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Makuch, Martin. "Circumplanetary dust dynamics application to Martian dust tori and Enceladus dust plumes /." Phd thesis, [S.l.] : [s.n.], 2007. http://opus.kobv.de/ubp/volltexte/2007/1440.
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Mueller, Felix. "Formation of spatio–temporal patterns in stochastic nonlinear systems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2012. http://dx.doi.org/10.18452/16527.
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Die vorliegende Arbeit befasst sich mit einer Reihe von Fragestellungen, die Forschungsfeldern wie rauschinduziertem Verhalten, Strukturbildung in aktiven Medien und Synchronisation nichlinearer Oszillatoren erwachsen. Die verwendeten nichtlinearen Modelle verfügen über erregbare, oszillatorische und bistabile Eigenschaften. Zusätzliche stochastische Fluktuationen tragen wesentlich zur Entstehung komplexer Dynamik bei. Modelliert wird, auf welche Weise sich extrazelluläre Kaliumkonzentration, gespeist von umliegenden Neuronen, auf die Aktivität dieser Neuronen auswirkt. Neben lokaler Dynamik wird die Ausbildung ausgedehnter Strukturen in einem heterogenem Medium analysiert. Die raum-zeitlichen Muster umfassen sowohl Wellenfronten und Spiralen als auch ungewöhnliche Strukturen, wie wandernde Cluster oder invertierte Wellen. Eine wesentliche Rolle bei der Ausprägung solcher Strukturen spielen die Randbedingungen des Systems. Sowohl für diskret gekoppelte bistabile Elemente als auch für kontinuierliche Fronten werden Methoden zur Berechnung von Frontgeschwindigkeiten bei fixierten Rändern vorgestellt. Typische Bifurkationen werden quantifiziert und diskutiert. Der Rückkopplungsmechanismus aus dem Modell neuronaler Einheiten und deren passiver Umgebung kann weiter abstrahiert werden. Ein Zweizustandsmodell wird über zwei Wartezeitverteilungen definiert, welche erregbares Verhalten widerspiegeln. Untersucht wird die instantane und die zeitverzögerte Antwort des Ensembles auf die Rückkopplung. Im Fall von Zeitverzögerung tritt eine Hopf-Bifurkation auf, die zu Oszillationen der mittleren Gesamtaktivität führt. Das letzte Kapitel befasst sich mit Diffusion und Transport von Brownschen Teilchen in einem raum-zeiltich periodischen Potential. Wieder sind es Synchronisationsmechanismen, die nahezu streuungsfreien Transport ermöglichen können. Für eine erhöhte effektiven Diffusion gelangen wir zu einer Abschätzung der maximierenden Parameter.In this work problems are investigated that arises from resarch fields of noise induced dynamics, pattern formation in active media and synchronisation of self-sustained oscillators. The applied model systems exhibit excitable, oscillatory and bistable behavior as basic modes of nonlinear dynamics. Addition of