, Mauricio
2006-01-01
Gravitoelectromagnetic inflation was recently introduced to describe, in an unified manner, electromagnetic, gravitatory and inflaton fields in the early (accelerated) inflationary universe from a 5D vacuum state. In this paper, we study a stochastic treatment for the gravitoelectromagnetic components $A_B=(A_{\\mu},\\phi)$, on cosmological scales. We focus our study on the seed magnetic fields on super Hubble scales, which could play an important role in large scale structure formation of the universe.
Holmes-Cerfon, Miranda
2016-11-01
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.
Identifiability in stochastic models
1992-01-01
The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.
Stochastic Thermodynamics of Learning
Goldt, Sebastian; Seifert, Udo
2017-01-01
Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency η ≤1 . We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.
Stochastic Games. I. Foundations,
1982-04-01
stimulate discussion and critical coment. Requests for single copies of a Paper will be filled by the Cowles Foundation within the limits of the supply...underpinning for the theory of stochastic games. Section 2 is a reworking of the Bevley- Kohlberg result integrated with Shapley’s; the "black magic" of... Kohlberg : The values of the r-discount game, and the stationary optimal strategies, have Puiseaux expansions. L.. 11" 6 3. More generally, consider an
Stochastic gravitoelectromagnetic inflation
Madriz Aguilar, José Edgar; Bellini, Mauricio
2006-11-01
Gravitoelectromagnetic inflation was recently introduced to describe, in an unified manner, electromagnetic, gravitatory and inflaton fields in the early (accelerated) inflationary universe from a 5D vacuum state. In this Letter, we study a stochastic treatment for the gravitoelectromagnetic components A=(A,φ), on cosmological scales. We focus our study on the seed magnetic fields on super-Hubble scales, which could play an important role in large scale structure formation of the universe.
Stochastic power system operation
Power, Michael
2010-01-01
This paper outlines how to economically and reliably operate a power system with high levels of renewable generation which are stochastic in nature. It outlines the challenges for system operators, and suggests tools and methods for meeting this challenge, which is one of the most fundamental since large scale power networks were instituted. The Ireland power system, due to its nature and level of renewable generation, is considered as an example in this paper.
Stochastic Thermodynamics of Learning
Goldt, Sebastian
2016-01-01
Virtually every organism gathers information about its noisy environment and builds models from that data, mostly using neural networks. Here, we use stochastic thermodynamics to analyse the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency $\\eta\\le1$. We discuss the conditions for optimal learning and analyse Hebbian learning in the thermodynamic limit.
Stochastic Nonlinear Aeroelasticity
2009-01-01
STOCHASTIC NONLINEAR AEROELASTICITY 5a. CONTRACT NUMBER In- house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0601102 6. AUTHOR(S) Philip S...ABSTRACT This report documents the culmination of in- house work in the area of uncertainty quantification and probabilistic techniques for... coff U∞ cs ea lw cw Figure 6: Wing and store geometry (left), wing box structural model (middle), flutter distribution (right
Stochasticity Modeling in Memristors
Naous, Rawan
2015-10-26
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Simulation of Stochastic Partial Differential Equations and Stochastic Active Contours
Lang, Annika
2007-01-01
This thesis discusses several aspects of the simulation of stochastic partial differential equations. First, two fast algorithms for the approximation of infinite dimensional Gaussian random fields with given covariance are introduced. Later Hilbert space-valued Wiener processes are constructed out of these random fields. A short introduction to infinite-dimensional stochastic analysis and stochastic differential equations is given. Furthermore different definitions of numerical stability for...
The effect of stochasticity on the lac operon: an evolutionary perspective.
Directory of Open Access Journals (Sweden)
Milan van Hoek
2007-06-01
Full Text Available The role of stochasticity on gene expression is widely discussed. Both potential advantages and disadvantages have been revealed. In some systems, noise in gene expression has been quantified, in among others the lac operon of Escherichia coli. Whether stochastic gene expression in this system is detrimental or beneficial for the cells is, however, still unclear. We are interested in the effects of stochasticity from an evolutionary point of view. We study this question in the lac operon, taking a computational approach: using a detailed, quantitative, spatial model, we evolve through a mutation-selection process the shape of the promoter function and therewith the effective amount of stochasticity. We find that noise values for lactose, the natural inducer, are much lower than for artificial, nonmetabolizable inducers, because these artificial inducers experience a stronger positive feedback. In the evolved promoter functions, noise due to stochasticity in gene expression, when induced by lactose, only plays a very minor role in short-term physiological adaptation, because other sources of population heterogeneity dominate. Finally, promoter functions evolved in the stochastic model evolve to higher repressed transcription rates than those evolved in a deterministic version of the model. This causes these promoter functions to experience less stochasticity in gene expression. We show that a high repression rate and hence high stochasticity increases the delay in lactose uptake in a variable environment. We conclude that the lac operon evolved such that the impact of stochastic gene expression is minor in its natural environment, but happens to respond with much stronger stochasticity when confronted with artificial inducers. In this particular system, we have shown that stochasticity is detrimental. Moreover, we demonstrate that in silico evolution in a quantitative model, by mutating the parameters of interest, is a promising way to unravel
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
2012-01-01
The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the...
Stochastic Simulation of Process Calculi for Biology
Directory of Open Access Journals (Sweden)
Andrew Phillips
2010-10-01
Full Text Available Biological systems typically involve large numbers of components with complex, highly parallel interactions and intrinsic stochasticity. To model this complexity, numerous programming languages based on process calculi have been developed, many of which are expressive enough to generate unbounded numbers of molecular species and reactions. As a result of this expressiveness, such calculi cannot rely on standard reaction-based simulation methods, which require fixed numbers of species and reactions. Rather than implementing custom stochastic simulation algorithms for each process calculus, we propose to use a generic abstract machine that can be instantiated to a range of process calculi and a range of reaction-based simulation algorithms. The abstract machine functions as a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. In this short paper we give a brief summary of the generic abstract machine, and show how it can be instantiated with the stochastic simulation algorithm known as Gillespie's Direct Method. We also discuss the wider implications of such an abstract machine, and outline how it can be used to simulate multiple calculi simultaneously within a common framework.
Some stochastic aspects of quantization
Indian Academy of Sciences (India)
Ichiro Ohba
2002-08-01
From the advent of quantum mechanics, various types of stochastic-dynamical approach to quantum mechanics have been tried. We discuss how to utilize Nelson’s stochastic quantum mechanics to analyze the tunneling phenomena, how to derive relativistic ﬁeld equations via the Poisson process and how to describe a quantum dynamics of open systems by the use of quantum state diffusion, or the stochastic Schrödinger equation.
Stochastic Analysis of Cylindrical Shell
Directory of Open Access Journals (Sweden)
Grzywiński Maksym
2014-06-01
Full Text Available The paper deals with some chosen aspects of stochastic structural analysis and its application in the engineering practice. The main aim of the study is to apply the generalized stochastic perturbation techniques based on classical Taylor expansion with a single random variable for solution of stochastic problems in structural mechanics. The study is illustrated by numerical results concerning an industrial thin shell structure modeled as a 3-D structure.
Verification of Stochastic Process Calculi
DEFF Research Database (Denmark)
Skrypnyuk, Nataliya
Stochastic process calculi represent widely accepted formalisms within Computer Science for modelling nondeterministic stochastic systems in a compositional way. Similar to process calculi in general, they are suited for modelling systems in a hierarchical manner, by explicitly specifying...... subsystems as well as their interdependences and communication channels. Stochastic process calculi incorporate both the quantified uncertainty on probabilities or durations of events and nondeterministic choices between several possible continuations of the system behaviour. Modelling of a system is often...
A recurrent stochastic binary network
Institute of Scientific and Technical Information of China (English)
赵杰煜
2001-01-01
Stochastic neural networks are usually built by introducing random fluctuations into the network. A natural method is to use stochastic connections rather than stochastic activation functions. We propose a new model in which each neuron has very simple functionality but all the connections are stochastic. It is shown that the stationary distribution of the network uniquely exists and it is approximately a Boltzmann-Gibbs distribution. The relationship between the model and the Markov random field is discussed. New techniques to implement simulated annealing and Boltzmann learning are proposed. Simulation results on the graph bisection problem and image recognition show that the network is powerful enough to solve real world problems.
A Developmental Basis for Stochasticity in Floral Organ Numbers
Directory of Open Access Journals (Sweden)
Miho S Kitazawa
2014-11-01
Full Text Available Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers: Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 49 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ number variations could be an indicator of the inherent stochasticity in both the expression domain of homeotic genes and the organ positioning.
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Stochastic ontogenetic growth model
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
Deduction as Stochastic Simulation
2013-07-01
Eab Oa b Eab Ob a Iab Aab Iab Aba Iab Eab Iab EbaIab Iab Iab Iba Iab Oa b Iab Ob a Oa bAa b Oa bAb a Oa bEa b Oa bEb a Oa bIa b Oa bIb a Oa bO ab Oa bO...Oa bIa b Oa bIb a Oa bO ab Oa bO ba % C or re ct A. B. stochastic system’s parameters could be tweaked for individual reasoners. For example, the λ
Carpentier, Pierre; Cohen, Guy; De Lara, Michel
2015-01-01
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.
Stochastic Runge-Kutta Software Package for Stochastic Differential Equations
Gevorkyan, M N; Korolkova, A V; Kulyabov, D S; Sevastyanov, L A
2016-01-01
As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, was obtained. These are partial differential equations (master equation, the Fokker--Planck equation) and stochastic differential equations (Langevin equation). However, analytical methods do not always allow to research these equations adequately. It is proposed to use the combined analytical and numerical approach studying these equations. For this purpose the numerical part is realized within the framework of symbolic computation. It is recommended to apply stochastic Runge--Kutta methods for numerical study of stochastic differential equations in the form of the Langevin. Under this approach, a program complex on the basis of analytical calculations metasystem Sage is developed. For model verification logarithmic walks and Black--Scholes two-dimensional model are used. To illustrate the stochastic "predator--prey" type model is us...
Pluralistic and stochastic gene regulation: examples, models and consistent theory.
Salas, Elisa N; Shu, Jiang; Cserhati, Matyas F; Weeks, Donald P; Ladunga, Istvan
2016-06-01
We present a theory of pluralistic and stochastic gene regulation. To bridge the gap between empirical studies and mathematical models, we integrate pre-existing observations with our meta-analyses of the ENCODE ChIP-Seq experiments. Earlier evidence includes fluctuations in levels, location, activity, and binding of transcription factors, variable DNA motifs, and bursts in gene expression. Stochastic regulation is also indicated by frequently subdued effects of knockout mutants of regulators, their evolutionary losses/gains and massive rewiring of regulatory sites. We report wide-spread pluralistic regulation in ≈800 000 tightly co-expressed pairs of diverse human genes. Typically, half of ≈50 observed regulators bind to both genes reproducibly, twice more than in independently expressed gene pairs. We also examine the largest set of co-expressed genes, which code for cytoplasmic ribosomal proteins. Numerous regulatory complexes are highly significant enriched in ribosomal genes compared to highly expressed non-ribosomal genes. We could not find any DNA-associated, strict sense master regulator. Despite major fluctuations in transcription factor binding, our machine learning model accurately predicted transcript levels using binding sites of 20+ regulators. Our pluralistic and stochastic theory is consistent with partially random binding patterns, redundancy, stochastic regulator binding, burst-like expression, degeneracy of binding motifs and massive regulatory rewiring during evolution.
Mixed effects in stochastic differential equation models
DEFF Research Database (Denmark)
Ditlevsen, Susanne; De Gaetano, Andrea
2005-01-01
maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes......maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes...
Stochastic Pi-calculus Revisited
DEFF Research Database (Denmark)
Cardelli, Luca; Mardare, Radu Iulian
2013-01-01
We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...
Stochastic ferromagnetism analysis and numerics
Brzezniak, Zdzislaw; Neklyudov, Mikhail; Prohl, Andreas
2013-01-01
This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). Comparative computational studies with the stochastic model are included. Constructive tools such as e.g. finite element methods are used to derive the theoretical results, which are then used for computational studies.
Discretization error of Stochastic Integrals
Fukasawa, Masaaki
2010-01-01
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed.
Stochastic Pi-calculus Revisited
DEFF Research Database (Denmark)
Cardelli, Luca; Mardare, Radu Iulian
2013-01-01
We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...
Stochastic power flow modeling
Energy Technology Data Exchange (ETDEWEB)
1980-06-01
The stochastic nature of customer demand and equipment failure on large interconnected electric power networks has produced a keen interest in the accurate modeling and analysis of the effects of probabilistic behavior on steady state power system operation. The principle avenue of approach has been to obtain a solution to the steady state network flow equations which adhere both to Kirchhoff's Laws and probabilistic laws, using either combinatorial or functional approximation techniques. Clearly the need of the present is to develop sound techniques for producing meaningful data to serve as input. This research has addressed this end and serves to bridge the gap between electric demand modeling, equipment failure analysis, etc., and the area of algorithm development. Therefore, the scope of this work lies squarely on developing an efficient means of producing sensible input information in the form of probability distributions for the many types of solution algorithms that have been developed. Two major areas of development are described in detail: a decomposition of stochastic processes which gives hope of stationarity, ergodicity, and perhaps even normality; and a powerful surrogate probability approach using proportions of time which allows the calculation of joint events from one dimensional probability spaces.
Recursive Concurrent Stochastic Games
Etessami, Kousha
2008-01-01
We study Recursive Concurrent Stochastic Games (RCSGs), extending our recent analysis of recursive simple stochastic games [16,17] to a concurrent setting where the two players choose moves simultaneously and independently at each state. For multi-exit games, our earlier work already showed undecidability for basic questions like termination, thus we focus on the important case of single-exit RCSGs (1-RCSGs). We first characterize the value of a 1-RCSG termination game as the least fixed point solution of a system of nonlinear minimax functional equations, and use it to show PSPACE decidability for the quantitative termination problem. We then give a strategy improvement technique, which we use to show that player 1 (maximizer) has \\epsilon-optimal randomized Stackless & Memoryless (r-SM) strategies for all \\epsilon > 0, while player 2 (minimizer) has optimal r-SM strategies. Thus, such games are r-SM-determined. These results mirror and generalize in a strong sense the randomized memoryless determinacy r...
AA, stochastic precooling pickup
1980-01-01
The freshly injected antiprotons were subjected to fast stochastic "precooling". In this picture of a precooling pickup, the injection orbit is to the left, the stack orbit to the far right. After several seconds of precooling with the system's kickers (in momentum and in the vertical plane), the precooled antiprotons were transferred, by means of RF, to the stack tail, where they were subjected to further stochastic cooling in momentum and in both transverse planes, until they ended up, deeply cooled, in the stack core. During precooling, a shutter near the central orbit shielded the pickups from the signals emanating from the stack-core, whilst the stack-core was shielded from the violent action of the precooling kickers by a shutter on these. All shutters were opened briefly during transfer of the precooled antiprotons to the stack tail. Here, the shutter is not yet mounted. Precooling pickups and kickers had the same design, except that the kickers had cooling circuits and the pickups had none. Peering th...
Stochastic Blind Motion Deblurring
Xiao, Lei
2015-05-13
Blind motion deblurring from a single image is a highly under-constrained problem with many degenerate solutions. A good approximation of the intrinsic image can therefore only be obtained with the help of prior information in the form of (often non-convex) regularization terms for both the intrinsic image and the kernel. While the best choice of image priors is still a topic of ongoing investigation, this research is made more complicated by the fact that historically each new prior requires the development of a custom optimization method. In this paper, we develop a stochastic optimization method for blind deconvolution. Since this stochastic solver does not require the explicit computation of the gradient of the objective function and uses only efficient local evaluation of the objective, new priors can be implemented and tested very quickly. We demonstrate that this framework, in combination with different image priors produces results with PSNR values that match or exceed the results obtained by much more complex state-of-the-art blind motion deblurring algorithms.
Schilstra, Maria J; Martin, Stephen R
2009-01-01
Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.
Wang, Qingyun; Zhang, Honghui; Chen, Guanrong
2012-12-01
We study the effect of heterogeneous neuron and information transmission delay on stochastic resonance of scale-free neuronal networks. For this purpose, we introduce the heterogeneity to the specified neuron with the highest degree. It is shown that in the absence of delay, an intermediate noise level can optimally assist spike firings of collective neurons so as to achieve stochastic resonance on scale-free neuronal networks for small and intermediate αh, which plays a heterogeneous role. Maxima of stochastic resonance measure are enhanced as αh increases, which implies that the heterogeneity can improve stochastic resonance. However, as αh is beyond a certain large value, no obvious stochastic resonance can be observed. If the information transmission delay is introduced to neuronal networks, stochastic resonance is dramatically affected. In particular, the tuned information transmission delay can induce multiple stochastic resonance, which can be manifested as well-expressed maximum in the measure for stochastic resonance, appearing every multiple of one half of the subthreshold stimulus period. Furthermore, we can observe that stochastic resonance at odd multiple of one half of the subthreshold stimulus period is subharmonic, as opposed to the case of even multiple of one half of the subthreshold stimulus period. More interestingly, multiple stochastic resonance can also be improved by the suitable heterogeneous neuron. Presented results can provide good insights into the understanding of the heterogeneous neuron and information transmission delay on realistic neuronal networks.
Wang, Qingyun; Zhang, Honghui; Chen, Guanrong
2012-12-01
We study the effect of heterogeneous neuron and information transmission delay on stochastic resonance of scale-free neuronal networks. For this purpose, we introduce the heterogeneity to the specified neuron with the highest degree. It is shown that in the absence of delay, an intermediate noise level can optimally assist spike firings of collective neurons so as to achieve stochastic resonance on scale-free neuronal networks for small and intermediate α(h), which plays a heterogeneous role. Maxima of stochastic resonance measure are enhanced as α(h) increases, which implies that the heterogeneity can improve stochastic resonance. However, as α(h) is beyond a certain large value, no obvious stochastic resonance can be observed. If the information transmission delay is introduced to neuronal networks, stochastic resonance is dramatically affected. In particular, the tuned information transmission delay can induce multiple stochastic resonance, which can be manifested as well-expressed maximum in the measure for stochastic resonance, appearing every multiple of one half of the subthreshold stimulus period. Furthermore, we can observe that stochastic resonance at odd multiple of one half of the subthreshold stimulus period is subharmonic, as opposed to the case of even multiple of one half of the subthreshold stimulus period. More interestingly, multiple stochastic resonance can also be improved by the suitable heterogeneous neuron. Presented results can provide good insights into the understanding of the heterogeneous neuron and information transmission delay on realistic neuronal networks.
Variance decomposition in stochastic simulators
Le Maître, O. P.
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators.
Le Maître, O P; Knio, O M; Moraes, A
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-01
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Brownian motion and stochastic calculus
Karatzas, Ioannis
1998-01-01
This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...
Stochastic Engine Convergence Diagnostics
Energy Technology Data Exchange (ETDEWEB)
Glaser, R
2001-12-11
The stochastic engine uses a Markov Chain Monte Carlo (MCMC) sampling device to allow an analyst to construct a reasonable estimate of the state of nature that is consistent with observed data and modeling assumptions. The key engine output is a sample from the posterior distribution, which is the conditional probability distribution of the state of nature, given the data. In applications the state of nature may refer to a complicated, multi-attributed feature like the lithology map of a volume of earth, or to a particular related parameter of interest, say the centroid of the largest contiguous sub-region of specified lithology type. The posterior distribution, which we will call f, can be thought of as the best stochastic description of the state of nature that incorporates all pertinent physical and theoretical models as well as observed data. Characterization of the posterior distribution is the primary goal in the Bayesian statistical paradigm. In applications of the stochastic engine, however, analytical calculation of the posterior distribution is precluded, and only a sample drawn from the distribution is feasible. The engine's MCMC technique, which employs the Metropolis-Hastings algorithm, provides a sample in the form of a sequence (chain) of possible states of nature, x{sup (1)}, x{sup (2)}, ..., x{sup (T)}, .... The sequencing is motivated by consideration of comparative likelihoods of the data. Asymptotic results ensure that the sample ultimately spans the entire posterior distribution and reveals the actual state frequencies that characterize the posterior. In mathematical jargon, the sample is an ergodic Markov chain with stationary distribution f. What this means is that once the chain has gone a sufficient number of steps, T{sub 0}, the (unconditional) distribution of the state, x{sup (T)}, at any step T {ge} T{sub 0} is the same (i.e., is ''stationary''), and is the posterior distribution, f. We call T{sub 0} the &apos
Stochastic population theories
Ludwig, Donald
1974-01-01
These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974. In order to make the material. accessible to a wide audience, it is assumed that the reader has only a slight acquaintance with probability theory and differential equations. The more sophisticated topics, such as the qualitative behavior of nonlinear models, are approached through a succession of simpler problems. Emphasis is placed upon intuitive interpretations, rather than upon formal proofs. In most cases, the reader is referred elsewhere for a rigorous development. On the other hand, an attempt has been made to treat simple, useful models in some detail. Thus these notes complement the existing mathematical literature, and there appears to be little duplication of existing works. The authors are indebted to Miss Jeanette Figueroa for her beautiful and speedy typing of this work. The research was supported by the Na...
Crystallization by stochastic flips
Bodini, Olivier; Fernique, Thomas; Regnault, Damien
2010-04-01
Tilings are often used as a toy model for quasicrystals, with the ground states corresponding to the tilings satisfying some local properties (matching rules). In this context, a challenging problem is to provide a theory for quasicrystals growth. One of the proposed theories is the relaxation process. One assumes that the entropy of a tiling increases with the number of tilings which can be formed with the same tiles, while its energy is proportional to the ratio of satisfied matching rules. Then, by starting from an entropically stabilized tiling at high temperature and by decreasing the temperature, the phason flips which decrease (resp. increase) the energy would become more and more favoured (resp. inhibited). Ideally, the tiling eventually satisfies all the matching rules, and thus shows a quasicrystalline structure. This paper describes a stochastic process inspired by this and discusses its convergence rate.
Stochastic reconstruction of sandstones
Manwart; Torquato; Hilfer
2000-07-01
A simulated annealing algorithm is employed to generate a stochastic model for a Berea sandstone and a Fontainebleau sandstone, with each a prescribed two-point probability function, lineal-path function, and "pore size" distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandstones. Also, the mean survival time of a random walker in the pore space is reproduced with good accuracy. However, a more detailed investigation by means of local porosity theory shows that there may be significant differences of the geometrical connectivity between the reconstructed and the experimental samples.
Stochastic Cell Fate Progression in Embryonic Stem Cells
Zou, Ling-Nan; Doyle, Adele; Jang, Sumin; Ramanathan, Sharad
2013-03-01
Studies on the directed differentiation of embryonic stem (ES) cells suggest that some early developmental decisions may be stochastic in nature. To identify the sources of this stochasticity, we analyzed the heterogeneous expression of key transcription factors in single ES cells as they adopt distinct germ layer fates. We find that under sufficiently stringent signaling conditions, the choice of lineage is unambiguous. ES cells flow into differentiated fates via diverging paths, defined by sequences of transitional states that exhibit characteristic co-expression of multiple transcription factors. These transitional states have distinct responses to morphogenic stimuli; by sequential exposure to multiple signaling conditions, ES cells are steered towards specific fates. However, the rate at which cells travel down a developmental path is stochastic: cells exposed to the same signaling condition for the same amount of time can populate different states along the same path. The heterogeneity of cell states seen in our experiments therefore does not reflect the stochastic selection of germ layer fates, but the stochastic rate of progression along a chosen developmental path. Supported in part by the Jane Coffin Childs Fund
Scattering matrix theory for stochastic scalar fields.
Korotkova, Olga; Wolf, Emil
2007-05-01
We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a generalized scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation this matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer. Apart from determining the angular distribution of the spectral intensity of the scattered field, the scattering matrix makes it possible also to determine the changes in the state of coherence of the field produced on scattering.
Stochastic dynamic equations on general time scales
Directory of Open Access Journals (Sweden)
Martin Bohner
2013-02-01
Full Text Available In this article, we construct stochastic integral and stochastic differential equations on general time scales. We call these equations stochastic dynamic equations. We provide the existence and uniqueness theorem for solutions of stochastic dynamic equations. The crucial tool of our construction is a result about a connection between the time scales Lebesgue integral and the Lebesgue integral in the common sense.
Overview of Stochastic Vehicle Routing Problems
Institute of Scientific and Technical Information of China (English)
郭耀煌; 谢秉磊; 郭强
2002-01-01
Stochastic vehicle routing problems (VRPs) play important roles in logistics, though they have not been studied systematically yet. The paper summaries the definition, properties and classification of stochastic VRPs, makes further discussion about two strategies in stochastic VRPs, and at last overviews dynamic and stochastic VRPs.
An introduction to probability and stochastic processes
Melsa, James L
2013-01-01
Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.
Frequency Resonance in Stochastic Systems
Institute of Scientific and Technical Information of China (English)
钱敏; 张雪娟
2003-01-01
The phenomenon of frequency resonance, which is usually related to deterministic systems, is investigated in stochastic systems. We show that for those autonomous systems driven only by white noise, if the output power spectrum exhibits a nonzero peak frequency, then applying a periodic signel just on this noise-induced central frequency can also induce a resonance phenomenon, which we call the frequency stochastic resonance. The effect of such a resonance in a coupled stochastic system is shown to be much better than that in a single-oscillator system.
Stochastic simulation in systems biology
Directory of Open Access Journals (Sweden)
Tamás Székely Jr.
2014-11-01
There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.
Introduction to stochastic dynamic programming
Ross, Sheldon M; Lukacs, E
1983-01-01
Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist-providing counterexamples where appropriate-and the
Uniqueness of stochastic entropy solutions for stochastic balance laws with Lipschitz fluxes
Wei, Jinlong; Liu, Bin
2014-01-01
In this paper, we consider a stochastic balance law with a Lipschitz flux and gain the uniqueness for stochastic entropy solutions. The argument is supported by the stochastic kinetic formulation, the It\\^{o} formula and the regularization techniques. Furthermore, as an application, we derive the uniqueness of stochastic entropy solutions for stochastic porous media type equations.
Optimal adaptive control for a class of stochastic systems
Bagchi, Arunabha; Chen, Han-Fu
1997-01-01
We study linear-quadratic adaptive tracking problems for a special class of stochastic systems expressed in the state-space form. This is a long-standing problem in the control of aircraft flying through atmospheric turbulence. Using an ELS-based algorithm and introducing dither in the control law w
Counting statistics of non-markovian quantum stochastic processes
DEFF Research Database (Denmark)
Flindt, Christian; Novotny, T.; Braggio, A.
2008-01-01
We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of t...
Solving stochastic multiobjective vehicle routing problem using probabilistic metaheuristic
Directory of Open Access Journals (Sweden)
Gannouni Asmae
2017-01-01
closed form expression. This novel approach is based on combinatorial probability and can be incorporated in a multiobjective evolutionary algorithm. (iiProvide probabilistic approaches to elitism and diversification in multiobjective evolutionary algorithms. Finally, The behavior of the resulting Probabilistic Multi-objective Evolutionary Algorithms (PrMOEAs is empirically investigated on the multi-objective stochastic VRP problem.
Nonlinear analysis of a structure loaded by a stochastic excitation
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
For a non-linear system excited by a stochastic load which is expressed as a time series, a recursive method based on the Z-transform is presented. To identify the obtained response time series, a discrete wavelet transform (DWT) technique is proposed.
Stochastic analysis of laminated composite plate considering stochastic homogenization problem
Institute of Scientific and Technical Information of China (English)
S. SAKATA; K. OKUDA; K. IKEDA
2015-01-01
This paper discusses a multiscale stochastic analysis of a laminated composite plate consisting of unidirectional fiber reinforced composite laminae. In particular, influence of a microscopic random variation of the elastic properties of component materials on mechanical properties of the laminated plate is investigated. Laminated composites are widely used in civil engineering, and therefore multiscale stochastic analysis of laminated composites should be performed for reliability evaluation of a composite civil structure. This study deals with the stochastic response of a laminated composite plate against the microscopic random variation in addition to a random variation of fiber orientation in each lamina, and stochastic properties of the mechanical responses of the laminated plate is investigated. Halpin-Tsai formula and the homogenization theory-based finite element analysis are employed for estimation of effective elastic properties of lamina, and the classical laminate theory is employed for analysis of a laminated plate. The Monte-Carlo simulation and the first-order second moment method with sensitivity analysis are employed for the stochastic analysis. From the numerical results, importance of the multiscale stochastic analysis for reliability evaluation of a laminated composite structure and applicability of the sensitivity-based approach are discussed.
A Note on Almost Stochastic Dominance
Guo, Xu; Zhu, Xuehu; Wong, Wing-Keung; Zhu, Lixing
2013-01-01
To satisfy the property of expected-utility maximization, Tzeng et al. (2012) modify the almost second-degree stochastic dominance proposed by Leshno and Levy (2002) and define almost higher-degree stochastic dominance. In this note, we further investigate the relevant properties. We define an almost third-degree stochastic dominance in the same way that Leshno and Levy (2002) define second-degree stochastic dominance and show that Leshno and Levy's (2002) almost stochastic dominance has t...
Computer Auxiliary Analysis for Stochasticity of Chaos
Institute of Scientific and Technical Information of China (English)
ZHAOGeng; FANGJin-qing
2003-01-01
In this work, we propose a mathematics-physical statistic analytical method for stochastic process of chaos, based on stochastic test via combination measurement of Monobit and Runs. Computer auxiliary analysis shows that it is of stochasticity for stochastic number produced from the chaotic circuit. Our software is written by VB and C++, the later can be tested by the former, and at the same time it is verified by stochastic number produced by the computer. So the data treatment results are reliable.
Stochastic Climate Theory and Modelling
Franzke, Christian L E; Berner, Judith; Williams, Paul D; Lucarini, Valerio
2014-01-01
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations as well as for model error representation, uncertainty quantification, data assimilation and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochast...
Stochastic Modelling of Hydrologic Systems
DEFF Research Database (Denmark)
Jonsdottir, Harpa
2007-01-01
In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains an introduct......In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains...... an introduction and an overview of the papers published. Then an introduction to basic concepts in hydrology along with a description of hydrological data is given. Finally an introduction to stochastic modelling is given. The second part contains the research papers. In the research papers the stochastic methods...
Detecting Stochastic Information of Electrocardiograms
Gutíerrez, R M; Guti'errez, Rafael M.; Sandoval, Luis A.
2003-01-01
In this work we present a method to detect, identify and characterize stochastic information contained in an electrocardiogram (ECG). We assume, as it is well known, that the ECG has information corresponding to many different processes related to the cardiac activity. We analyze scaling and Markov processes properties of the detected stochastic information using the power spectrum of the ECG and the Fokker-Planck equation respectively. The detected stochastic information is then characterized by three measures. First, the slope of the power spectrum in a particular range of frequencies as a scaling parameter. Second, an empirical estimation of the drift and diffusion coefficients of the Fokker-Planck equation through the Kramers-Moyal coefficients which define the evolution of the probability distribution of the detected stochastic information.
Stochastic Still Water Response Model
DEFF Research Database (Denmark)
Friis-Hansen, Peter; Ditlevsen, Ove Dalager
2002-01-01
In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...... the stochastic cargo container load field is based on a queuing and loading policy that assumes containers are handled by a first-come-first-serve policy. The load field is assumed to be Gaussian. The ballast system is imposed to counteract the angle of heel and to regulate both the draft and the trim caused...
Stochastic Integration in Abstract Spaces
Directory of Open Access Journals (Sweden)
J. K. Brooks
2010-01-01
-valued process (∫ called the stochastic integral. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.
Stochastic Analysis and Related Topics
Ustunel, Ali
1988-01-01
The Silvri Workshop was divided into a short summer school and a working conference, producing lectures and research papers on recent developments in stochastic analysis on Wiener space. The topics treated in the lectures relate to the Malliavin calculus, the Skorohod integral and nonlinear functionals of white noise. Most of the research papers are applications of these subjects. This volume addresses researchers and graduate students in stochastic processes and theoretical physics.
STochastic OPTimization library in C++
Gevret, Hugo; Lelong, Jerome; Warin, Xavier
2016-01-01
The STochastic OPTimization library (StOpt) aims at providing tools in C++ for solving somestochastic optimization problems encountered in finance or in the industry.A python binding is available for some C++ objects provided permitting to easily solve an optimization problem by regression.Different methods are available : dynamic programming methods based on Monte Carlo with regressions (global, local and sparse regressors), for underlying states following some uncontrolled Stochastic Differ...
Stochastic superparameterization in quasigeostrophic turbulence
Energy Technology Data Exchange (ETDEWEB)
Grooms, Ian, E-mail: grooms@cims.nyu.edu [Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Majda, Andrew J., E-mail: jonjon@cims.nyu.edu [Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Center for Prototype Climate Modelling, NYU-Abu Dhabi (United Arab Emirates)
2014-08-15
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional superparameterization simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic superparameterization replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on the embedded domains from the length of the time step used on the coarse grid, and sensitivity to certain assumed properties of the eddies (e.g. the shape of the assumed eddy energy spectrum). We present four closures based on stochastic superparameterization which elucidate the properties of the underlying framework: a ‘null hypothesis’ stochastic closure that uncouples the eddies from the mean, a stochastic closure with nonlinearly coupled eddies and mean, a nonlinear deterministic closure, and a stochastic closure based on energy conservation. The different algorithms are compared and contrasted on a stringent test suite for quasigeostrophic turbulence involving two-layer dynamics on a β-plane forced by an imposed background shear. The success of the algorithms developed here suggests that they may be fruitfully applied to more realistic situations. They are expected to be particularly useful in providing accurate and
Stochastic roots of growth phenomena
De Lauro, E.; De Martino, S.; De Siena, S.; Giorno, V.
2014-05-01
We show that the Gompertz equation describes the evolution in time of the median of a geometric stochastic process. Therefore, we induce that the process itself generates the growth. This result allows us further to exploit a stochastic variational principle to take account of self-regulation of growth through feedback of relative density variations. The conceptually well defined framework so introduced shows its usefulness by suggesting a form of control of growth by exploiting external actions.
Foliated stochastic calculus: Harmonic measures
Catuogno, Pedro J; Ruffino, Paulo R
2010-01-01
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on harmonic measures. Other results include a decomposition of the Laplacian in terms of the foliated and basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.
Stochastic Resonance in Linear Regime of a Single- Mode Laser
Institute of Scientific and Technical Information of China (English)
ZHANG Liang-Ying; CAO Li; WU Da-Jin; WANG Jun
2003-01-01
We present an analytic investigation of the signal-to-noise ratio by studying the linear model of a single-mode laser driven by coloured pump noise (TI) and coloured quantum noise (TZ) with coloured cross-correlation (TS), and obtain an exact analytic expression of the signal-to-noise ratio. We detect that the stochastic resonance occurs when the noise correlation coefficient A < 0. Furthermore, we analyse the effect of TI , T2 and Ta on the signal-to-noise ratio, and derive the condition under which the stochastic resonance occurs.
Phenomenology of stochastic exponential growth
Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya
2017-06-01
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
Steganalysis of stochastic modulation steganography
Institute of Scientific and Technical Information of China (English)
HE Junhui; HUANG Jiwu
2006-01-01
Stochastic modulation steganography embeds secret message within the cover image by adding stego-noise with a specific probabilistic distribution. No method is known to be applicable to the estimation of stochastic modulation steganography. By analyzing the distributions of the horizontal pixel difference of images before and after stochastic modulation embedding, we present a new steganalytic approach to accurately estimate the length of secret message in stochastic modulation steganography. The proposed method first establishes a model describing the statistical relationship among the differences of the cover image, stego-image and stego-noise. In the case of stego- image-only steganalysis, rough estimate of the distributional parameters of the cover image's pixel difference is obtained with the use of the provided stego-image. And grid search and Chi-square goodness of fit test are exploited to estimate the length of the secret message embedded with stochastic modulation steganography. The experimental results demonstrate that our new approach is effective for steganalyzing stochastic modulation steganography and accurately estimating the length of the secret message.
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Stacking with Stochastic Cooling
Caspers, Friedhelm
2004-01-01
Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles seen by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly protected from the Schottky noise of the stack. Vice versa the stack has to be efficiently shielded against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 105, the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters)....
Stochastic Processes in Gravitropism
Directory of Open Access Journals (Sweden)
Yasmine eMeroz
2014-11-01
Full Text Available In this short review we focus on the role of noise in gravitropism of plants - the reorientation of plants according to the direction of gravity. We briefly introduce the conventional picture of static gravisensing in cells specialized in sensing. This model hinges on the sedimentation of statoliths (high in density and mass relative to other organelles to the lowest part of the sensing cell. We then present experimental observations that cannot currently be understood within this framework. Lastly we introduce some current alternative models and directions that attempt to incorporate and interpret these experimental observations, including: (i {it dynamic sensing}, where gravisensing is suggested to be enhanced by stochastic events due to thermal and mechanical noise. These events both effectively lower the threshold of response, and lead to small-distance sedimentation, allowing amplification and integration of the signal. (ii The role of the cytoskeleton in signal-to-noise modulation and (iii in signal transduction. In closing, we discuss directions that seem to either not have been explored, or that are still poorly understood.
Energy Technology Data Exchange (ETDEWEB)
Brennan J. M.; Blaskiewicz, M.; Mernick, K.
2012-05-20
The full 6-dimensional [x,x'; y,y'; z,z'] stochastic cooling system for RHIC was completed and operational for the FY12 Uranium-Uranium collider run. Cooling enhances the integrated luminosity of the Uranium collisions by a factor of 5, primarily by reducing the transverse emittances but also by cooling in the longitudinal plane to preserve the bunch length. The components have been deployed incrementally over the past several runs, beginning with longitudinal cooling, then cooling in the vertical planes but multiplexed between the Yellow and Blue rings, next cooling both rings simultaneously in vertical (the horizontal plane was cooled by betatron coupling), and now simultaneous horizontal cooling has been commissioned. The system operated between 5 and 9 GHz and with 3 x 10{sup 8} Uranium ions per bunch and produces a cooling half-time of approximately 20 minutes. The ultimate emittance is determined by the balance between cooling and emittance growth from Intra-Beam Scattering. Specific details of the apparatus and mathematical techniques for calculating its performance have been published elsewhere. Here we report on: the method of operation, results with beam, and comparison of results to simulations.
Adaptation in stochastic environments
Clark, Colib
1993-01-01
The classical theory of natural selection, as developed by Fisher, Haldane, and 'Wright, and their followers, is in a sense a statistical theory. By and large the classical theory assumes that the underlying environment in which evolution transpires is both constant and stable - the theory is in this sense deterministic. In reality, on the other hand, nature is almost always changing and unstable. We do not yet possess a complete theory of natural selection in stochastic environ ments. Perhaps it has been thought that such a theory is unimportant, or that it would be too difficult. Our own view is that the time is now ripe for the development of a probabilistic theory of natural selection. The present volume is an attempt to provide an elementary introduction to this probabilistic theory. Each author was asked to con tribute a simple, basic introduction to his or her specialty, including lively discussions and speculation. We hope that the book contributes further to the understanding of the roles of "Cha...
Kallianpur, Gopinath; Hida, Takeyuki
1987-01-01
The use of probabilistic methods in the biological sciences has been so well established by now that mathematical biology is regarded by many as a distinct dis cipline with its own repertoire of techniques. The purpose of the Workshop on sto chastic methods in biology held at Nagoya University during the week of July 8-12, 1985, was to enable biologists and probabilists from Japan and the U. S. to discuss the latest developments in their respective fields and to exchange ideas on the ap plicability of the more recent developments in stochastic process theory to problems in biology. Eighteen papers were presented at the Workshop and have been grouped under the following headings: I. Population genetics (five papers) II. Measure valued diffusion processes related to population genetics (three papers) III. Neurophysiology (two papers) IV. Fluctuation in living cells (two papers) V. Mathematical methods related to other problems in biology, epidemiology, population dynamics, etc. (six papers) An important f...
Turbulence and Stochastic Processes
Celani, Antonio; Mazzino, Andrea; Pumir, Alain
sec:08-1In 1931 the monograph Analytical Methods in Probability Theory appeared, in which A.N. Kolmogorov laid the foundations for the modern theory of Markov processes [1]. According to Gnedenko: "In the history of probability theory it is difficult to find other works that changed the established points of view and basic trends in research work in such a decisive way". Ten years later, his article on fully developed turbulence provided the framework within which most, if not all, of the subsequent theoretical investigations have been conducted [2] (see e.g. the review by Biferale et al. in this volume [3]. Remarkably, the greatest advances made in the last few years towards a thorough understanding of turbulence developed from the successful marriage between the theory of stochastic processes and the phenomenology of turbulent transport of scalar fields. In this article we will summarize these recent developments which expose the direct link between the intermittency of transported fields and the statistical properties of particle trajectories advected by the turbulent flow (see also [4], and, for a more thorough review, [5]. We also discuss the perspectives of the Lagrangian approach beyond passive scalars, especially for the modeling of hydrodynamic turbulence.
AA, stochastic precooling kicker
1980-01-01
The freshly injected antiprotons were subjected to fast stochastic "precooling", while a shutter shielded the deeply cooled antiproton stack from the violent action of the precooling kicker. In this picture, the injection orbit is to the left, the stack orbit to the far right, the separating shutter is in open position. After several seconds of precooling (in momentum and in the vertical plane), the shutter was opened briefly, so that by means of RF the precooled antiprotons could be transferred to the stack tail, where they were subjected to further cooling in momentum and both transverse planes, until they ended up, deeply cooled, in the stack core. The fast shutter, which had to open and close in a fraction of a second was an essential item of the cooling scheme and a mechanical masterpiece. Here the shutter is in the open position. The precooling pickups were of the same design, with the difference that the kickers had cooling circuits and the pickups not. 8401150 shows a precooling pickup with the shutte...
Energy Technology Data Exchange (ETDEWEB)
Bulsara, Adi R., E-mail: bulsara@spawar.navy.mil [SPAWAR Systems Center Pacific, San Diego, CA 92152-5001 (United States); Dari, Anna, E-mail: adari@asu.edu [Ira A. Fulton School of Engineering, Arizona State University, Tempe, AZ 85287-9309 (United States); Ditto, William L., E-mail: william.ditto@asu.edu [Ira A. Fulton School of Engineering, Arizona State University, Tempe, AZ 85287-9309 (United States); Murali, K., E-mail: kmurali@annauniv.edu [Department of Physics, Anna University, Chennai 600 025 (India); Sinha, Sudeshna, E-mail: sudeshna@imsc.res.in [Institute of Mathematical Sciences, Taramani, Chennai 600 113 (India); Indian Institute of Science Education and Research, Mohali, Transit Campus: MGSIPAP Complex, Sector 26 Chandigarh (India)
2010-10-05
In a recent publication it was shown that, when one drives a two-state system with two square waves as input, the response of the system mirrors a logical output (NOR/OR). The probability of obtaining the correct logic response is controlled by the interplay between the noise-floor and the nonlinearity. As one increases the noise intensity, the probability of the output reflecting a NOR/OR operation increases to unity and then decreases. Varying the nonlinearity (or the thresholds) of the system allows one to morph the output into another logic operation (NAND/AND) whose probability displays analogous behavior. Thus, the outcome of the interplay of nonlinearity and noise is a flexible logic gate with enhanced performance. Here we review this concept of 'Logical Stochastic Resonance' (LSR) and provide details of an electronic circuit system demonstrating LSR. Our proof-of-principle experiment involves a particularly simple realization of a two-state system realized by two adjustable thresholds. We also review CMOS implementations of a simple LSR circuit, and the concatenation of these LSR modules to emulate combinational logic, such as data flip-flop and full adder operations.
Epigenetic stochasticity, nuclear structure and cancer: the implications for medicine.
Feinberg, A P
2014-07-01
The aim of this review is to summarize an evolution of thinking about the epigenetic basis of human cancer, from the earliest studies of altered DNA methylation in cancer to the modern comprehensive epigenomic era. Converging data from epigenetic studies of primary cancers and from experimental studies of chromatin in development and epithelial-mesenchymal transition suggest a role for epigenetic stochasticity as a driving force of cancer, with Darwinian selection of tumour cells at the expense of the host. This increased epigenetic stochasticity appears to be mediated by large-scale changes in DNA methylation and chromatin in domains associated with the nuclear lamina. The implications for diagnosis include the potential to identify stochastically disrupted progenitor cells years before cancer develops, and to target drugs to epigenetic drivers of gene expression instability rather than to mean effects per se. © 2014 The Association for the Publication of the Journal of Internal Medicine.
Segmentation of stochastic images with a stochastic random walker method.
Pätz, Torben; Preusser, Tobias
2012-05-01
We present an extension of the random walker segmentation to images with uncertain gray values. Such gray-value uncertainty may result from noise or other imaging artifacts or more general from measurement errors in the image acquisition process. The purpose is to quantify the influence of the gray-value uncertainty onto the result when using random walker segmentation. In random walker segmentation, a weighted graph is built from the image, where the edge weights depend on the image gradient between the pixels. For given seed regions, the probability is evaluated for a random walk on this graph starting at a pixel to end in one of the seed regions. Here, we extend this method to images with uncertain gray values. To this end, we consider the pixel values to be random variables (RVs), thus introducing the notion of stochastic images. We end up with stochastic weights for the graph in random walker segmentation and a stochastic partial differential equation (PDE) that has to be solved. We discretize the RVs and the stochastic PDE by the method of generalized polynomial chaos, combining the recent developments in numerical methods for the discretization of stochastic PDEs and an interactive segmentation algorithm. The resulting algorithm allows for the detection of regions where the segmentation result is highly influenced by the uncertain pixel values. Thus, it gives a reliability estimate for the resulting segmentation, and it furthermore allows determining the probability density function of the segmented object volume.
Stochastic switching in biology: from genotype to phenotype
Bressloff, Paul C.
2017-03-01
There has been a resurgence of interest in non-equilibrium stochastic processes in recent years, driven in part by the observation that the number of molecules (genes, mRNA, proteins) involved in gene expression are often of order 1-1000. This means that deterministic mass-action kinetics tends to break down, and one needs to take into account the discrete, stochastic nature of biochemical reactions. One of the major consequences of molecular noise is the occurrence of stochastic biological switching at both the genotypic and phenotypic levels. For example, individual gene regulatory networks can switch between graded and binary responses, exhibit translational/transcriptional bursting, and support metastability (noise-induced switching between states that are stable in the deterministic limit). If random switching persists at the phenotypic level then this can confer certain advantages to cell populations growing in a changing environment, as exemplified by bacterial persistence in response to antibiotics. Gene expression at the single-cell level can also be regulated by changes in cell density at the population level, a process known as quorum sensing. In contrast to noise-driven phenotypic switching, the switching mechanism in quorum sensing is stimulus-driven and thus noise tends to have a detrimental effect. A common approach to modeling stochastic gene expression is to assume a large but finite system and to approximate the discrete processes by continuous processes using a system-size expansion. However, there is a growing need to have some familiarity with the theory of stochastic processes that goes beyond the standard topics of chemical master equations, the system-size expansion, Langevin equations and the Fokker-Planck equation. Examples include stochastic hybrid systems (piecewise deterministic Markov processes), large deviations and the Wentzel-Kramers-Brillouin (WKB) method, adiabatic reductions, and queuing/renewal theory. The major aim of this
Directory of Open Access Journals (Sweden)
Wang-Xia Wang
2014-02-01
Full Text Available The miR-15/107 family comprises a group of 10 paralogous microRNAs (miRNAs, sharing a 5′ AGCAGC sequence. These miRNAs have overlapping targets. In order to characterize the expression of miR-15/107 family miRNAs, we employed customized TaqMan Low-Density micro-fluid PCR-array to investigate the expression of miR-15/107 family members, and other selected miRNAs, in 11 human tissues obtained at autopsy including the cerebral cortex, frontal cortex, primary visual cortex, thalamus, heart, lung, liver, kidney, spleen, stomach and skeletal muscle. miR-103, miR-195 and miR-497 were expressed at similar levels across various tissues, whereas miR-107 is enriched in brain samples. We also examined the expression patterns of evolutionarily conserved miR-15/107 miRNAs in three distinct primary rat brain cell preparations (enriched for cortical neurons, astrocytes and microglia, respectively. In primary cultures of rat brain cells, several members of the miR-15/107 family are enriched in neurons compared to other cell types in the central nervous system (CNS. In addition to mature miRNAs, we also examined the expression of precursors (pri-miRNAs. Our data suggested a generally poor correlation between the expression of mature miRNAs and their precursors. In summary, we provide a detailed study of the tissue and cell type-specific expression profile of this highly expressed and phylogenetically conserved family of miRNA genes.
General N-th Degree Stochastic Dominance
Institute of Scientific and Technical Information of China (English)
张顺明
2001-01-01
This paper examines N-th degree stochastic dominance which isused to compare the risk factor of risky assets after summarizing the definitions of first degree stochastic dominance and second degree stochastic dominance. The paper defines general N-th degree stochastic dominance, presents a sufficient and necessary condition which is the equivalent theorem of general N-th degree stochastic dominance. The feasible utility form is constructed to explain the economic meaning of N-th degree stochastic dominance in the field of financial economics. The equivalent condition is described by the probability distribution functions of risky assets, which are not related to utility functions (preference relations).
Stability Analysis for Stochastic Optimization Problems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
A Stochastic Collocation Algorithm for Uncertainty Analysis
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
Institute of Scientific and Technical Information of China (English)
Chang-shui FENG; Wei-qiu ZHU
2009-01-01
We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged Ito stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov (FPK) equation associated with the averaged Ito equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus-trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.
Ali, M Syed; Rani, M Esther
2015-01-01
This paper investigates the problem of robust passivity of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Lyapunov functional method, the Itô differential rule, and matrix analysis techniques, we establish a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the stochastic neural network is robustly passive in the sense of expectation. A delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be less than 1 is removed. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.
Stochastic models: theory and simulation.
Energy Technology Data Exchange (ETDEWEB)
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Stochastic simulation in systems biology.
Székely, Tamás; Burrage, Kevin
2014-11-01
Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.
A stochastic differential equation model for transcriptional regulatory networks
Directory of Open Access Journals (Sweden)
Quirk Michelle D
2007-05-01
Full Text Available Abstract Background This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets. The dynamics of the gene expression level are fitted via a stochastic differential equation model, yielding a set of specific regulators and their contribution. Results We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic differential equation model follows well the dynamic of the gene expression levels. Conclusion When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved models of the transcriptional regulatory networks.
Stochastic differential equation model for cerebellar granule cell excitability.
Saarinen, Antti; Linne, Marja-Leena; Yli-Harja, Olli
2008-02-29
Neurons in the brain express intrinsic dynamic behavior which is known to be stochastic in nature. A crucial question in building models of neuronal excitability is how to be able to mimic the dynamic behavior of the biological counterpart accurately and how to perform simulations in the fastest possible way. The well-established Hodgkin-Huxley formalism has formed to a large extent the basis for building biophysically and anatomically detailed models of neurons. However, the deterministic Hodgkin-Huxley formalism does not take into account the stochastic behavior of voltage-dependent ion channels. Ion channel stochasticity is shown to be important in adjusting the transmembrane voltage dynamics at or close to the threshold of action potential firing, at the very least in small neurons. In order to achieve a better understanding of the dynamic behavior of a neuron, a new modeling and simulation approach based on stochastic differential equations and Brownian motion is developed. The basis of the work is a deterministic one-compartmental multi-conductance model of the cerebellar granule cell. This model includes six different types of voltage-dependent conductances described by Hodgkin-Huxley formalism and simple calcium dynamics. A new model for the granule cell is developed by incorporating stochasticity inherently present in the ion channel function into the gating variables of conductances. With the new stochastic model, the irregular electrophysiological activity of an in vitro granule cell is reproduced accurately, with the same parameter values for which the membrane potential of the original deterministic model exhibits regular behavior. The irregular electrophysiological activity includes experimentally observed random subthreshold oscillations, occasional spontaneous spikes, and clusters of action potentials. As a conclusion, the new stochastic differential equation model of the cerebellar granule cell excitability is found to expand the range of dynamics
Stochastic superparameterization in quasigeostrophic turbulence
Grooms, Ian
2013-01-01
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization (SP) algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional SP simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic SP replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on th...
Stochastic models for atmospheric dispersion
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2003-01-01
Simple stochastic differential equation models have been applied by several researchers to describe the dispersion of tracer particles in the planetary atmospheric boundary layer and to form the basis for computer simulations of particle paths. To obtain the drift coefficient, empirical vertical...... positions close to the boundaries. Different rules have been suggested in the literature with justifications based on simulation studies. Herein the relevant stochastic differential equation model is formulated in a particular way. The formulation is based on the marginal transformation of the position...... dependent particle velocity into a position independent Gaussian velocity. Boundary conditions are obtained from Itos rule of stochastic differentiation. The model directly point at a canonical rule of reflection for the approximating random walk with finite time step. This reflection rule is different from...
Intrinsic optimization using stochastic nanomagnets
Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo
2017-01-01
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets. PMID:28295053
Mechanical autonomous stochastic heat engines
Serra-Garcia, Marc; Foehr, Andre; Moleron, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara; . Team
Stochastic heat engines extract work from the Brownian motion of a set of particles out of equilibrium. So far, experimental demonstrations of stochastic heat engines have required extreme operating conditions or nonautonomous external control systems. In this talk, we will present a simple, purely classical, autonomous stochastic heat engine that uses the well-known tension induced nonlinearity in a string. Our engine operates between two heat baths out of equilibrium, and transfers energy from the hot bath to a work reservoir. This energy transfer occurs even if the work reservoir is at a higher temperature than the hot reservoir. The talk will cover a theoretical investigation and experimental results on a macroscopic setup subject to external noise excitations. This system presents an opportunity for the study of non equilibrium thermodynamics and is an interesting candidate for innovative energy conversion devices.
Principal axes for stochastic dynamics.
Vasconcelos, V V; Raischel, F; Haase, M; Peinke, J; Wächter, M; Lind, P G; Kleinhans, D
2011-09-01
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
Stochastic models of cell motility
DEFF Research Database (Denmark)
Gradinaru, Cristian
2012-01-01
Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new...... interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic...... models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental...
Principal axes for stochastic dynamics
Vasconcelos, V V; Haase, M; Peinke, J; Wächter, M; Lind, P G; Kleinhans, D
2011-01-01
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf-bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
Applied probability and stochastic processes
Sumita, Ushio
1999-01-01
Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...
Fundamentals of stochastic nature sciences
Klyatskin, Valery I
2017-01-01
This book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens – or doesn’t! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability. In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under wh...
Stacking with stochastic cooling
Energy Technology Data Exchange (ETDEWEB)
Caspers, Fritz E-mail: Fritz.Caspers@cern.ch; Moehl, Dieter
2004-10-11
Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles 'seen' by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly 'protected' from the Schottky noise of the stack. Vice versa the stack has to be efficiently 'shielded' against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 10{sup 5} the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters). In the 'old AA', where the antiproton collection and stacking was done in one single ring, the injected beam was further shielded during cooling by means of a movable shutter. The complexity of these systems is very high. For more modest stacking ratios, one might use azimuthal rather than radial separation of stack and injected beam. Schematically half of the circumference would be used to accept and cool new beam and the remainder to house the stack. Fast gating is then required between the high gain cooling of the injected beam and the low gain stack cooling. RF-gymnastics are used to merge the pre-cooled batch with the stack, to re-create free space for the next injection, and to capture the new batch. This scheme is less demanding for the storage ring lattice, but at the expense of some reduction in stacking rate. The talk reviews the 'radial' separation schemes and also gives some
Lacksonen, Thomas A.
1994-01-01
Small space flight project design at NASA Langley Research Center goes through a multi-phase process from preliminary analysis to flight operations. The process insures that each system achieves its technical objectives with demonstrated quality and within planned budgets and schedules. A key technical component of early phases is decision analysis, which is a structure procedure for determining the best of a number of feasible concepts based upon project objectives. Feasible system concepts are generated by the designers and analyzed for schedule, cost, risk, and technical measures. Each performance measure value is normalized between the best and worst values and a weighted average score of all measures is calculated for each concept. The concept(s) with the highest scores are retained, while others are eliminated from further analysis. This project automated and enhanced the decision analysis process. Automation of the decision analysis process was done by creating a user-friendly, menu-driven, spreadsheet macro based decision analysis software program. The program contains data entry dialog boxes, automated data and output report generation, and automated output chart generation. The enhancements to the decision analysis process permit stochastic data entry and analysis. Rather than enter single measure values, the designers enter the range and most likely value for each measure and concept. The data can be entered at the system or subsystem level. System level data can be calculated as either sum, maximum, or product functions of the subsystem data. For each concept, the probability distributions are approximated for each measure and the total score for each concept as either constant, triangular, normal, or log-normal distributions. Based on these distributions, formulas are derived for the probability that the concept meets any given constraint, the probability that the concept meets all constraints, and the probability that the concept is within a given
A Game-Based Approach for PCTL* Stochastic Model Checking with Evidence
Institute of Scientific and Technical Information of China (English)
Yang Liu; Xuan-Dong Li; Yan Ma
2016-01-01
Stochastic model checking is a recent extension and generalization of the classical model checking, which focuses on quantitatively checking the temporal property of a system model. PCTL* is one of the important quantitative property specification languages, which is strictly more expressive than either PCTL (probabilistic computation tree logic) or LTL (linear temporal logic) with probability bounds. At present, PCTL* stochastic model checking algorithm is very complicated, and cannot provide any relevant explanation of why a formula does or does not hold in a given model. For dealing with this problem, an intuitive and succinct approach for PCTL* stochastic model checking with evidence is put forward in this paper, which includes: presenting the game semantics for PCTL* in release-PNF (release-positive normal form), defining the PCTL*stochastic model checking game, using strategy solving in game to achieve the PCTL*stochastic model checking, and refining winning strategy as the evidence to certify stochastic model checking result. The soundness and the completeness of game-based PCTL* stochastic model checking are proved, and its complexity matches the known lower and upper bounds. The game-based PCTL*stochastic model checking algorithm is implemented in a visual prototype tool, and its feasibility is demonstrated by an illustrative example.
Delay-induced multiple stochastic resonances on scale-free neuronal networks.
Wang, Qingyun; Perc, Matjaz; Duan, Zhisheng; Chen, Guanrong
2009-06-01
We study the effects of periodic subthreshold pacemaker activity and time-delayed coupling on stochastic resonance over scale-free neuronal networks. As the two extreme options, we introduce the pacemaker, respectively, to the neuron with the highest degree and to one of the neurons with the lowest degree within the network, but we also consider the case when all neurons are exposed to the periodic forcing. In the absence of delay, we show that an intermediate intensity of noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble, irrespective to its placing, thus providing evidences for stochastic resonance on the scale-free neuronal networks. Interestingly thereby, if the forcing in form of a periodic pulse train is introduced to all neurons forming the network, the stochastic resonance decreases as compared to the case when only a single neuron is paced. Moreover, we show that finite delays in coupling can significantly affect the stochastic resonance on scale-free neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances independently of the placing of the pacemaker, but they can also altogether destroy stochastic resonance. Delay-induced multiple stochastic resonances manifest as well-expressed maxima of the correlation measure, appearing at every multiple of the pacemaker period. We argue that fine-tuned delays and locally active pacemakers are vital for assuring optimal conditions for stochastic resonance on complex neuronal networks.
When greediness fails: examples from stochastic scheduling
Uetz, Marc Jochen
The purpose of this paper is to present examples for the sometimes surprisingly different behavior of deterministic and stochastic scheduling problems. In particular, it demonstrates some seemingly counterintuitive properties of optimal scheduling policies for stochastic machine scheduling problems.
A Fractionally Integrated Wishart Stochastic Volatility Model
M. Asai (Manabu); M.J. McAleer (Michael)
2013-01-01
textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of
When greediness fails: examples from stochastic scheduling
Uetz, Marc
2003-01-01
The purpose of this paper is to present examples for the sometimes surprisingly different behavior of deterministic and stochastic scheduling problems. In particular, it demonstrates some seemingly counterintuitive properties of optimal scheduling policies for stochastic machine scheduling problems.
Transport properties of stochastic Lorentz models
Beijeren, H. van
1982-01-01
Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed waiti
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Stochastic methods in quantum mechanics
Gudder, Stanley P
2005-01-01
Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun
Stochastic epidemic models: a survey
Britton, Tom
2009-01-01
This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic model properties (relying on a large community) are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Stochastic and infinite dimensional analysis
Carpio-Bernido, Maria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria; Silva, José
2016-01-01
This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Schwinger Mechanism with Stochastic Quantization
Fukushima, Kenji
2014-01-01
We prescribe a formulation of the particle production with real-time Stochastic Quantization. To construct the retarded and the time-ordered propagators we decompose the stochastic variables into positive- and negative-energy parts. In this way we demonstrate how to derive the Schwinger mechanism under a time-dependent electric field. We also discuss a physical interpretation with help of numerical simulations and develop an analogue to the one-dimensional scattering with the non-relativistic Schroedinger equation. We can then reformulate the Schwinger mechanism as the high-energy quantum reflection problem rather than tunneling.
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2011-01-01
A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that d
QB1 - Stochastic Gene Regulation
Energy Technology Data Exchange (ETDEWEB)
Munsky, Brian [Los Alamos National Laboratory
2012-07-23
Summaries of this presentation are: (1) Stochastic fluctuations or 'noise' is present in the cell - Random motion and competition between reactants, Low copy, quantization of reactants, Upstream processes; (2) Fluctuations may be very important - Cell-to-cell variability, Cell fate decisions (switches), Signal amplification or damping, stochastic resonances; and (3) Some tools are available to mode these - Kinetic Monte Carlo simulations (SSA and variants), Moment approximation methods, Finite State Projection. We will see how modeling these reactions can tell us more about the underlying processes of gene regulation.
Algebraic and stochastic coding theory
Kythe, Dave K
2012-01-01
Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes.
Stochastic Kinetics of Nascent RNA
Xu, Heng; Skinner, Samuel O.; Sokac, Anna Marie; Golding, Ido
2016-09-01
The stochastic kinetics of transcription is typically inferred from the distribution of RNA numbers in individual cells. However, cellular RNA reflects additional processes downstream of transcription, hampering this analysis. In contrast, nascent (actively transcribed) RNA closely reflects the kinetics of transcription. We present a theoretical model for the stochastic kinetics of nascent RNA, which we solve to obtain the probability distribution of nascent RNA per gene. The model allows us to evaluate the kinetic parameters of transcription from single-cell measurements of nascent RNA. The model also predicts surprising discontinuities in the distribution of nascent RNA, a feature which we verify experimentally.
The dynamics of stochastic processes
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
In the present thesis the dynamics of stochastic processes is studied with a special attention to the semimartingale property. This is mainly motivated by the fact that semimartingales provide the class of the processes for which it is possible to define a reasonable stochastic calculus due...... average processes, and when the driving process is a Lévy or a chaos process the semimartingale property is characterized in the filtration spanned by the driving process and in the natural filtration when the latter is a Brownian motion. To obtain some of the above results an integrability of seminorm...
Stochastic model in microwave propagation
Energy Technology Data Exchange (ETDEWEB)
Ranfagni, A. [“Nello Carrara” Institute of Applied Physics, CNR Florence Research Area, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy); Mugnai, D., E-mail: d.mugnai@ifac.cnr.it [“Nello Carrara” Institute of Applied Physics, CNR Florence Research Area, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy)
2011-11-28
Further experimental results of delay time in microwave propagation are reported in the presence of a lossy medium (wood). The measurements show that the presence of a lossy medium makes the propagation slightly superluminal. The results are interpreted on the basis of a stochastic (or path integral) model, showing how this model is able to describe each kind of physical system in which multi-path trajectories are present. -- Highlights: ► We present new experimental results on electromagnetic “anomalous” propagation. ► We apply a path integral theoretical model to wave propagation. ► Stochastic processes and multi-path trajectories in propagation are considered.
Representing Turbulence Model Uncertainty with Stochastic PDEs
Oliver, Todd; Moser, Robert
2012-11-01
Validation of and uncertainty quantification for extrapolative predictions of RANS turbulence models are necessary to ensure that the models are not used outside of their domain of applicability and to properly inform decisions based on such predictions. In previous work, we have developed and calibrated statistical models for these purposes, but it has been found that incorporating all the knowledge of a domain expert--e.g., realizability, spatial smoothness, and known scalings--in such models is difficult. Here, we explore the use of stochastic PDEs for this purpose. The goal of this formulation is to pose the uncertainty model in a setting where it is easier for physical modelers to express what is known. To explore the approach, multiple stochastic models describing the error in the Reynolds stress are coupled with multiple deterministic turbulence models to make uncertain predictions of channel flow. These predictions are compared with DNS data to assess their credibility. This work is supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615].
Observability Estimate for Stochastic Schroedinger Equations
2012-01-01
In this paper, we establish a boundary observability estimate for stochastic Schr\\"{o}dinger equations by means of the global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a stochastic Schr\\"{o}dinger-like operator. Applications to the state observation problem for semilinear stochastic Schr\\"{o}dinger equations and the unique continuation problem for stochastic Schr\\"{o}dinger equations are also addressed.
Transport in a stochastic magnetic field
Energy Technology Data Exchange (ETDEWEB)
White, R.B.; Wu, Yanlin [Princeton Univ., NJ (United States). Plasma Physics Lab.; Rax, J.M. [Association Euratom-CEA, Centre d`Etudes Nucleaires de Cadarache, 13 -Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee
1992-09-01
Collisional heat transport in a stochastic magnetic field configuration is investigated. Well above stochastic threshold, a numerical solution of a Chirikov-Taylor model shows a short-time nonlocal regime, but at large time the Rechester-Rosenbluth effective diffusion is confirmed. Near stochastic threshold, subdiffusive behavior is observed for short mean free paths. The nature of this subdiffusive behavior is understood in terms of the spectrum of islands in the stochastic sea.
Transport in a stochastic magnetic field
Energy Technology Data Exchange (ETDEWEB)
White, R.B.; Wu, Yanlin (Princeton Univ., NJ (United States). Plasma Physics Lab.); Rax, J.M. (Association Euratom-CEA, Centre d' Etudes Nucleaires de Cadarache, 13 -Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee)
1992-01-01
Collisional heat transport in a stochastic magnetic field configuration is investigated. Well above stochastic threshold, a numerical solution of a Chirikov-Taylor model shows a short-time nonlocal regime, but at large time the Rechester-Rosenbluth effective diffusion is confirmed. Near stochastic threshold, subdiffusive behavior is observed for short mean free paths. The nature of this subdiffusive behavior is understood in terms of the spectrum of islands in the stochastic sea.
Stochastic modeling and analysis of telecoms networks
Decreusefond, Laurent
2012-01-01
This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an
Exact Algorithms for Solving Stochastic Games
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels;
2012-01-01
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games.......Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....
Michta, Mariusz
2017-02-01
In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations with respect to semimartingale integrators. We present new connections between their solutions. In particular, we show that attainable sets of solutions to stochastic inclusions are subsets of values of multivalued solutions of certain set-valued stochastic equations. We also show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. The results obtained in the paper generalize results dealing with this topic known both in deterministic and stochastic cases.
Stochastic Circumplanetary Dynamics of Rotating Non-Spherical Dust Particles
Makuch, Martin; Brilliantov, N. V.; Sremcevic, M.; Spahn, F.; Krivov, A. V.
2006-12-01
Influence of stochastically fluctuating radiation pressure on the dynamics of dust grains on circumplanetary orbits was studied. Stochasticity stems from the permanent change of the particle cross-section due to rotation of nonspherical grains, exposed to the solar radiation. We found that stochasticity depends on the characteristic angular velocity of particles which, according to our estimates, spins very fast on the time scale of the orbital motion. According to this we modelled the stochastic part of the radiation pressure by a Gaussian white noise. Gauss perturbation equations with the radiation pressure being a sum of the deterministic and stochastic component have been used. We observed monotonous increasing standard deviation of the orbital elements, that is, the diffusive-like behaviour of the ensemble, which results in a spatial spreading of initially confined set of particles. By linear approximation we obtained expression for the effective diffusion coefficients and estimate their dependence on the geometrical characteristics of particles and their spin. Teoretical results were compared with numerical simulations performed for the putative dust tori of Mars. Our theory agrees fairly well with simulations for the initial period of the system evolution. The agreement however deteriorates with increasing time where impact of the non-linear terms of the perturbation equations becomes important. Analysis shows that the theoretical results may estimate the low boundary of the time-dependent standard deviation of the orbital elements. In the case of dust ejected from Martian moon Deimos we observed a change of orbital elements up to 10% of their initial values during the first 1000 years of orbital evolution. Our results indicate that the stochastic modulation of the radiation pressure can play an important role in the circumplanetary dynamics of dust and may, together with further noise sources (shadow, planetary bowshock, charge fluctuations, etc
EDITORIAL: Stochasticity in fusion plasmas Stochasticity in fusion plasmas
Unterberg, Bernhard
2010-03-01
Structure formation and transport in stochastic plasmas is a topic of growing importance in many fields of plasma physics from astrophysics to fusion research. In particular, the possibility to control transport in the boundary of confined fusion plasmas by resonant magnetic perturbations has been investigated extensively during recent years. A major research achievement was finding that the intense transient particle and heat fluxes associated with edge localized modes (here type-I ELMs) in magnetically confined fusion plasmas can be mitigated or even suppressed by resonant magnetic perturbation fields. This observation opened up a possible scheme to avoid too large erosion and material damage by such transients in future fusion devices such as ITER. However, it is widely recognized that a more basic understanding is needed to extrapolate the results obtained in present experiments to future fusion devices. The 4th workshop on Stochasticity in Fusion Plasmas was held in Jülich, Germany, from 2 to 4 March 2009. This series of workshops aims at gathering fusion experts from various plasma configurations such as tokamaks, stellarators and reversed field pinches to exchange knowledge on structure formation and transport in stochastic fusion plasmas. The workshops have attracted colleagues from both experiment and theory and stimulated fruitful discussions about the basics of stochastic fusion plasmas. Important papers from the first three workshops in 2003, 2005 and 2007 have been published in previous special issues of Nuclear Fusion (stacks.iop.org/NF/44/i=6, stacks.iop.org/NF/46/i=4 and stacks.iop.org/NF/48/i=2). This special issue comprises contributions presented at the 4th SFP workshop, dealing with the main subjects such as formation of stochastic magnetic layers, energy and particle transport in stochastic magnetic fields, plasma response to external, non-axis-symmetric perturbations and last but not least application of resonant magnetic perturbations for
Variational principles for stochastic soliton dynamics.
Holm, Darryl D; Tyranowski, Tomasz M
2016-03-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa-Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler-Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling.
Symmetrized solutions for nonlinear stochastic differential equations
Directory of Open Access Journals (Sweden)
G. Adomian
1981-01-01
Full Text Available Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized forms which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly+ym=x where x is a stochastic process and L is a linear stochastic operator.
Stochastic Programming with Simple Integer Recourse
Louveaux, François V.; van der Vlerk, Maarten H.
1993-01-01
Stochastic integer programs are notoriously difficult. Very few properties are known and solution algorithms are very scarce. In this paper, we introduce the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in stochastic c
Symmetry reduction for stochastic hybrid systems
Bujorianu, L.M.; Katoen, J.P.
2009-01-01
This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. We first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA). Then, we genera
Symmetry Reduction For Stochastic Hybrid Systems
Bujorianu, L.M.; Katoen, J.P.
2008-01-01
This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. To that end, we first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA). Th
Models and algorithms for stochastic online scheduling
Megow, N.; Uetz, Marc Jochen; Vredeveld, T.
We consider a model for scheduling under uncertainty. In this model, we combine the main characteristics of online and stochastic scheduling in a simple and natural way. Job processing times are assumed to be stochastic, but in contrast to traditional stochastic scheduling models, we assume that
Stability of stochastic switched SIRS models
Meng, Xiaoying; Liu, Xinzhi; Deng, Feiqi
2011-11-01
Stochastic stability problems of a stochastic switched SIRS model with or without distributed time delay are considered. By utilizing the Lyapunov methods, sufficient stability conditions of the disease-free equilibrium are established. Stability conditions about the subsystem of the stochastic switched SIRS systems are also obtained.
OPTIMUM DESIGN BASED ON RELIABILITY IN STOCHASTIC STRUCTURE SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The optimum design method based on the reliability is presented to the stochastic structure systems (i. e., the sectional area, length, elastic module and strength of the structural member are random variables) under the random loads. The sensitivity expression of system reliability index and the safety margins were presented in the stochastic structure systems. The optimum vector method was given. First, the expressions of the reliability index of the safety margins with the improved first-order second-moment and the stochastic finite element method were deduced, and then the expressions of the systemic failure probability by probabilistic network evaluation technique(PNET) method were obtained. After derivation calculus, the expressions of the sensitivity analysis for the system reliability were obtained. Moreover, the optimum design with the optimum vector algorithm was undertaken. In the optimum iterative procedure, the gradient step and the optimum vector step were adopted to calculate. At the last, a numerical example was provided to illustrate that the method is efficient in the calculation, stably converges and fits the application in engineering.
Mathematics of small stochastic reaction networks: a boundary layer theory for eigenstate analysis.
Mjolsness, Eric; Prasad, Upendra
2013-03-14
We study and analyze the stochastic dynamics of a reversible bimolecular reaction A + B ↔ C called the "trivalent reaction." This reaction is of a fundamental nature and is part of many biochemical reaction networks. The stochastic dynamics is given by the stochastic master equation, which is difficult to solve except when the equilibrium state solution is desired. We present a novel way of finding the eigenstates of this system of difference-differential equations, using perturbation analysis of ordinary differential equations arising from approximation of the difference equations. The time evolution of the state probabilities can then be expressed in terms of the eigenvalues and the eigenvectors.
Directory of Open Access Journals (Sweden)
Yan Che
2012-01-01
Full Text Available The estimation problem is investigated for a class of stochastic nonlinear systems with distributed time-varying delays and missing measurements. The considered distributed time-varying delays, stochastic nonlinearities, and missing measurements are modeled in random ways governed by Bernoulli stochastic variables. The discussed nonlinearities are expressed by the statistical means. By using the linear matrix inequality method, a sufficient condition is established to guarantee the mean-square stability of the estimation error, and then the estimator parameters are characterized by the solution to a set of LMIs. Finally, a simulation example is exploited to show the effectiveness of the proposed design procedures.
A Novel Formal Analysis Method of Network Survivability Based on Stochastic Process Algebra
Institute of Scientific and Technical Information of China (English)
ZHAO Guosheng; WANG Huiqiang; WANG Jian
2007-01-01
Stochastic process algebras have been proposed as compositional specification formalisms for performance models. A formal analysis method of survivable network was proposed based on stochastic process algebra, which incorporates formal modeling into performance analysis perfectly, and then various performance parameters of survivable network can be simultaneously obtained after formal modeling. The formal description with process expression to the survivable network system was carried out based on the simply introduced syntax and operational semantics of stochastic process algebra. Then PEPA workbench tool was used to obtain the probability of system's steady state availability and transient state availability. Simulation experiments show the effectiveness and feasibility of the developed method.
Stochastic nonlinear differential equations. I
Heilmann, O.J.; Kampen, N.G. van
1974-01-01
A solution method is developed for nonlinear differential equations having the following two properties. Their coefficients are stochastic through their dependence on a Markov process. The magnitude of the fluctuations, multiplied with their auto-correlation time, is a small quantity. Under these co
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models...
The bicriterion stochastic knapsack problem
DEFF Research Database (Denmark)
Andersen, Kim Allan
We discuss the bicriterion stochastic knapsack problem. It is described as follows. We have a known capacity of some resource, and a finite set of projects. Each project requires some units of the resource which is not known in advance, but given by a discrete probability distribution with a finite...
Stochastic Volatility and DSGE Models
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper argues that a specification of stochastic volatility commonly used to analyze the Great Moderation in DSGE models may not be appropriate, because the level of a process with this specification does not have conditional or unconditional moments. This is unfortunate because agents may...
Stochastic Processes in Epidemic Theory
Lefèvre, Claude; Picard, Philippe
1990-01-01
This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.
Stochastic-field cavitation model
Energy Technology Data Exchange (ETDEWEB)
Dumond, J., E-mail: julien.dumond@areva.com [AREVA Nuclear Professional School, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen (Germany); Magagnato, F. [Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstrasse 12, D-76131 Karlsruhe (Germany); Class, A. [AREVA Nuclear Professional School, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); Institute for Nuclear and Energy Technologies, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany)
2013-07-15
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Stochastic-field cavitation model
Dumond, J.; Magagnato, F.; Class, A.
2013-07-01
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Model checking mobile stochastic logic.
De Nicola, Rocco; Katoen, Joost P.; Latella, Diego; Loreti, Michele; Massink, Mieke
2007-01-01
The Temporal Mobile Stochastic Logic (MOSL) has been introduced in previous work by the authors for formulating properties of systems specified in STOKLAIM, a Markovian extension of KLAIM. The main purpose of MOSL is to address key functional aspects of global computing such as distribution
Model checking mobile stochastic logic.
De Nicola, Rocco; Katoen, Joost-Pieter; Latella, Diego; Loreti, Michele; Massink, Mieke
2007-01-01
The Temporal Mobile Stochastic Logic (MOSL) has been introduced in previous work by the authors for formulating properties of systems specified in STOKLAIM, a Markovian extension of KLAIM. The main purpose of MOSL is to address key functional aspects of global computing such as distribution awarenes
Stochastic resin transfer molding process
Park, M
2016-01-01
We consider one-dimensional and two-dimensional models of stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and numerically in the two-dimensional case. We show how variability of time to fill depends on correlation lengths and smoothness of a random permeability field.
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Stochastic Subspace Modelling of Turbulence
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Pedersen, B. J.; Nielsen, Søren R.K.
2009-01-01
Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper...
Modelling conjugation with stochastic differential equations.
Philipsen, K R; Christiansen, L E; Hasman, H; Madsen, H
2010-03-07
Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared to the model without plate conjugation. The modelling approach described in this article can be applied generally when modelling dynamical systems.
Error analysis of stochastic gradient descent ranking.
Chen, Hong; Tang, Yi; Li, Luoqing; Yuan, Yuan; Li, Xuelong; Tang, Yuanyan
2013-06-01
Ranking is always an important task in machine learning and information retrieval, e.g., collaborative filtering, recommender systems, drug discovery, etc. A kernel-based stochastic gradient descent algorithm with the least squares loss is proposed for ranking in this paper. The implementation of this algorithm is simple, and an expression of the solution is derived via a sampling operator and an integral operator. An explicit convergence rate for leaning a ranking function is given in terms of the suitable choices of the step size and the regularization parameter. The analysis technique used here is capacity independent and is novel in error analysis of ranking learning. Experimental results on real-world data have shown the effectiveness of the proposed algorithm in ranking tasks, which verifies the theoretical analysis in ranking error.
Mixing properties of stochastic quantum Hamiltonians
Onorati, E; Kliesch, M; Brown, W; Werner, A H; Eisert, J
2016-01-01
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and quantum information theory. In this work, we present a framework describing the mixing properties of continuous-time unitary evolutions originating from local Hamiltonians having time-fluctuating terms, reflecting a Brownian motion on the unitary group. The induced stochastic time evolution is shown to converge to a unitary design. As a first main result, we present bounds to the mixing time. By developing tools in representation theory, we analytically derive an expression for a local k-th moment operator that is entirely independent of k, giving rise to approximate unitary k-designs and quantum tensor product expanders. As a second main result, we introduce tools for proving bounds on the rate of decoupling from an environment with random quantum processes. By tying the mathema...
Stochastic averaging of quasi-Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
朱位秋
1996-01-01
A stochastic averaging method is proposed for quasi-Hamiltonian systems (Hamiltonian systems with light dampings subject to weakly stochastic excitations). Various versions of the method, depending on whether the associated Hamiltonian systems are integrable or nonintegrable, resonant or nonresonant, are discussed. It is pointed out that the standard stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method of quasi-Hamiltonian systems and that the results obtained by this method for several examples prove its effectiveness.
Research on nonlinear stochastic dynamical price model
Energy Technology Data Exchange (ETDEWEB)
Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail: jiaoruili@mail.nwpu.edu.cn; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2008-09-15
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.
2013-01-01
Single-cell variations in gene and protein expression are important during development and disease. Cell-to-cell heterogeneities can be directly inspected one cell at a time, but global methods are usually not sensitive enough to work with such a small amount of starting material. Here, we provide a detailed protocol for stochastic profiling, a method that infers single-cell regulatory heterogeneities by repeatedly sampling small collections of cells at random. Repeated stochastic sampling is...
Stochastic Reachability Analysis of Hybrid Systems
Bujorianu, Luminita Manuela
2012-01-01
Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then...
Stochastic Analysis : A Series of Lectures
Dozzi, Marco; Flandoli, Franco; Russo, Francesco
2015-01-01
This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields o...
Internal signal stochastic resonance of a synthetic gene network
Institute of Scientific and Technical Information of China (English)
WANG; Zhiwei; HOU; Zhonghuai; XIN; Houwen
2005-01-01
The dynamics behavior of a synthetic gene network controlled by random noise is investigated using a model proposed recently. The phenomena of noise induced oscillation (NIO) of the protein concentrations and internal signal stochastic resonance (SR) are studied by computer simulation. We also find that there exists an optimal noise intensity that can most favor the occurrence of effective oscillation (EO). Finally we discuss the potential constructive roles of SR on gene expression systems.
Stochastic calculus for uncoupled continuous-time random walks.
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L
2009-06-01
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingale transform theorem, if the CTRW is a martingale, the Itō integral is a martingale too. It is shown how the definition of the stochastic integrals can be used to easily compute them by Monte Carlo simulation. The relations between a CTRW, its quadratic variation, its Stratonovich integral, and its Itō integral are highlighted by numerical calculations when the jumps in space of the CTRW have a symmetric Lévy alpha -stable distribution and its waiting times have a one-parameter Mittag-Leffler distribution. Remarkably, these distributions have fat tails and an unbounded quadratic variation. In the diffusive limit of vanishing scale parameters, the probability density of this kind of CTRW satisfies the space-time fractional diffusion equation (FDE) or more in general the fractional Fokker-Planck equation, which generalizes the standard diffusion equation, solved by the probability density of the Wiener process, and thus provides a phenomenologic model of anomalous diffusion. We also provide an analytic expression for the quadratic variation of the stochastic process described by the FDE and check it by Monte Carlo.
Directory of Open Access Journals (Sweden)
Kyung-Min Chung
Full Text Available Despite years of research, the reprogramming of human somatic cells to pluripotency remains a slow, inefficient process, and a detailed mechanistic understanding of reprogramming remains elusive. Current models suggest reprogramming to pluripotency occurs in two-phases: a prolonged stochastic phase followed by a rapid deterministic phase. In this paradigm, the early stochastic phase is marked by the random and gradual expression of pluripotency genes and is thought to be a major rate-limiting step in the successful generation of induced Pluripotent Stem Cells (iPSCs. Recent evidence suggests that the epigenetic landscape of the somatic cell is gradually reset during a period known as the stochastic phase, but it is known neither how this occurs nor what rate-limiting steps control progress through the stochastic phase. A precise understanding of gene expression dynamics in the stochastic phase is required in order to answer these questions. Moreover, a precise model of this complex process will enable the measurement and mechanistic dissection of treatments that enhance the rate or efficiency of reprogramming to pluripotency. Here we use single-cell transcript profiling, FACS and mathematical modeling to show that the stochastic phase is an ordered probabilistic process with independent gene-specific dynamics. We also show that partially reprogrammed cells infected with OSKM follow two trajectories: a productive trajectory toward increasingly ESC-like expression profiles or an alternative trajectory leading away from both the fibroblast and ESC state. These two pathways are distinguished by the coordinated expression of a small group of chromatin modifiers in the productive trajectory, supporting the notion that chromatin remodeling is essential for successful reprogramming. These are the first results to show that the stochastic phase of reprogramming in human fibroblasts is an ordered, probabilistic process with gene-specific dynamics and to
Chung, Kyung-Min; Kolling, Frederick W; Gajdosik, Matthew D; Burger, Steven; Russell, Alexander C; Nelson, Craig E
2014-01-01
Despite years of research, the reprogramming of human somatic cells to pluripotency remains a slow, inefficient process, and a detailed mechanistic understanding of reprogramming remains elusive. Current models suggest reprogramming to pluripotency occurs in two-phases: a prolonged stochastic phase followed by a rapid deterministic phase. In this paradigm, the early stochastic phase is marked by the random and gradual expression of pluripotency genes and is thought to be a major rate-limiting step in the successful generation of induced Pluripotent Stem Cells (iPSCs). Recent evidence suggests that the epigenetic landscape of the somatic cell is gradually reset during a period known as the stochastic phase, but it is known neither how this occurs nor what rate-limiting steps control progress through the stochastic phase. A precise understanding of gene expression dynamics in the stochastic phase is required in order to answer these questions. Moreover, a precise model of this complex process will enable the measurement and mechanistic dissection of treatments that enhance the rate or efficiency of reprogramming to pluripotency. Here we use single-cell transcript profiling, FACS and mathematical modeling to show that the stochastic phase is an ordered probabilistic process with independent gene-specific dynamics. We also show that partially reprogrammed cells infected with OSKM follow two trajectories: a productive trajectory toward increasingly ESC-like expression profiles or an alternative trajectory leading away from both the fibroblast and ESC state. These two pathways are distinguished by the coordinated expression of a small group of chromatin modifiers in the productive trajectory, supporting the notion that chromatin remodeling is essential for successful reprogramming. These are the first results to show that the stochastic phase of reprogramming in human fibroblasts is an ordered, probabilistic process with gene-specific dynamics and to provide a precise
Stochastic integration and differential equations
Protter, Philip E
2003-01-01
It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, t...
Optical stochastic cooling in Tevatron
Lebedev, V
2012-01-01
Intrabeam scattering is the major mechanism resulting in a growth of beam emittances and fast luminosity degradation in the Tevatron. As a result in the case of optimal collider operation only about 40% of antiprotons are used to the store end and the rest are discarded. Beam cooling is the only effective remedy to increase the particle burn rate and, consequently, the luminosity. Unfortunately neither electron nor stochastic cooling can be effective at the Tevatron energy and bunch density. Thus the optical stochastic cooling (OSC) is the only promising technology capable to cool the Tevatron beam. Possible ways of such cooling implementation in the Tevatron and advances in the OSC cooling theory are discussed in this paper. The technique looks promising and potentially can double the average Tevatron luminosity without increasing its peak value and the antiproton production.
Stochastic Generalized Method of Moments
Yin, Guosheng
2011-08-16
The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online. © 2011 American Statistical Association.
Stochastic Modeling of Soil Salinity
Suweis, S; Van der Zee, S E A T M; Daly, E; Maritan, A; Porporato, A; 10.1029/2010GL042495
2012-01-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The long term probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equation to a single stochastic differential equation driven by multiplicative Poisson noise. The novel analytical solutions provide insight on the interplay of the main soil, plant and climate parameters responsible for long-term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in long-term soil salinization trend...
Stochastic Vehicle Routing with Recourse
Goertz, Inge Li; Saket, Rishi
2012-01-01
We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed -- but costs here become more expensive by a factor lambda. We present an O(log^2 n log(n lambda))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Self-Organising Stochastic Encoders
Luttrell, Stephen
2010-01-01
The processing of mega-dimensional data, such as images, scales linearly with image size only if fixed size processing windows are used. It would be very useful to be able to automate the process of sizing and interconnecting the processing windows. A stochastic encoder that is an extension of the standard Linde-Buzo-Gray vector quantiser, called a stochastic vector quantiser (SVQ), includes this required behaviour amongst its emergent properties, because it automatically splits the input space into statistically independent subspaces, which it then separately encodes. Various optimal SVQs have been obtained, both analytically and numerically. Analytic solutions which demonstrate how the input space is split into independent subspaces may be obtained when an SVQ is used to encode data that lives on a 2-torus (e.g. the superposition of a pair of uncorrelated sinusoids). Many numerical solutions have also been obtained, using both SVQs and chains of linked SVQs: (1) images of multiple independent targets (encod...
Stochastic vehicle routing with recourse
DEFF Research Database (Denmark)
Gørtz, Inge Li; Nagarajan, Viswanath; Saket, Rishi
2012-01-01
We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand...... instantiations, a recourse route is computed - but costs here become more expensive by a factor λ. We present an O(log2n ·log(nλ))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular...... orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based ω(1) hardness of approximation for StochVRP, even on star-like metrics on which our...
Non-Gaussian Stochastic Gravity
Bates, Jason D.
2013-01-01
This paper presents a new, non-Gaussian formulation of stochastic gravity by incorporating the higher moments of the fluctuations of the quantum stress energy tensor for a free quantum scalar field in a consistent way. A scheme is developed for obtaining realizations of these fluctuations in terms of the Wightman function, and the behavior of the fluctuations is investigated. The resulting probability distribution for fluctuations of the energy density in Minkowski spacetime is found to be si...
Stochastic processes and filtering theory
Jazwinski, Andrew H
2007-01-01
This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well.Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probab
Stochastic Gravity: Theory and Applications
Directory of Open Access Journals (Sweden)
Hu Bei Lok
2008-05-01
Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein–Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman–Vernon influence functional and the Schwinger–Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein–Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out
Stochastic control of traffic patterns
DEFF Research Database (Denmark)
Gaididei, Yuri B.; Gorria, Carlos; Berkemer, Rainer
2013-01-01
A stochastic modulation of the safety distance can reduce traffic jams. It is found that the effect of random modulation on congestive flow formation depends on the spatial correlation of the noise. Jam creation is suppressed for highly correlated noise. The results demonstrate the advantage...... of heterogeneous performance of the drivers in time as well as individually. This opens the possibility for the construction of technical tools to control traffic jam formation....
Foundations of infinitesimal stochastic analysis
Stroyan, KD
2011-01-01
This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.
Stochastic cooling technology at Fermilab
Energy Technology Data Exchange (ETDEWEB)
Pasquinelli, R.J. E-mail: pasquin@fnal.gov
2004-10-11
The first antiproton cooling systems were installed and commissioned at Fermilab in 1984-1985. In the interim period, there have been several major upgrades, system improvements, and complete reincarnation of cooling systems. This paper will present some of the technology that was pioneered at Fermilab to implement stochastic cooling systems in both the Antiproton Source and Recycler accelerators. Current performance data will also be presented.
Alekseev, Oleg; Mineev-Weinstein, Mark
2016-12-01
A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all possible scenarios leading to the same final shape. The classical point for the action, defined as a minus logarithm of the growth probability, describes the most probable scenario and reproduces the Laplacian growth equation, which embraces numerous fundamental free boundary dynamics in nonequilibrium physics. For nonclassical scenarios we introduce virtual point sources, in which presence the action becomes the Kullback-Leibler entropy. Strikingly, this entropy is shown to be the sum of electrostatic energies of layers grown per elementary time unit. Hence the growth probability of the presented nonequilibrium process obeys the Gibbs-Boltzmann statistics, which, as a rule, is not applied out from equilibrium. Each layer's probability is expressed as a product of simple factors in an auxiliary complex plane after a properly chosen conformal map. The action at this plane is a sum of Robin functions, which solve the Liouville equation. At the end we establish connections of our theory with the τ function of the integrable Toda hierarchy and with the Liouville theory for noncritical quantum strings.
Stochastic analysis of biochemical systems
Anderson, David F
2015-01-01
This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations, and elementary probability and who are well-motivated by the applications will find this book of interest. David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other ar...
Stochastic gravity: beyond semiclassical gravity
Energy Technology Data Exchange (ETDEWEB)
Verdaguer, E [Departament de Fisica Fonamental and CER en Astrofisica, Fisica de Particules i Cosmologia, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain)
2007-05-15
The back-reaction of a classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equation, which has the expectation value of the quantum matter fields stress tensor as a source. The semiclassical theory may be obtained from the quantum field theory of gravity interacting with N matter fields in the large N limit. This theory breaks down when the fields quantum fluctuations are important. Stochastic gravity goes beyond the semiclassical limit and allows for a systematic and self-consistent description of the metric fluctuations induced by these quantum fluctuations. The correlation functions of the metric fluctuations obtained in stochastic gravity reproduce the correlation functions in the quantum theory to leading order in an 1/N expansion. Two main applications of stochastic gravity are discussed. The first, in cosmology, to obtain the spectrum of primordial metric perturbations induced by the inflaton fluctuations, even beyond the linear approximation. The second, in black hole physics, to study the fluctuations of the horizon of an evaporating black hole.
Nonlinear and Stochastic Morphological Segregation
Blanton, M R
1999-01-01
I perform a joint counts-in-cells analysis of galaxies of different spectral types using the Las Campanas Redshift Survey (LCRS). Using a maximum-likelihood technique to fit for the relationship between the density fields of early- and late-type galaxies, I find a relative linear bias of $b=0.76\\pm 0.02$. This technique can probe the nonlinearity and stochasticity of the relationship as well. However, the degree to which nonlinear and stochastic fits improve upon the linear fit turns out to depend on the redshift range in question. In particular, there seems to be a systematic difference between the high- and low-redshift halves of the data (respectively, further than and closer than $cz\\approx 36,000$ km/s); all of the signal of stochasticity and nonlinearity comes from the low-redshift portion. Analysis of mock catalogs shows that the peculiar geometry and variable flux limits of the LCRS do not cause this effect. I speculate that the central surface brightness selection criteria of the LCRS may be responsi...
Mechanical Autonomous Stochastic Heat Engine
Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara
2016-07-01
Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Stochastic dynamics for reinfection by transmitted diseases
Barros, Alessandro S.; Pinho, Suani T. R.
2017-06-01
The use of stochastic models to study the dynamics of infectious diseases is an important tool to understand the epidemiological process. For several directly transmitted diseases, reinfection is a relevant process, which can be expressed by endogenous reactivation of the pathogen or by exogenous reinfection due to direct contact with an infected individual (with smaller reinfection rate σ β than infection rate β ). In this paper, we examine the stochastic susceptible, infected, recovered, infected (SIRI) model simulating the endogenous reactivation by a spontaneous reaction, while exogenous reinfection by a catalytic reaction. Analyzing the mean-field approximations of a site and pairs of sites, and Monte Carlo (MC) simulations for the particular case of exogenous reinfection, we obtained continuous phase transitions involving endemic, epidemic, and no transmission phases for the simple approach; the approach of pairs is better to describe the phase transition from endemic phase (susceptible, infected, susceptible (SIS)-like model) to epidemic phase (susceptible, infected, and removed or recovered (SIR)-like model) considering the comparison with MC results; the reinfection increases the peaks of outbreaks until the system reaches endemic phase. For the particular case of endogenous reactivation, the approach of pairs leads to a continuous phase transition from endemic phase (SIS-like model) to no transmission phase. Finally, there is no phase transition when both effects are taken into account. We hope the results of this study can be generalized for the susceptible, exposed, infected, and removed or recovered (SEIRIE) model, for which the state exposed (infected but not infectious), describing more realistically transmitted diseases such as tuberculosis. In future work, we also intend to investigate the effect of network topology on phase transitions when the SIRI model describes both transmitted diseases (σ 1 ).
Stochastic Multi-Resonance in a Linear System Driven by Multiplicative Polynomial Dichotomous Noise
Institute of Scientific and Technical Information of China (English)
ZHANG Lu; ZHONG Su-Chuan; PENG Hao; LUO Mao-Kang
2011-01-01
We investigate stochastic resonance in a linear system subjected to multiplicative noise that is a polynomial function of colored noise. Using the stochastic averaging method, the analytical expression of the output signal-to-noise ratio (SNR) is derived. Theoretical analysis and numerical results show that the output SNR is a nonmonotonic function of both the noise intensity and the correlation rate. Moreover, the phenomoenon of stochastic multi-resonance (SMR) is found, which is not observed in conventional linear systems driven by multiplicative noise with only a linear term.%@@ We investigate stochastic resonance in a linear system subjected to multiplicative noise that is a polynomial function of colored noise.Using the stochastic averaging method,the analytical expression of the output signalto-noise ratio(SNR)is derived.Theoretical analysis and numerical results show that the output SNR is a nonmonotonic function of both the noise intensity and the correlation rate.Moreover,the phenomoenon of stochastic multi-resonance(SMR)is found,which is not observed in conventional linear systems driven by multiplicative
Brownian motion, martingales, and stochastic calculus
Le Gall, Jean-François
2016-01-01
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-01-01
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400--407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305--320]. The application of the trajectory averaging estimator to other stochastic approximation MCMC algorithms, for example, a stochastic approximation MLE al...
Intrinsic Simulations between Stochastic Cellular Automata
Directory of Open Access Journals (Sweden)
Pablo Arrighi
2012-08-01
Full Text Available The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between deterministic cellular automata, to the non-deterministic and stochastic settings. We then provide explicit tools to prove or disprove the existence of such a simulation between two stochastic cellular automata, even though the intrinsic simulation relation is shown to be undecidable in dimension two and higher. The key result behind this is the caracterization of equality of stochastic global maps by the existence of a coupling between the random sources. We then prove that there is a universal non-deterministic cellular automaton, but no universal stochastic cellular automaton. Yet we provide stochastic cellular automata achieving optimal partial universality.
Consistent Stochastic Modelling of Meteocean Design Parameters
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Sterndorff, M. J.
2000-01-01
Consistent stochastic models of metocean design parameters and their directional dependencies are essential for reliability assessment of offshore structures. In this paper a stochastic model for the annual maximum values of the significant wave height, and the associated wind velocity, current...... velocity, and water level is presented. The stochastic model includes statistical uncertainty and dependency between the four stochastic variables. Further, a new stochastic model for annual maximum directional significant wave heights is presented. The model includes dependency between the maximum wave...... height from neighboring directional sectors. Numerical examples are presented where the models are calibrated using the Maximum Likelihood method to data from the central part of the North Sea. The calibration of the directional distributions is made such that the stochastic model for the omnidirectional...
Stochastic synaptic plasticity with memristor crossbar arrays
Naous, Rawan
2016-11-01
Memristive devices have been shown to exhibit slow and stochastic resistive switching behavior under low-voltage, low-current operating conditions. Here we explore such mechanisms to emulate stochastic plasticity in memristor crossbar synapse arrays. Interfaced with integrate-and-fire spiking neurons, the memristive synapse arrays are capable of implementing stochastic forms of spike-timing dependent plasticity which parallel mean-rate models of stochastic learning with binary synapses. We present theory and experiments with spike-based stochastic learning in memristor crossbar arrays, including simplified modeling as well as detailed physical simulation of memristor stochastic resistive switching characteristics due to voltage and current induced filament formation and collapse. © 2016 IEEE.
Kulasiri, Don
2002-01-01
Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas ...
Allen, B; Allen, Bruce; Romano, Joseph D.
1999-01-01
We analyze the signal processing required for the optimal detection of a stochastic background of gravitational radiation using laser interferometric detectors. Starting with basic assumptions about the statistical properties of a stochastic gravity-wave background, we derive expressions for the optimal filter function and signal-to-noise ratio for the cross-correlation of the outputs of two gravity-wave detectors. Sensitivity levels required for detection are then calculated. Issues related to: (i) calculating the signal-to-noise ratio for arbitrarily large stochastic backgrounds, (ii) performing the data analysis in the presence of nonstationary detector noise, (iii) combining data from multiple detector pairs to increase the sensitivity of a stochastic background search, (iv) correlating the outputs of 4 or more detectors, and (v) allowing for the possibility of correlated noise in the outputs of two detectors are discussed. We briefly describe a computer simulation which mimics the generation and detectio...
Structure and Properties of Hughston's Stochastic Extension of the Schrödinger Equation
Adler, Stephen Louis; Adler, Stephen L.; Horwitz, Lawrence P.
1999-01-01
Hughston has recently proposed a stochastic extension of the Schrödinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston's equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston's equation to earlier work on norm-preserving stochastic equations, and show that Hughston's equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston's, suffices to give an objective interpretation of the measurement process in quantum mechanics.
Pham, Huyen
2010-01-01
We formulate and investigate a general stochastic control problem under a progressive enlargement of filtration. The global information is enlarged from a reference filtration and the knowledge of multiple random times together with associated marks when they occur. By working under a density hypothesis on the conditional joint distribution of the random times and marks, we prove a decomposition of the original stochastic control problem under the global filtration into classical stochastic control problems under the reference filtration, which are determined in a finite backward induction. Our method revisits and extends in particular stochastic control of diffusion processes with finite number of jumps. This study is motivated by optimization problems arising in default risk management, and we provide applications of our decomposition result for the indifference pricing of defaultable claims, and the optimal investment under bilateral counterparty risk. The solutions are expressed in terms of BSDEs involvin...
Energy Technology Data Exchange (ETDEWEB)
Kryvohuz, Maksym, E-mail: mkryvohu@uci.edu; Mukamel, Shaul [Chemistry Department, University of California, Irvine, California 92697-2025 (United States)
2015-06-07
Generalized nonlinear response theory is presented for stochastic dynamical systems. Experiments in which multiple measurements of dynamical quantities are used along with multiple perturbations of parameters of dynamical systems are described by generalized response functions (GRFs). These constitute a new type of multidimensional measures of stochastic dynamics either in the time or the frequency domains. Closed expressions for GRFs in stochastic dynamical systems are derived and compared with numerical non-equilibrium simulations. Several types of perturbations are considered: impulsive and periodic perturbations of temperature and impulsive perturbations of coordinates. The present approach can be used to study various types of stochastic processes ranging from single-molecule conformational dynamics to chemical kinetics of finite-size reactors such as biocells.
Quadratic stabilization for uncertain stochastic systems
Institute of Scientific and Technical Information of China (English)
Jun'e FENG; Weihai ZHANG
2005-01-01
This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.
Ambit processes and stochastic partial differential equations
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole; Benth, Fred Espen; Veraart, Almut
Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between...... ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis....
Stochastic Descent Analysis of Representation Learning Algorithms
Golden, Richard M.
2014-01-01
Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic approximation theorems typically possess assumptions which are difficult to communicate and verify. This paper presents a new stochastic approximation theorem for state-dependent noise with easily verifiable assumptions applicable to the analysis and design of import...
Impulsive control of stochastic system under the sense of stochastic asymptotical stability
Institute of Scientific and Technical Information of China (English)
Niu Yu-Jun; Ma Ge
2010-01-01
This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations,and establishes a comparison theory to ensure the trivial solution's stochastic asymptotical stability.From the comparison theory,it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterimpulsive control method,and numerical simulations are employed to verify the feasibility of this method.
Efficient numerical integrators for stochastic models
De Fabritiis, G; Español, P; Coveney, P V
2006-01-01
The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.
A minicourse on stochastic partial differential equations
Rassoul-Agha, Firas
2009-01-01
In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations. The goal of this minicourse was to introduce graduate students and recent Ph.D.s to various modern topics in stochastic PDEs, and to bring together several experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic partial differential equations. This monograph contains an up-to-date compilation of many of those lectures. Particular emphasis is paid to showcasing central ideas and displaying some of the many deep connections between the mentioned disciplines, all the time keeping a realistic pace for the student of the subject.
Stochastic versus deterministic systems of differential equations
Ladde, G S
2003-01-01
This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/flu
Introduction to stochastic models in biology
DEFF Research Database (Denmark)
Ditlevsen, Susanne; Samson, Adeline
2013-01-01
be exposed to influences that are not completely understood or not feasible to model explicitly. Ignoring these phenomena in the modeling may affect the analysis of the studied biological systems. Therefore there is an increasing need to extend the deterministic models to models that embrace more complex...... variations in the dynamics. A way of modeling these elements is by including stochastic influences or noise. A natural extension of a deterministic differential equations model is a system of stochastic differential equations (SDEs), where relevant parameters are modeled as suitable stochastic processes......, or stochastic processes are added to the driving system equations. This approach assumes that the dynamics are partly driven by noise....
ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin
2006-01-01
Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of t he solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.
Diffusion with stochastic resetting at power-law times
Nagar, Apoorva; Gupta, Shamik
2016-06-01
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals τ distributed as a power law ˜τ-(1 +α );α >0 ? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for α 1 . The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal α that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.
Modelling the SOS Response by Semi-Stochastic Simulation
Institute of Scientific and Technical Information of China (English)
NI Ming; WANG Si-Yuan; OUYANG Qi
2008-01-01
The SOS (save our soul) response induced by DNA damage in bacteria E coli has raised a great interests in biophysics and has been extensively studied. Previously we have developed a stochastic simulation model to explain the oscillatory-like modulation of SOS gene expression observed in experiment. Here we present an improved semi-stochastic model which has higher simulation efficiency, taking into account the updated knowledge about SOS response. The improved model suggests that frequency of the modulation is controlled by the negative feedback in the system. DNA polymerase V, the key enzyme for error-prone translesion synthesis during SOS response, plays a major role in closing up the negative feedback. It is also indicated that the correlation between the modulation and cellular growth observed in experiment is due to DNA damage induced slowing down of transcription and translation.
Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition
Aman, Auguste
2010-01-01
This paper is an attempt to extend the notion of viscosity solution to nonlinear stochastic partial differential integral equations with nonlinear Neumann boundary condition. Using the recently developed theory on generalized backward doubly stochastic differential equations driven by a L\\'evy process, we prove the existence of the stochastic viscosity solution, and further extend the nonlinear Feynman-Kac formula.
Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility
van Haastrecht, A.; Lord, R.; Pelsser, A.; Schrager, D.
2009-01-01
We consider the pricing of long-dated insurance contracts under stochastic interest rates and stochastic volatility. In particular, we focus on the valuation of insurance options with long-term equity or foreign exchange exposures. Our modeling framework extends the stochastic volatility model of Sc
Wei, Katy; Moinat, Maxim; Maarleveld, Timo R; Bruggeman, Frank J
2014-07-29
Signal transduction by prokaryotes almost exclusively relies on two-component systems for sensing and responding to (extracellular) signals. Here, we use stochastic models of two-component systems to better understand the impact of stochasticity on the fidelity and robustness of signal transmission, the outcome of autoregulatory gene expression and the influence of cell growth and division. We report that two-component systems are remarkably robust against copy number fluctuations of the signalling proteins they are composed of, which enhances signal transmission fidelity. Furthermore, we find that due to stochasticity these systems can get locked in an active state for extended time periods when (initially high) signal levels drop to zero. This behaviour can contribute to a bet-hedging adaptation strategy, aiding survival in fluctuating environments. Additionally, autoregulatory gene expression can cause two-component systems to become bistable at realistic parameter values. As a result, two sub-populations of cells can co-exist-active and inactive cells, which contributes to fitness in unpredictable environments. Bistability proved robust with respect to cell growth and division, and is tunable by the growth rate. In conclusion, our results indicate how single cells can cope with the inevitable stochasticity occurring in the activity of their two-component systems. They are robust to disadvantageous fluctuations that scramble signal transduction and they exploit beneficial stochasticity that generates fitness-enhancing heterogeneity across an isogenic population of cells.
Controllability of quasilinear stochastic evolution equations in Hilbert spaces
Directory of Open Access Journals (Sweden)
P. Balasubramaniam
2001-01-01
Full Text Available Controllability of the quasilinear stochastic evolution equation is studied using semigroup theory and a stochastic version of the well known fixed point theorem. An application to stochastic partial differential equations is given.
A note on maximal estimates for stochastic convolutions
Veraar, M.; Weis, L.
2011-01-01
In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.
Constrained Stochastic Extended Redundancy Analysis.
DeSarbo, Wayne S; Hwang, Heungsun; Stadler Blank, Ashley; Kappe, Eelco
2015-06-01
We devise a new statistical methodology called constrained stochastic extended redundancy analysis (CSERA) to examine the comparative impact of various conceptual factors, or drivers, as well as the specific predictor variables that contribute to each driver on designated dependent variable(s). The technical details of the proposed methodology, the maximum likelihood estimation algorithm, and model selection heuristics are discussed. A sports marketing consumer psychology application is provided in a Major League Baseball (MLB) context where the effects of six conceptual drivers of game attendance and their defining predictor variables are estimated. Results compare favorably to those obtained using traditional extended redundancy analysis (ERA).
Boundary layers in stochastic thermodynamics.
Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo
2012-02-01
We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give an alternative interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).
Stochastic noise in splicing machinery
Melamud, Eugene; Moult, John
2009-01-01
The number of known alternative human isoforms has been increasing steadily with the amount of available transcription data. To date, over 100 000 isoforms have been detected in EST libraries, and at least 75% of human genes have at least one alternative isoform. In this paper, we propose that most alternative splicing events are the result of noise in the splicing process. We show that the number of isoforms and their abundance can be predicted by a simple stochastic noise model that takes i...
Mathematical statistics and stochastic processes
Bosq, Denis
2013-01-01
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today's practitioners.Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and rob
Stochastic models for atmospheric dispersion
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2003-01-01
Simple stochastic differential equation models have been applied by several researchers to describe the dispersion of tracer particles in the planetary atmospheric boundary layer and to form the basis for computer simulations of particle paths. To obtain the drift coefficient, empirical vertical...... velocity distributions that depend on height above the ground both with respect to standard deviation and skewness are substituted into the stationary Fokker/Planck equation. The particle position distribution is taken to be uniform *the well/mixed condition( and also a given dispersion coefficient...
Stochastic singular optics (Conference paper)
CSIR Research Space (South Africa)
Roux, FS
2014-09-01
Full Text Available optics, stochastic optical field, optical vortex density, topological charge density 1. INTRODUCTION Speckle patterns are a typical phenomenon in random optical fields, resulting from coherent light being scattered from a random rough surface. It has been... and their topological charges are mixed such that neighbouring vortices tend to have opposite topological charge.11 As a result, the topological charge density of a speckle field is on average zero.14, 16 On the other hand, the vortex density is not zero, it is given...
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2012-01-01
This book provides a unique and balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and
Stochastic Model of Microtubule Dynamics
Hryniv, Ostap; Martínez Esteban, Antonio
2017-10-01
We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth (v>0) and the shrinking (v<0) regimes of the dynamics.
Stochastic modeling analysis and simulation
Nelson, Barry L
1995-01-01
A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Suitable for advanced undergraduates and graduate-level industrial engineers and management science majors, it proposes modeling systems in terms of their simulation, regardless of whether simulation is employed for analysis. Beginning with a view of the conditions that permit a mathematical-numerical analysis, the text explores Poisson and renewal processes, Markov chains in discrete and continuous time, se
Dynamic analysis of stochastic transcription cycles.
Directory of Open Access Journals (Sweden)
Claire V Harper
2011-04-01
Full Text Available In individual mammalian cells the expression of some genes such as prolactin is highly variable over time and has been suggested to occur in stochastic pulses. To investigate the origins of this behavior and to understand its functional relevance, we quantitatively analyzed this variability using new mathematical tools that allowed us to reconstruct dynamic transcription rates of different reporter genes controlled by identical promoters in the same living cell. Quantitative microscopic analysis of two reporter genes, firefly luciferase and destabilized EGFP, was used to analyze the dynamics of prolactin promoter-directed gene expression in living individual clonal and primary pituitary cells over periods of up to 25 h. We quantified the time-dependence and cyclicity of the transcription pulses and estimated the length and variation of active and inactive transcription phases. We showed an average cycle period of approximately 11 h and demonstrated that while the measured time distribution of active phases agreed with commonly accepted models of transcription, the inactive phases were differently distributed and showed strong memory, with a refractory period of transcriptional inactivation close to 3 h. Cycles in transcription occurred at two distinct prolactin-promoter controlled reporter genes in the same individual clonal or primary cells. However, the timing of the cycles was independent and out-of-phase. For the first time, we have analyzed transcription dynamics from two equivalent loci in real-time in single cells. In unstimulated conditions, cells showed independent transcription dynamics at each locus. A key result from these analyses was the evidence for a minimum refractory period in the inactive-phase of transcription. The response to acute signals and the result of manipulation of histone acetylation was consistent with the hypothesis that this refractory period corresponded to a phase of chromatin remodeling which significantly
A stochastic indicator for sovereign debt sustainability
Lukkezen, J.H.J.; Rojas-Romagosa, Hugo
2016-01-01
We propose a stochastic indicator to assess government debt sustainability. This indicator combines the effect of economic uncertainty –represented by stochastic simulations of interest and growth rates– with the expected fiscal response that provides information on the long-term country specific at
Stochastic models for uncertain flexible systems
Curtain, R.F.; Kotelenez, P.
1987-01-01
If a spectral operator is perturbed by an infinite-dimensional white noise process, it generates a stochastic evolution operator which has well defined second order properties. This type of stochastic bilinear spectral evolution equation may be used to model uncertainty of the higher modes in flexib
Safety Analysis of Stochastic Dynamical Systems
DEFF Research Database (Denmark)
Sloth, Christoffer; Wisniewski, Rafael
2015-01-01
This paper presents a method for verifying the safety of a stochastic system. In particular, we show how to compute the largest set of initial conditions such that a given stochastic system is safe with probability p. To compute the set of initial conditions we rely on the moment method that via...
From Complex to Simple: Interdisciplinary Stochastic Models
Mazilu, D. A.; Zamora, G.; Mazilu, I.
2012-01-01
We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…
Parallel transports associated to stochastic holonomies
Institute of Scientific and Technical Information of China (English)
CHEN; Shiping(陈世平); XIANG; Kainan(向开南)
2002-01-01
A stochastic holonomy along a loop obtained from the OU process on the path space over acompact Riemannian manifold is computed. The result shows that the stochastic holonomy just gives theparallel transport with respect to the Markov connection along the OU process on the path space.
Integration of stochastic generation in power systems
Papaefthymiou, G.
2007-01-01
Stochastic Generation is the electrical power production by the use of an uncontrollable prime energy mover, corresponding mainly to renewable energy sources. For the large-scale integration of stochastic generation in power systems, methods are necessary for the modeling of power generation
Stochastic stabilization analysis of networked control systems
Institute of Scientific and Technical Information of China (English)
Ma Changlin; Fang Huajing
2007-01-01
Considering the stochastic delay problems existing in networked control systems, a new control mode is proposed for networked control systems whose delay is longer than a sampling period. Under the control mode, the mathematical model of such a system is established. A stochastic stabilization condition for the system is given. The maximum delay can be derived from the stabilization condition.
Integration of stochastic generation in power systems
Papaefthymiou, G.
2007-01-01
Stochastic Generation is the electrical power production by the use of an uncontrollable prime energy mover, corresponding mainly to renewable energy sources. For the large-scale integration of stochastic generation in power systems, methods are necessary for the modeling of power generation uncerta
Stochastic Forcing for Ocean Uncertainty Prediction
2013-09-30
shallow water waves governed by Korteweg-de Vries ( KdV ) dynamics with stochastic forcing. Uncertain Boundary Conditions and DO Equations: A...schemes to time-integrate shallow water surface waves governed by KdV equations with external stochastic forcing. We find that the DO scheme is
Modeling Departure Time Choice with Stochastic Networks
Li, H.; Bliemer, M.C.J.; Bovy, P.H.L.
2010-01-01
Stochastic supply and fluctuating travel demand lead to stochasticity in travel times and travel costs experienced by travelers from time to time within a day and at the same time from day to day. Many studies show that travel time un-reliability has significant impacts on traveler’s choice behavior
Stochastic Modelling and Analysis of Warehouse Operations
Y. Gong (Yeming)
2009-01-01
textabstractThis thesis has studied stochastic models and analysis of warehouse operations. After an overview of stochastic research in warehouse operations, we explore the following topics. Firstly, we search optimal batch sizes in a parallel-aisle warehouse with online order arrivals. We employ a
Integration of stochastic generation in power systems
Papaefthymiou, G.
2007-01-01
Stochastic Generation is the electrical power production by the use of an uncontrollable prime energy mover, corresponding mainly to renewable energy sources. For the large-scale integration of stochastic generation in power systems, methods are necessary for the modeling of power generation uncerta
Products of Generalized Stochastic Sarymsakov Matrices
Xia, Weiguo; Liu, Ji; Cao, Ming; Johansson, Karl; Basar, Tamer
2015-01-01
In the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of stochastic Sarymsakov matrices is the largest known subset (i) that is closed under matrix multiplication and (ii) the inﬁnitely long left-product of the elements from a compact subset converges to a rank-one matrix. In
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique ap...
Variational principles for stochastic fluid dynamics.
Holm, Darryl D
2015-04-08
This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler-Boussinesq and quasi-geostropic approximations.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Multiple Fields in Stochastic Inflation
Assadullahi, Hooshyar; Noorbala, Mahdiyar; Vennin, Vincent; Wands, David
2016-01-01
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary $e$-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of $e$-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the...
Stochastic Methods for Aircraft Design
Pelz, Richard B.; Ogot, Madara
1998-01-01
The global stochastic optimization method, simulated annealing (SA), was adapted and applied to various problems in aircraft design. The research was aimed at overcoming the problem of finding an optimal design in a space with multiple minima and roughness ubiquitous to numerically generated nonlinear objective functions. SA was modified to reduce the number of objective function evaluations for an optimal design, historically the main criticism of stochastic methods. SA was applied to many CFD/MDO problems including: low sonic-boom bodies, minimum drag on supersonic fore-bodies, minimum drag on supersonic aeroelastic fore-bodies, minimum drag on HSCT aeroelastic wings, FLOPS preliminary design code, another preliminary aircraft design study with vortex lattice aerodynamics, HSR complete aircraft aerodynamics. In every case, SA provided a simple, robust and reliable optimization method which found optimal designs in order 100 objective function evaluations. Perhaps most importantly, from this academic/industrial project, technology has been successfully transferred; this method is the method of choice for optimization problems at Northrop Grumman.
Single-Molecule Stochastic Resonance
Directory of Open Access Journals (Sweden)
K. Hayashi
2012-08-01
Full Text Available Stochastic resonance (SR is a well-known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic (random or probabilistic noise. Here we carry out the first experimental study of SR in single DNA hairpins which exhibit cooperatively transitions from folded to unfolded configurations under the action of an oscillating mechanical force applied with optical tweezers. By varying the frequency of the force oscillation, we investigate the folding and unfolding kinetics of DNA hairpins in a periodically driven bistable free-energy potential. We measure several SR quantifiers under varied conditions of the experimental setup such as trap stiffness and length of the molecular handles used for single-molecule manipulation. We find that a good quantifier of the SR is the signal-to-noise ratio (SNR of the spectral density of measured fluctuations in molecular extension of the DNA hairpins. The frequency dependence of the SNR exhibits a peak at a frequency value given by the resonance-matching condition. Finally, we carry out experiments on short hairpins that show how SR might be useful for enhancing the detection of conformational molecular transitions of low SNR.
Single-molecule stochastic resonance
Hayashi, K; Manosas, M; Huguet, J M; Ritort, F; 10.1103/PhysRevX.2.031012
2012-01-01
Stochastic resonance (SR) is a well known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic noise. Here we carry out the first experimental study of SR in single DNA hairpins which exhibit cooperatively folding/unfolding transitions under the action of an applied oscillating mechanical force with optical tweezers. By varying the frequency of the force oscillation, we investigated the folding/unfolding kinetics of DNA hairpins in a periodically driven bistable free-energy potential. We measured several SR quantifiers under varied conditions of the experimental setup such as trap stiffness and length of the molecular handles used for single-molecule manipulation. We find that the signal-to-noise ratio (SNR) of the spectral density of measured fluctuations in molecular extension of the DNA hairpins is a good quantifier of the SR. The frequency dependence of the SNR exhibits a peak at a frequency value given by the resonance match...
Energy Technology Data Exchange (ETDEWEB)
Laslett, L. Jackson.
1974-05-01
Detailed examination of computed particle trajectories has revealed a complexity and disorder that is of increasing interest to accelerator specialists. To introduce this topic, the author would like you to consider for a moment the analysis of synchrotron oscillations for a particle in a coasting beam, regarded as a problem in one degree of freedom. A simple analysis replaces the electric field of the RF-v cavity system by a traveling wave, having the speed of a synchronous reference particle, and leads to a pair of differential equations of the form dy/dn = -K sin {pi}x, (1A) where y measures the fractional departure of energy from the reference value {pi}x measures the electrical phase angle at which the particle traverses the cavity, and K is proportional to the cavity voltage; and dx/dn = {lambda}{prime}y, (1b) in which {lambda}{prime} is proportional to the change of revolution period with respect to particle energy. It will be recognized that these equations can be derived from a Hamiltonian function H = (1/2){lambda}{prime}y{sup 2}-(K/{pi})cos {pi}x. (2) Because this Hamiltonian function does not contain the independent variable explicitly, it will constitute a constant of the motion and possible trajectories in the x,y phase space will be just the curves defined by H = Constant, namely the familiar simple curves in phase space that are characteristic of a physical (non-linear) pendulum.
Analytic framework for a stochastic binary biological switch
Innocentini, Guilherme C. P.; Guiziou, Sarah; Bonnet, Jerome; Radulescu, Ovidiu
2016-12-01
We propose and solve analytically a stochastic model for the dynamics of a binary biological switch, defined as a DNA unit with two mutually exclusive configurations, each one triggering the expression of a different gene. Such a device has the potential to be used as a memory unit for biological computing systems designed to operate in noisy environments. We discuss a recent implementation of this switch in living cells, the recombinase addressable data (RAD) module. In order to understand the behavior of a RAD module we compute the exact time-dependent joint distribution of the two expressed genes starting in one state and evolving to another asymptotic state. We consider two operating regimes of the RAD module, a fast and a slow stochastic switching regime. The fast regime is aggregative and produces unimodal distributions, whereas the slow regime is separative and produces bimodal distributions. Both regimes can serve to prepare pure memory states when all cells are expressing the same gene. The slow regime can also separate mixed states by producing two subpopulations, each one expressing a different gene. Compared to the genetic toggle switch based on positive feedback, the RAD module ensures more rapid memory operations for the same quality of the separation between binary states. Our model provides a simplified phenomenological framework for studying RAD memory devices and our analytic solution can be further used to clarify theoretical concepts in biocomputation and for optimal design in synthetic biology.
Modelling and application of stochastic processes
1986-01-01
The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...
A Temporal Approach to Stochastic Network Calculus
Xie, Jing; Xie, Min
2011-01-01
Stochastic network calculus is a newly developed theory for stochastic service guarantee analysis of computer networks. In the current stochastic network calculus literature, its fundamental models are based on the cumulative amount of traffic or cumulative amount of service. However, there are network scenarios where direct application of such models is difficult. This paper presents a temporal approach to stochastic network calculus. The key idea is to develop models and derive results from the time perspective. Particularly, we define traffic models and service models based on the cumulative packet inter-arrival time and the cumulative packet service time, respectively. Relations among these models as well as with the existing models in the literature are established. In addition, we prove the basic properties of the proposed models, such as delay bound and backlog bound, output characterization, concatenation property and superposition property. These results form a temporal stochastic network calculus an...
Some Recent Developments in Ambit Stochastics
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Hedevang, Emil; Schmiegel, Jürgen
Some of the recent developments in the rapidly expanding field of Ambit Stochastics are here reviewed. After a brief recall of the framework of Ambit Stochastics three topics are considered: (i) Methods of modelling and inference for volatility/intermittency processes and fields (ii) Universal la...... in turbulence and finance in relation to temporal processes (iii) Stochastic integration for time changed volatility modulated Levy-driven Volterra processes.......Some of the recent developments in the rapidly expanding field of Ambit Stochastics are here reviewed. After a brief recall of the framework of Ambit Stochastics three topics are considered: (i) Methods of modelling and inference for volatility/intermittency processes and fields (ii) Universal laws...
Evaluation of Uncertainty in Runoff Analysis Incorporating Theory of Stochastic Process
Yoshimi, Kazuhiro; Wang, Chao-Wen; Yamada, Tadashi
2015-04-01
The aim of this paper is to provide a theoretical framework of uncertainty estimate on rainfall-runoff analysis based on theory of stochastic process. SDE (stochastic differential equation) based on this theory has been widely used in the field of mathematical finance due to predict stock price movement. Meanwhile, some researchers in the field of civil engineering have investigated by using this knowledge about SDE (stochastic differential equation) (e.g. Kurino et.al, 1999; Higashino and Kanda, 2001). However, there have been no studies about evaluation of uncertainty in runoff phenomenon based on comparisons between SDE (stochastic differential equation) and Fokker-Planck equation. The Fokker-Planck equation is a partial differential equation that describes the temporal variation of PDF (probability density function), and there is evidence to suggest that SDEs and Fokker-Planck equations are equivalent mathematically. In this paper, therefore, the uncertainty of discharge on the uncertainty of rainfall is explained theoretically and mathematically by introduction of theory of stochastic process. The lumped rainfall-runoff model is represented by SDE (stochastic differential equation) due to describe it as difference formula, because the temporal variation of rainfall is expressed by its average plus deviation, which is approximated by Gaussian distribution. This is attributed to the observed rainfall by rain-gauge station and radar rain-gauge system. As a result, this paper has shown that it is possible to evaluate the uncertainty of discharge by using the relationship between SDE (stochastic differential equation) and Fokker-Planck equation. Moreover, the results of this study show that the uncertainty of discharge increases as rainfall intensity rises and non-linearity about resistance grows strong. These results are clarified by PDFs (probability density function) that satisfy Fokker-Planck equation about discharge. It means the reasonable discharge can be
Directory of Open Access Journals (Sweden)
Joshua T Dudman
2009-02-01
Full Text Available The transformation of synaptic input into patterns of spike output is a fundamental operation that is determined by the particular complement of ion channels that a neuron expresses. Although it is well established that individual ion channel proteins make stochastic transitions between conducting and non-conducting states, most models of synaptic integration are deterministic, and relatively little is known about the functional consequences of interactions between stochastically gating ion channels. Here, we show that a model of stellate neurons from layer II of the medial entorhinal cortex implemented with either stochastic or deterministically gating ion channels can reproduce the resting membrane properties of stellate neurons, but only the stochastic version of the model can fully account for perithreshold membrane potential fluctuations and clustered patterns of spike output that are recorded from stellate neurons during depolarized states. We demonstrate that the stochastic model implements an example of a general mechanism for patterning of neuronal output through activity-dependent changes in the probability of spike firing. Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization. Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization. Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.
Stochastic Heating, Differential Flow, and the Alpha-to-Proton Temperature Ratio in the Solar Wind
Chandran, B D G; Quataert, E; Kasper, J C; Isenberg, P A; Bourouaine, S
2013-01-01
We extend previous theories of stochastic ion heating to account for the motion of ions along the magnetic field. We derive an analytic expression for the ion-to-proton perpendicular temperature ratio in the solar wind for any ion species, assuming that stochastic heating is the dominant ion heating mechanism. This expression describes how this temperature ratio depends upon the average velocity of the ions along the magnetic field direction and the ratio of the parallel proton pressure to the magnetic pressure. We compare our model with previously published measurements of alpha particles and protons from the WIND spacecraft. We find that stochastic heating offers a promising explanation for these measurements when the fractional cross helicity and Alfven ratio at the proton-gyroradius scale have values that are broadly consistent with solar-wind measurements.
Analyzing stochastic transcription to elucidate the nucleoid's organization
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Chéron Angélique
2008-03-01
Full Text Available Abstract Background The processes of gene transcription, translation, as well as the reactions taking place between gene products, are subject to stochastic fluctuations. These stochastic events are being increasingly examined as it emerges that they can be crucial in the cell's survival. In a previous study we had examined the transcription patterns of two bacterial species (Escherichia coli and Bacillus subtilis to elucidate the nucleoid's organization. The basic idea is that genes that share transcription patterns, must share some sort of spatial relationship, even if they are not close to each other on the chromosome. We had found that picking any gene at random, its transcription will be correlated with genes at well-defined short – as well as long-range distances, leaving the explanation of the latter an open question. In this paper we study the transcription correlations when the only transcription taking place is stochastic, in other words, no active or "deterministic" transcription takes place. To this purpose we use transcription data of Sinorhizobium meliloti. Results Even when only stochastic transcription takes place, the co-expression of genes varies as a function of the distance between genes: we observe again the short-range as well as the regular, long-range correlation patterns. Conclusion We explain these latter with a model based on the physical constraints acting on the DNA, forcing it into a conformation of groups of a few successive large and transcribed loops, which are evenly spaced along the chromosome and separated by small, non-transcribed loops. We discuss the question about the link between shared transcription patterns and physiological relationship and come to the conclusion that when genes are distantly placed along the chromosome, the transcription correlation does not imply a physiological relationship.
Stochastic Time Models of Syllable Structure
Shaw, Jason A.; Gafos, Adamantios I.
2015-01-01
Drawing on phonology research within the generative linguistics tradition, stochastic methods, and notions from complex systems, we develop a modelling paradigm linking phonological structure, expressed in terms of syllables, to speech movement data acquired with 3D electromagnetic articulography and X-ray microbeam methods. The essential variable in the models is syllable structure. When mapped to discrete coordination topologies, syllabic organization imposes systematic patterns of variability on the temporal dynamics of speech articulation. We simulated these dynamics under different syllabic parses and evaluated simulations against experimental data from Arabic and English, two languages claimed to parse similar strings of segments into different syllabic structures. Model simulations replicated several key experimental results, including the fallibility of past phonetic heuristics for syllable structure, and exposed the range of conditions under which such heuristics remain valid. More importantly, the modelling approach consistently diagnosed syllable structure proving resilient to multiple sources of variability in experimental data including measurement variability, speaker variability, and contextual variability. Prospects for extensions of our modelling paradigm to acoustic data are also discussed. PMID:25996153
Multimodal Network Equilibrium with Stochastic Travel Times
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M. Meng
2014-01-01
Full Text Available The private car, unlike public traffic modes (e.g., subway, trolley running along dedicated track-ways, is invariably subject to various uncertainties resulting in travel time variation. A multimodal network equilibrium model is formulated that explicitly considers stochastic link capacity variability in the road network. The travel time of combined-mode trips is accumulated based on the concept of the mean excess travel time (METT which is a summation of estimated buffer time and tardy time. The problem is characterized by an equivalent VI (variational inequality formulation where the mode choice is expressed in a hierarchical logit structure. Specifically, the supernetwork theory and expansion technique are used herein to represent the multimodal transportation network, which completely represents the combined-mode trips as constituting multiple modes within a trip. The method of successive weighted average is adopted for problem solutions. The model and solution method are further applied to study the trip distribution and METT variations caused by the different levels of the road conditions. Results of numerical examples show that travelers prefer to choose the combined travel mode as road capacity decreases. Travelers with different attitudes towards risk are shown to exhibit significant differences when making travel choice decisions.
A Stochastic Cobweb Dynamical Model
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Serena Brianzoni
2008-01-01
_,__0__1, and the forward predictor with probability (1−, so that the expected price at time is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.
Parameterization of stochastic multiscale triads
Wouters, Jeroen; Iankov Dolaptchiev, Stamen; Lucarini, Valerio; Achatz, Ulrich
2016-11-01
We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast degrees of freedom. The weak coupling model reduction method results in general in a non-Markovian system; we therefore discuss the Markovianization of the system to allow for straightforward numerical integration. We compare the applied method to the equations obtained through homogenization in the limit of large timescale separation between slow and fast degrees of freedom. We numerically compare the ensemble spread from a fixed initial condition, correlation functions and exit times from a domain. The weak coupling method gives more accurate results in all test cases, albeit with a higher numerical cost.
Stochastic sensing through covalent interactions
Bayley, Hagan; Shin, Seong-Ho; Luchian, Tudor; Cheley, Stephen
2013-03-26
A system and method for stochastic sensing in which the analyte covalently bonds to the sensor element or an adaptor element. If such bonding is irreversible, the bond may be broken by a chemical reagent. The sensor element may be a protein, such as the engineered P.sub.SH type or .alpha.HL protein pore. The analyte may be any reactive analyte, including chemical weapons, environmental toxins and pharmaceuticals. The analyte covalently bonds to the sensor element to produce a detectable signal. Possible signals include change in electrical current, change in force, and change in fluorescence. Detection of the signal allows identification of the analyte and determination of its concentration in a sample solution. Multiple analytes present in the same solution may be detected.
Efficient Discretization of Stochastic Integrals
Fukasawa, Masaaki
2012-01-01
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.
Multiscale Stochastic Simulation and Modeling
Energy Technology Data Exchange (ETDEWEB)
James Glimm; Xiaolin Li
2006-01-10
Acceleration driven instabilities of fluid mixing layers include the classical cases of Rayleigh-Taylor instability, driven by a steady acceleration and Richtmyer-Meshkov instability, driven by an impulsive acceleration. Our program starts with high resolution methods of numerical simulation of two (or more) distinct fluids, continues with analytic analysis of these solutions, and the derivation of averaged equations. A striking achievement has been the systematic agreement we obtained between simulation and experiment by using a high resolution numerical method and improved physical modeling, with surface tension. Our study is accompanies by analysis using stochastic modeling and averaged equations for the multiphase problem. We have quantified the error and uncertainty using statistical modeling methods.
Improved bounds for stochastic matching
Li, Jian
2010-01-01
In this paper we study stochastic matching problems that are motivated by applications in online dating and kidney exchange programs. We consider two probing models: edge probing and matching probing. Our main result is an algorithm that finds a matching-probing strategy attaining a small constant approximation ratio. An interesting aspect of our approach is that we compare the cost our solution to the best edge-probing strategy. Thus, we indirectly show that the best matching-probing strategy is only a constant factor away from the best edge-probing strategy. Even though our algorithm has a slightly worse approximation ratio than a greedy algorithm for edge-probing strategies, we show that the two algorithms can be combined to get improved approximations.
Stochastic evolution of staying together.
Ghang, Whan; Nowak, Martin A
2014-11-07
Staying together means that replicating units do not separate after reproduction, but remain attached to each other or in close proximity. Staying together is a driving force for evolution of complexity, including the evolution of multi-cellularity and eusociality. We analyze the fixation probability of a mutant that has the ability to stay together. We assume that the size of the complex affects the reproductive rate of its units and the probability of staying together. We examine the combined effect of natural selection and random drift on the emergence of staying together in a finite sized population. The number of states in the underlying stochastic process is an exponential function of population size. We develop a framework for any intensity of selection and give closed form solutions for special cases. We derive general results for the limit of weak selection. Copyright © 2014 Elsevier Ltd. All rights reserved.
Stochastic control with rough paths
Energy Technology Data Exchange (ETDEWEB)
Diehl, Joscha [University of California San Diego (United States); Friz, Peter K., E-mail: friz@math.tu-berlin.de [TU & WIAS Berlin (Germany); Gassiat, Paul [CEREMADE, Université Paris-Dauphine, PSL Research University (France)
2017-04-15
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
Energy Technology Data Exchange (ETDEWEB)
Gutierrez T, C.; Hernandez A, O. [Instituto Nacional de Investigaciones Nucleares, A.P. 18-1027, 11801 Mexico D.F. (Mexico)
1999-07-01
The study of the different schemes of plasma heating by radiofrequency waves is a very actual problem related with the plasma heating in different machines and the particle acceleration mechanisms. In this work, it is obtained the expression for the temporal evolution of the energy absorbed in the cyclotron resonance of electrons where it is showed the stochastic character of the energy absorption. It is obtained the stochastic criteria in a magnetic configuration of an Ecr type plasma source. (Author)
Stochastic simulations of the tetracycline operon
Directory of Open Access Journals (Sweden)
Kaznessis Yiannis N
2011-01-01
Full Text Available Abstract Background The tetracycline operon is a self-regulated system. It is found naturally in bacteria where it confers resistance to antibiotic tetracycline. Because of the performance of the molecular elements of the tetracycline operon, these elements are widely used as parts of synthetic gene networks where the protein production can be efficiently turned on and off in response to the presence or the absence of tetracycline. In this paper, we investigate the dynamics of the tetracycline operon. To this end, we develop a mathematical model guided by experimental findings. Our model consists of biochemical reactions that capture the biomolecular interactions of this intriguing system. Having in mind that small biological systems are subjects to stochasticity, we use a stochastic algorithm to simulate the tetracycline operon behavior. A sensitivity analysis of two critical parameters embodied this system is also performed providing a useful understanding of the function of this system. Results Simulations generate a timeline of biomolecular events that confer resistance to bacteria against tetracycline. We monitor the amounts of intracellular TetR2 and TetA proteins, the two important regulatory and resistance molecules, as a function of intrecellular tetracycline. We find that lack of one of the promoters of the tetracycline operon has no influence on the total behavior of this system inferring that this promoter is not essential for Escherichia coli. Sensitivity analysis with respect to the binding strength of tetracycline to repressor and of repressor to operators suggests that these two parameters play a predominant role in the behavior of the system. The results of the simulations agree well with experimental observations such as tight repression, fast gene expression, induction with tetracycline, and small intracellular TetR2 amounts. Conclusions Computer simulations of the tetracycline operon afford augmented insight into the
Stochastic regulator theory for a class of abstract wave equations
Balakrishnan, A. V.
1991-01-01
A class of steady-state stochastic regulator problems for abstract wave equations in a Hilbert space - of relevance to the problem of feedback control of large space structures using co-located controls/sensors - is studied. Both the control operator, as well as the observation operator, are finite-dimensional. As a result, the usual condition of exponential stabilizability invoked for existence of solutions to the steady-state Riccati equations is not valid. Fortunately, for the problems considered it turns out that strong stabilizability suffices. In particular, a closed form expression is obtained for the minimal (asymptotic) performance criterion as the control effort is allowed to grow without bound.
Quantum mechanics emerging from stochastic dynamics of virtual particles
Tsekov, R
2015-01-01
It is demonstrated how quantum mechanics emerges from the stochastic dynamics of force-carriers. It is shown that the quantum Moyal equation corresponds to some dynamic correlations between the momentum of a real particle and the position of a virtual particle, which are not present in classical mechanics. The new concept throws light on the physical meaning of quantum theory, showing that the Planck constant square is a second-second cross-cumulant. The novel approach to quantum systems is extended to the relativistic case and an expression is derived for the relativistic mass in the Wigner quantum phase-space.
Mona Lisa:. the Stochastic View and Fractality in Color Space
Pedram, Pouria; Jafari, G. R.
A painting consists of objects which are arranged in specific ways. The art of painting is drawing the objects, which can be considered as known trends, in an expressive manner. Detrended methods are suitable for characterizing the artistic works of the painter by eliminating trends. It means that the study of paintings, regardless of its apparent purpose, as a stochastic process. Multifractal detrended fluctuation analysis is applied to characterize the statistical properties of Mona Lisa, as an instance, to exhibit the fractality of the painting. The results show that Mona Lisa is a long-range correlated and almost behaves similar in various scales.
Effective cosmological constant induced by stochastic fluctuations of Newton's constant
de Cesare, Marco; Lizzi, Fedele; Sakellariadou, Mairi
2016-09-01
We consider implications of the microscopic dynamics of spacetime for the evolution of cosmological models. We argue that quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which is thus considered as a macroscopic effective dynamical quantity. Consistency with Riemannian geometry entails the presence of a time-dependent dark energy term in the modified field equations, which can be expressed in terms of the dynamical gravitational constant. We suggest that the late-time accelerated expansion of the Universe may be ascribed to quantum fluctuations in the geometry of spacetime rather than the vacuum energy from the matter sector.
Effective cosmological constant induced by stochastic fluctuations of Newton's constant
de Cesare, Marco; Sakellariadou, Mairi
2016-01-01
We consider implications of the microscopic dynamics of spacetime for the evolution of cosmological models. We argue that quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which is thus considered as a macroscopic effective dynamical quantity. Consistency with Riemannian geometry entails the presence of a time-dependent dark energy term in the modified field equations, which can be expressed in terms of the dynamical gravitational constant. We suggest that the late-time accelerated expansion of the Universe may be ascribed to quantum fluctuations in the geometry of spacetime rather than the vacuum energy from the matter sector.
Stochastic algorithms for computing means of probability measures
Arnaudon, Marc; Phan, Anthony; Yang, Le
2011-01-01
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that the functional to minimize is regular around the p-mean, we prove that a natural renormalization of the inhomogeneous Markov chain converges in law into an inhomogeneous diffusion process. We give an explicit expression of this process, as well as its local characteristic.
Observability estimate and state observation problems for stochastic hyperbolic equations
2013-01-01
In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. By these inequalities, we study a state observation problem for stochastic hyperbolic equations. As a consequence, we also establish a unique continuation property for stochastic hyperbolic equations.
An Internal Observability Estimate for Stochastic Hyperbolic Equations
2015-01-01
This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate for forward stochastic hyperbolic equations in the $L^2$-space. Different from the deterministic case, a delicate analysis of the adaptedness for some stochastic processes is required in the stochastic setting.
On stochastic fractional Volterra equations in Hilbert space
Karczewska, Anna; Lizama, Carlos
2006-01-01
In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition for a stochastic convolution to be a strong solution to a stochastic Volterra equation.
Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations
Ren, Jiagang; Zhang, Xicheng
2008-01-01
We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear stochastic partial differential equations, such as stochastic porous medium equations and stochastic reaction diffusion equations with polynomial growth zero order term and $p$-Laplacian second order term.
Asymptotic analysis for functional stochastic differential equations
Bao, Jianhai; Yuan, Chenggui
2016-01-01
This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity. This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.
Quantum Stochastic Resonance in Electron Shelving
Huelga, S F
2000-01-01
Stochastic resonance shows that under some circumstances noise can enhance the response of a system to a periodic force. While this effect has been extensively investigated theoretically and demonstrated experimentally in classical systems, there is complete lack of experimental evidence within the purely quantum mechanical domain. Here we demonstrate that stochastic resonance can be exhibited in a single ion and would be experimentally observable using well mastered experimental techniques. We discuss the use of this scheme for the detection of the frequency difference of two lasers to demonstrate that stochastic resonance may have applications in precision measurements at the quantum limit.
Stochastic system identification in structural dynamics
Safak, Erdal
1988-01-01
Recently, new identification methods have been developed by using the concept of optimal-recursive filtering and stochastic approximation. These methods, known as stochastic identification, are based on the statistical properties of the signal and noise, and do not require the assumptions of current methods. The criterion for stochastic system identification is that the difference between the recorded output and the output from the identified system (i.e., the residual of the identification) should be equal to white noise. In this paper, first a brief review of the theory is given. Then, an application of the method is presented by using ambient vibration data from a nine-story building.
Stochastic transition model for pedestrian dynamics
Schultz, Michael
2012-01-01
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion model is extended by both a grid-based path planning and mid-range agent interaction component. The stochastic model proves its capabilities for a quantitative reproduction of the characteristic shape of the common fundamental diagram of pedestrian dynamics. Moreover, effects of self-organizing behavior are successfully reproduced. The stochastic cellular automata approach is found to be adequate with respect to uncertainties in human motion patterns, a feature previously held by artificial noise terms alone.
Stochastic Einstein equations with fluctuating volume
Dzhunushaliev, Vladimir
2016-01-01
We develop a simple model to study classical fields on the background of a fluctuating spacetime volume. It is applied to formulate the stochastic Einstein equations with a perfect-fluid source. We investigate the particular case of a stochastic Friedmann-Lema\\^itre-Robertson-Walker cosmology, and show that the resulting field equations can lead to solutions which avoid the initial big bang singularity. By interpreting the fluctuations as the result of the presence of a quantum spacetime, we conclude that classical singularities can be avoided even within a stochastic model that include quantum effects in a very simple manner.
Stochastic differential equations and diffusion processes
Ikeda, N
1989-01-01
Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sectio
Stochastic deformation of a thermodynamic symplectic structure
Kazinski, P. O.
2009-01-01
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation is analogous to the deformation of an algebra of observables such as deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transformations and gauge fields is given. An application of the formalism to a description of systems with distributed parameters in a local thermodynamic equilibrium is considered.
On stochastic motion in quantum mechanics
Schürmann, T
2003-01-01
We want to investigate the stochastic parameters, drift and diffusion, in F\\'enyes' and Nelson's approach of stochastic mechanics. In contrast to the postulate of a constant diffusion parameter, we consider coordinate dependent alternatives. Therefore, we assume that the trajectory of a particle can be described by a continuous stochastic process with space- and/or time-dependent diffusion. For an illustration of the main features that can be explained within this context, we examine the time-evolution of the free particle with the Gaussian (minimum-uncertainty) initial state and obtain a time-dependent diffusion $\\propto t$.
CAM Stochastic Volatility Model for Option Pricing
Directory of Open Access Journals (Sweden)
Wanwan Huang
2016-01-01
Full Text Available The coupled additive and multiplicative (CAM noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks of the model. We also derive an approximation for the characteristic function of the model.
Modeling and analysis of stochastic systems
Kulkarni, Vidyadhar G
2011-01-01
Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edi
Stochastic Control Model on Rent Seeking
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A continuous-time stochastic model is constructed to analyze how to control rent seeking behaviors. Using the stochastic optimization methods based on the modern risky theory, a unique positive solution to the dynamic model is derived. The effects of preference-related parameters on the optimal control level of rent seeking are discussed, and some policy measures are given. The results show that there exists a unique solution to the stochastic dynamic model under some macroeconomic assumptions, and that raising public expenditure may have reverse effects on rent seeking in an underdeveloped or developed economic environment.
Permanence of Stochastic Lotka-Volterra Systems
Liu, Meng; Fan, Meng
2017-04-01
This paper proposes a new definition of permanence for stochastic population models, which overcomes some limitations and deficiency of the existing ones. Then, we explore the permanence of two-dimensional stochastic Lotka-Volterra systems in a general setting, which models several different interactions between two species such as cooperation, competition, and predation. Sharp sufficient criteria are established with the help of the Lyapunov direct method and some new techniques. This study reveals that the stochastic noises play an essential role in the permanence and characterize the systems being permanent or not.
Selected papers on noise and stochastic processes
Wax, Nelson
1954-01-01
Six classic papers on stochastic process, selected to meet the needs of physicists, applied mathematicians, and engineers. Contents: 1.Chandrasekhar, S.: Stochastic Problems in Physics and Astronomy. 2. Uhlenbeck, G. E. and Ornstein, L. S.: On the Theory of the Browninan Motion. 3. Ming Chen Wang and Uhlenbeck, G. E.: On the Theory of the Browninan Motion II. 4. Rice, S. O.: Mathematical Analysis of Random Noise. 5. Kac, Mark: Random Walk and the Theory of Brownian Motion. 6. Doob, J. L.: The Brownian Movement and Stochastic Equations. Unabridged republication of the Dover reprint (1954). Pre
Statistical Methods for Stochastic Differential Equations
Kessler, Mathieu; Sorensen, Michael
2012-01-01
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a sp
The astrophysical gravitational wave stochastic background
Institute of Scientific and Technical Information of China (English)
Tania Regimbau
2011-01-01
A stochastic background of gravitational waves with astrophysical origins may have resulted from the superposition of a large number of unresolved sources since the beginning of stellar activity.Its detection would put very strong constraints on the physical properties of compact objects, the initial mass function and star formarion history.On the other hand, it could be a ‘noise' that would mask the stochastic background of its cosmological origin.We review the main astrophysical processes which are able to produce a stochastic background and discuss how they may differ from the primordial contribution in terms of statistical properties.Current detection methods are also presented.
Molecular logic behind the three-way stochastic choices that expand butterfly colour vision.
Perry, Michael; Kinoshita, Michiyo; Saldi, Giuseppe; Huo, Lucy; Arikawa, Kentaro; Desplan, Claude
2016-07-06
Butterflies rely extensively on colour vision to adapt to the natural world. Most species express a broad range of colour-sensitive Rhodopsin proteins in three types of ommatidia (unit eyes), which are distributed stochastically across the retina. The retinas of Drosophila melanogaster use just two main types, in which fate is controlled by the binary stochastic decision to express the transcription factor Spineless in R7 photoreceptors. We investigated how butterflies instead generate three stochastically distributed ommatidial types, resulting in a more diverse retinal mosaic that provides the basis for additional colour comparisons and an expanded range of colour vision. We show that the Japanese yellow swallowtail (Papilio xuthus, Papilionidae) and the painted lady (Vanessa cardui, Nymphalidae) butterflies have a second R7-like photoreceptor in each ommatidium. Independent stochastic expression of Spineless in each R7-like cell results in expression of a blue-sensitive (Spineless(ON)) or an ultraviolet (UV)-sensitive (Spineless(OFF)) Rhodopsin. In P. xuthus these choices of blue/blue, blue/UV or UV/UV sensitivity in the two R7 cells are coordinated with expression of additional Rhodopsin proteins in the remaining photoreceptors, and together define the three types of ommatidia. Knocking out spineless using CRISPR/Cas9 (refs 5, 6) leads to the loss of the blue-sensitive fate in R7-like cells and transforms retinas into homogeneous fields of UV/UV-type ommatidia, with corresponding changes in other coordinated features of ommatidial type. Hence, the three possible outcomes of Spineless expression define the three ommatidial types in butterflies. This developmental strategy allowed the deployment of an additional red-sensitive Rhodopsin in P. xuthus, allowing for the evolution of expanded colour vision with a greater variety of receptors. This surprisingly simple mechanism that makes use of two binary stochastic decisions coupled with local coordination may prove
Expanded color vision in butterflies: molecular logic behind three way stochastic choices
Perry, Michael; Kinoshita, Michiyo; Saldi, Giuseppe; Huo, Lucy; Arikawa, Kentaro; Desplan, Claude
2016-01-01
Butterflies rely on color vision extensively to adapt to the natural world. Most species express a broad range of color sensitive Rhodopsins in three stochastically distributed types of ommatidia (unit eyes)1–3. The retinas of Drosophila deploy just two main types, where fate is controlled by the binary stochastic decision to express the transcription factor Spineless (Ss) in R7 photoreceptors4. We investigated how butterflies instead generate three stochastically distributed ommatidial types, resulting in a more diverse retinal mosaic that provides the basis for additional color comparisons and an expanded range of color vision. We show that the Japanese Yellow Swallowtail (Papilio xuthus, Papilionidae) and the Painted Lady (Vanessa cardui, Nymphalidae) have a second R7-like photoreceptor in each ommatidium. Independent stochastic expression of Ss in each R7-like cell results in expression of a Blue (Ss-ON) or a UV (Ss-OFF) Rhodopsin. In Papilio, these choices of Blue/Blue, Blue/UV, or UV/UV in the two R7s are coordinated with expression of additional Rhodopsins in the remaining photoreceptors, and together define the three types of ommatidia. Knocking out ss using CRISPR/Cas95,6 leads to the loss of the Blue fate in R7-like cells and transforms retinas into homogeneous fields of UV/UV-type ommatidia, with all corresponding features. Hence, the three possible outcomes of Ss expression define the three ommatidial types in butterflies. This developmental strategy allowed the deployment of an additional red-sensitive Rhodopsin in Papilio, allowing for the evolution of expanded color vision with a richer variety of receptors7,8. This surprisingly simple mechanism that makes use of two binary stochastic decisions coupled with local coordination may prove to be a general means of generating an increased diversity of developmental outcomes. PMID:27383790
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Veraart, Almut
Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on general...... properties of ambit fields. Moreover, it develops the concept of tempo-spatial stochastic volatility/intermittency within ambit fields. Various types of volatility modulation ranging from stochastic scaling of the amplitude, to stochastic time change and extended subordination of random measures...... and to probability and L\\'{e}vy mixing of volatility/intensity parameters will be developed. Important examples for concrete model specifications within the class of ambit fields are given....
ON THE ANISOTROPIC NORM OF DISCRETE TIME STOCHASTIC SYSTEMS WITH STATE DEPENDENT NOISE
Directory of Open Access Journals (Sweden)
Isaac Yaesh
2013-01-01
Full Text Available The purpose of this paper is to determine conditions for the bound-edness of the anisotropic norm of discrete-time linear stochastic sys-tems with state dependent noise. It is proved that these conditions canbe expressed in terms of the feasibility of a specific system of matrixinequalities.
Stochastic pump effect and geometric phases in dissipative and stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Sinitsyn, Nikolai [Los Alamos National Laboratory
2008-01-01
The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).
Directory of Open Access Journals (Sweden)
Fei Long
2013-01-01
Full Text Available For a class of Itô stochastic linear systems with the Markov jumping and linear fractional uncertainty, the stochastic stabilization problem is investigated via state feedback and dynamic output feedback, respectively. In order to guarantee the stochastic stability of such uncertain systems, state feedback and dynamic output control law are, respectively, designed by using multiple Lyapunov function technique and LMI approach. Finally, two numerical examples are presented to illustrate our results.
Kierzek, Andrzej M; Zhou, Lu; Wanner, Barry L
2010-03-01
Two-component systems (TCSs) are prevalent signal transduction systems in bacteria that control innumerable adaptive responses to environmental cues and host-pathogen interactions. We constructed a detailed stochastic kinetic model of two component signalling based on published data. Our model has been validated with flow cytometry data and used to examine reporter gene expression in response to extracellular signal strength. The model shows that, depending on the actual kinetic parameters, TCSs exhibit all-or-none, graded or mixed mode responses. In accordance with other studies, positively autoregulated TCSs exhibit all-or-none responses. Unexpectedly, our model revealed that TCSs lacking a positive feedback loop exhibit not only graded but also mixed mode responses, in which variation of the signal strength alters the level of gene expression in induced cells while the regulated gene continues to be expressed at the basal level in a substantial fraction of cells. The graded response of the TCS changes to mixed mode response by an increase of the translation initiation rate of the histidine kinase. Thus, a TCS is an evolvable design pattern capable of implementing deterministic regulation and stochastic switches associated with both graded and threshold responses. This has implications for understanding the emergence of population diversity in pathogenic bacteria and the design of genetic circuits in synthetic biology applications. The model is available in systems biology markup language (SBML) and systems biology graphical notation (SBGN) formats and can be used as a component of large-scale biochemical reaction network models.
Li, Juan
2012-01-01
In this paper we study the optimal stochastic control problem for stochastic differential systems reflected in a domain. The cost functional is a recursive one, which is defined via generalized backward stochastic differential equations developed by Pardoux and Zhang [17]. The value function is shown to be the viscosity solution to the associated Hamilton-Jacobi-Bellman equation, which is a fully nonlinear parabolic partial differential equation with a nonlinear Neumann boundary condition. The method of stochastic "backward semigroups" introduced by Peng [18] is adapted to our context.
Liu, Meng; Wang, Ke; Wu, Qiong
2011-09-01
Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived.
Dimension Reduction and Discretization in Stochastic Problems by Regression Method
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
1996-01-01
The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation, ......, Slepian models, Stochastic finite elements.......The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation...
New results in global stabilization for stochastic nonlinear systems
Institute of Scientific and Technical Information of China (English)
Tao BIAN; Zhong-Ping JIANG
2016-01-01
This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.
Stochastic multireference Epstein-Nesbet perturbation theory
Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali; Umrigar, C J
2016-01-01
We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 12, 3674 (2016)], by introducing a stochastic algorithm for performing multireference Epstein-Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed stochastic algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods. Second, instead of using Metropolis-Hastings sampling, we use the Alias method to directly sample determinants from the reference wavefunction, thus avoiding correlations between consecutive samples. Third, in addition to removing the memory bottleneck, stochastic-HCI (s-HCI) is faster than the deterministic variant for most systems if a stochastic error of 0.1 mHa is acceptable. Fourth, within the s-HCI algorithm one can trade memory for a modest increase in computer time. Fifth, the perturbative calculation is embarrassingly par...
Extending Stochastic Network Calculus to Loss Analysis
Directory of Open Access Journals (Sweden)
Chao Luo
2013-01-01
Full Text Available Loss is an important parameter of Quality of Service (QoS. Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.
Synchronization of noisy systems by stochastic signals
Energy Technology Data Exchange (ETDEWEB)
Neiman, A.; Schimansky-Geier, L.; Moss, F. [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Schimansky-Geier, L. [Institute of Physics, Humboldt University at Berlin, Invalidenstrasse 110, D-10115 Berlin (Germany); Shulgin, B.; Collins, J.J. [Center for BioDynamics and Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, Massachusetts 02215 (United States)
1999-07-01
We study, in terms of synchronization, the {ital nonlinear response} of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching frequency, and synchronization regions. Theoretical results are compared with numerical simulations of a noisy overdamped bistable oscillator. We show that dichotomic noise can instantaneously synchronize the switching process of the system. We also show that synchronization is most pronounced at an optimal noise level{emdash}this effect connects this phenomenon with aperiodic stochastic resonance. Similar synchronization effects are observed for a stochastic neuron model stimulated by a stochastic spike train. {copyright} {ital 1999} {ital The American Physical Society}
Stochasticity in plant cellular growth and patterning
Directory of Open Access Journals (Sweden)
Heather M. Meyer
2014-09-01
Full Text Available Plants, along with other multicellular organisms, have evolved specialized regulatory mechanisms to achieve proper tissue growth and morphogenesis. During development, growing tissues generate specialized cell types and complex patterns necessary for establishing the function of the organ. Tissue growth is a tightly regulated process that yields highly reproducible outcomes. Nevertheless, the underlying cellular and molecular behaviors are often stochastic. Thus, how does stochasticity, together with strict genetic regulation, give rise to reproducible tissue development? This review draws examples from plants as well as other systems to explore stochasticity in plant cell division, growth, and patterning. We conclude that stochasticity is often needed to create small differences between identical cells, which are amplified and stabilized by genetic and mechanical feedback loops to begin cell differentiation. These first few differentiating cells initiate traditional patterning mechanisms to ensure regular development.
Perspective: Stochastic algorithms for chemical kinetics.
Gillespie, Daniel T; Hellander, Andreas; Petzold, Linda R
2013-05-01
We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.
Stochastic oscillations of general relativistic disks
Harko, Tiberiu
2012-01-01
We analyze the general relativistic oscillations of thin accretion disks around compact astrophysical objects interacting with the surrounding medium through non-gravitational forces. The interaction with the external medium (a thermal bath) is modeled via a friction force, and a random force, respectively. The general equations describing the stochastically perturbed disks are derived by considering the perturbations of trajectories of the test particles in equatorial orbits, assumed to move along the geodesic lines. By taking into account the presence of a viscous dissipation and of a stochastic force we show that the dynamics of the stochastically perturbed disks can be formulated in terms of a general relativistic Langevin equation. The stochastic energy transport equation is also obtained. The vertical oscillations of the disks in the Schwarzschild and Kerr geometries are considered in detail, and they are analyzed by numerically integrating the corresponding Langevin equations. The vertical displacement...
Discretizing a backward stochastic differential equation
Yinnan Zhang; Weian Zheng
2002-01-01
We show a simple method to discretize Pardoux-Peng's nonlinear backward stochastic differential equation. This discretization scheme also gives a numerical method to solve a class of semi-linear PDEs.
Asynchronous stochastic approximation with differential inclusions
Directory of Open Access Journals (Sweden)
David S. Leslie
2012-01-01
Full Text Available The asymptotic pseudo-trajectory approach to stochastic approximation of Benaïm, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of an equivalent synchronous process. In addition, this allows many of the restrictive assumptions previously associated with asynchronous stochastic approximation to be removed. The framework is extended for a coupled asynchronous stochastic approximation process with set-valued mean fields. Two-timescales arguments are used here in a similar manner to the original work in this area by Borkar. The applicability of this approach is demonstrated through learning in a Markov decision process.
Stochastic structure formation in random media
Klyatskin, V. I.
2016-01-01
Stochastic structure formation in random media is considered using examples of elementary dynamical systems related to the two-dimensional geophysical fluid dynamics (Gaussian random fields) and to stochastically excited dynamical systems described by partial differential equations (lognormal random fields). In the latter case, spatial structures (clusters) may form with a probability of one in almost every system realization due to rare events happening with vanishing probability. Problems involving stochastic parametric excitation occur in fluid dynamics, magnetohydrodynamics, plasma physics, astrophysics, and radiophysics. A more complicated stochastic problem dealing with anomalous structures on the sea surface (rogue waves) is also considered, where the random Gaussian generation of sea surface roughness is accompanied by parametric excitation.
Normal forms for reduced stochastic climate models
Majda, A.J.; Franzke, C.; Crommelin, D.T.
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive highdimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Here techniques from
Transient Growth in Stochastic Burgers Flows
Poças, Diogo
2015-01-01
This study considers the problem of the extreme behavior exhibited by solutions to Burgers equation subject to stochastic forcing. More specifically, we are interested in the maximum growth achieved by the "enstrophy" (the Sobolev $H^1$ seminorm of the solution) as a function of the initial enstrophy $\\mathcal{E}_0$, in particular, whether in the stochastic setting this growth is different than in the deterministic case considered by Ayala & Protas (2011). This problem is motivated by questions about the effect of noise on the possible singularity formation in hydrodynamic models. The main quantities of interest in the stochastic problem are the expected value of the enstrophy and the enstrophy of the expected value of the solution. The stochastic Burgers equation is solved numerically with a Monte Carlo sampling approach. By studying solutions obtained for a range of optimal initial data and different noise magnitudes, we reveal different solution behaviors and it is demonstrated that the two quantities ...
Quantum Fields, Stochastic PDE, and Reflection Positivity
Jaffe, Arthur
2014-01-01
We outline some known relations between classical random fields and quantum fields. In the scalar case, the existence of a quantum field is equivalent to the existence of a Euclidean-invariant, reflection-positive (RP) measure on the Schwartz space tempered distributions. Martin Hairer recently investigated random fields in a series of interesting papers, by studying non-linear stochastic partial differential equations, with a white noise driving term. To understand such stochastic quantization, we consider a linear example. We ask: does the measure on the solution induced by the stochastic driving term yield a quantum field? The RP property yields a general method to implement quantization. We show that the RP property fails for finite stochastic parameter $\\lambda$, although it holds in the limiting case $\\lambda=\\infty$.
Evolutionary stability concepts in a stochastic environment
Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi
2017-09-01
Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.
Dynamics of a Stochastic Intraguild Predation Model
Directory of Open Access Journals (Sweden)
Zejing Xing
2016-04-01
Full Text Available Intraguild predation (IGP is a widespread ecological phenomenon which occurs when one predator species attacks another predator species with which it competes for a shared prey species. The objective of this paper is to study the dynamical properties of a stochastic intraguild predation model. We analyze stochastic persistence and extinction of the stochastic IGP model containing five cases and establish the sufficient criteria for global asymptotic stability of the positive solutions. This study shows that it is possible for the coexistence of three species under the influence of environmental noise, and that the noise may have a positive effect for IGP species. A stationary distribution of the stochastic IGP model is established and it has the ergodic property, suggesting that the time average of population size with the development of time is equal to the stationary distribution in space. Finally, we show that our results may be extended to two well-known biological systems: food chains and exploitative competition.
Stochastic differential equation model to Prendiville processes
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Stochastic differential equation model to Prendiville processes
Granita, Bahar, Arifah
2015-10-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Testing for Stochastic Dominance with Diversification Possibilities
G.T. Post (Thierry)
2001-01-01
textabstractWe derive empirical tests for stochastic dominance that allow for diversification between choice alternatives. The tests can be computed using straightforward linear programming. Bootstrapping techniques and asymptotic distribution theory can approximate the sampling properties of the te
Modelling Cow Behaviour Using Stochastic Automata
DEFF Research Database (Denmark)
Jónsson, Ragnar Ingi
This report covers an initial study on the modelling of cow behaviour using stochastic automata with the aim of detecting lameness. Lameness in cows is a serious problem that needs to be dealt with because it results in less profitable production units and in reduced quality of life...... of which describe the cows' activity in the two regarded behavioural scenarios, non-lame and lame. Using the experimental measurement data the different behavioural relations for the two regarded behavioural scenarios are assessed. The three models comprise activity within last hour, activity within last...... for the affected livestock. By featuring training data consisting of measurements of cow activity, three different models are obtained, namely an autonomous stochastic automaton, a stochastic automaton with coinciding state and output and an autonomous stochastic automaton with coinciding state and output, all...
Fractional Smoothness of Some Stochastic Integrals
Institute of Scientific and Technical Information of China (English)
Peng XIE; Xi Cheng ZHANG
2007-01-01
We study the fractional smoothness in the sense of Malliavin calculus of stochastic integralsof the form ∫10 φ(Xs)d Xs,where Xs is a semimartingale and φ belongs to some fractional Sobolev spaceover R.
Assessing the quality of stochastic oscillations
Indian Academy of Sciences (India)
Guillermo Abramson; Sebastián Risau-Gusman
2008-06-01
We analyze the relationship between the macroscopic and microscopic descriptions of two-state systems, in particular the regime in which the microscopic one shows sustained `stochastic oscillations' while the macroscopic tends to a fixed point. We propose a quantification of the oscillatory appearance of the fluctuating populations, and show that good stochastic oscillations are present if a parameter of the macroscopic model is small, and that no microscopic model will show oscillations if that parameter is large. The transition between these two regimes is smooth. In other words, given a macroscopic deterministic model, one can know whether any microscopic stochastic model that has it as a limit, will display good sustained stochastic oscillations.
Perspective: Stochastic algorithms for chemical kinetics
Gillespie, Daniel T.; Hellander, Andreas; Petzold, Linda R.
2013-05-01
We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.
Extending stochastic network calculus to loss analysis.
Luo, Chao; Yu, Li; Zheng, Jun
2013-01-01
Loss is an important parameter of Quality of Service (QoS). Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.
Testing for Stochastic Dominance with Diversification Possibilities
G.T. Post (Thierry)
2001-01-01
textabstractWe derive empirical tests for stochastic dominance that allow for diversification between choice alternatives. The tests can be computed using straightforward linear programming. Bootstrapping techniques and asymptotic distribution theory can approximate the sampling properties of the
ECE6010 - Stochastic Processes, Spring 2006
Moon, Todd K.
2006-01-01
This course provides an introduction to stochastic processes in communications, signal processing, digital and computer systems, and control. Topics include continuous and discrete random processes, correlation and power spectral density, optimal filtering, Markov chains, and queuing theory. Technical Requirements: MATLAB
Stochastic description of quantum Brownian dynamics
Yan, Yun-An; Shao, Jiushu
2016-08-01
Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems
Stochastic differential games with inside information
Draouil, Olfa; Øksendal, Bernt
2016-08-01
We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noise, Hida-Malliavin calculus, forward integrals and the Donsker delta functional. We obtain a characterization of Nash equilibria of such games in terms of the corresponding Hamiltonians. This is used to study applications to insider games in finance, specifically optimal insider consumption and optimal insider portfolio under model uncertainty.
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique...... applied for implementing this semantics in the UPPAAL-SMC simulation engine. We report on two applications of the resulting tool-set coming from systems biology and energy aware buildings....
Stability of the Stochastic Differential Equations
Klimešová, M.
2015-01-01
Stability of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its applications. The method of Lyapunov functions for the analysis of qualitative behavior of SDEs provide some very powerful instruments in the study of stability properties for concrete stochastic dynamical systems, conditions of existence the stationary solutions of SDEs and related problems. The study of exponential stability of the moments makes natural the conside...
Complexity and synchronization in stochastic chaotic systems
Son Dang, Thai; Palit, Sanjay Kumar; Mukherjee, Sayan; Hoang, Thang Manh; Banerjee, Santo
2016-02-01
We investigate the complexity of a hyperchaotic dynamical system perturbed by noise and various nonlinear speech and music signals. The complexity is measured by the weighted recurrence entropy of the hyperchaotic and stochastic systems. The synchronization phenomenon between two stochastic systems with complex coupling is also investigated. These criteria are tested on chaotic and perturbed systems by mean conditional recurrence and normalized synchronization error. Numerical results including surface plots, normalized synchronization errors, complexity variations etc show the effectiveness of the proposed analysis.
A Note on Indefinite Stochastic Riccati Equations
Qian, Zhongmin
2012-01-01
An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of such equations (including the existence of solutions) driven by one-dimensional Brownian motion. The idea is to replace the original equation by a system of BSDEs (without involving any algebraic constraint) whose existence of solutions automatically enforces the original algebraic constraint to be satisfied.
Desynchronization of stochastically synchronized chemical oscillators
Energy Technology Data Exchange (ETDEWEB)
Snari, Razan; Tinsley, Mark R., E-mail: mark.tinsley@mail.wvu.edu, E-mail: kshowalt@wvu.edu; Faramarzi, Sadegh; Showalter, Kenneth, E-mail: mark.tinsley@mail.wvu.edu, E-mail: kshowalt@wvu.edu [C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045 (United States); Wilson, Dan; Moehlis, Jeff [Department of Mechanical Engineering, University of California, Santa Barbara, California 93106 (United States); Netoff, Theoden Ivan [Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455 (United States)
2015-12-15
Experimental and theoretical studies are presented on the design of perturbations that enhance desynchronization in populations of oscillators that are synchronized by periodic entrainment. A phase reduction approach is used to determine optimal perturbation timing based upon experimentally measured phase response curves. The effectiveness of the perturbation waveforms is tested experimentally in populations of periodically and stochastically synchronized chemical oscillators. The relevance of the approach to therapeutic methods for disrupting phase coherence in groups of stochastically synchronized neuronal oscillators is discussed.
Stochastic Evolution Equations Driven by Fractional Noises
2016-11-28
Stochastic Calculus , Monte Carlo Methods and Mathematical Finance, University of Le Mans, October 6-9, 2015. "Parabolic Anderson model driven by...is based on the techniques of Malliavin calculus or stochastic calculus of variations. In the second part of this project, we have studied two...xi|2Hi−2, where Hi > 1 2 and condition (10) is satisfied if and only if ∑d i=1Hi > d− 1. This particular structure has been examined in [20]. ( ii
Stochastic relations foundations for Markov transition systems
Doberkat, Ernst-Erich
2007-01-01
Collecting information previously scattered throughout the vast literature, including the author's own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition systems. After an introduction to the basic mathematical tools from topology, measure theory, and categories, the book examines the central topics of congruences and morphisms, applies these to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. The author views developments from the general
Monostable array-enhanced stochastic resonance.
Lindner, J F; Breen, B J; Wills, M E; Bulsara, A R; Ditto, W L
2001-05-01
We present a simple nonlinear system that exhibits multiple distinct stochastic resonances. By adjusting the noise and coupling of an array of underdamped, monostable oscillators, we modify the array's natural frequencies so that the spectral response of a typical oscillator in an array of N oscillators exhibits N-1 different stochastic resonances. Such families of resonances may elucidate and facilitate a variety of noise-mediated cooperative phenomena, such as noise-enhanced propagation, in a broad class of similar nonlinear systems.
On the stochastic dynamics of molecular conformation
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
An important functioning mechanism of biological macromolecules is the transition between different conformed states due to thermal fluctuation. In the present paper, a biological macromolecule is modeled as two strands with side chains facing each other, and its stochastic dynamics including the statistics of stationary motion and the statistics of conformational transition is studied by using the stochastic averaging method for quasi Hamiltonian systems. The theoretical results are confirmed with the results from Monte Carlo simulation.
Second Quantization Approach to Stochastic Epidemic Models
Mondaini, Leonardo
2015-01-01
We show how the standard field theoretical language based on creation and annihilation operators may be used for a straightforward derivation of closed master equations describing the population dynamics of multivariate stochastic epidemic models. In order to do that, we introduce an SIR-inspired stochastic model for hepatitis C virus epidemic, from which we obtain the time evolution of the mean number of susceptible, infected, recovered and chronically infected individuals in a population whose total size is allowed to change.
Stochastic Simulations of Cellular Biological Processes
2007-06-01
model kinetics of a system of chemical reactions is to use a stochastic 2. Stochastic Simulation Algorithm approach in terms of the Chemical Master...number of processors and running time) for interactive disk spae ad, herfor, my ceat meory simulations. Therefore, in addition to running in an...management problems for simulations involving a large inteative mode, foNScan as o run in ’n number of long runs or for large reaction networks. interactive
Stochastic genome-nuclear lamina interactions
Kind, Jop; van Steensel, Bas
2014-01-01
The nuclear lamina (NL) is thought to aid in the spatial organization of interphase chromosomes by providing an anchoring platform for hundreds of large genomic regions named lamina associated domains (LADs). Recently, a new live-cell imaging approach demonstrated directly that LAD-NL interactions are dynamic and in part stochastic. Here we discuss implications of these new findings and introduce Lamin A and BAF as potential modulators of stochastic LAD positioning. PMID:24717229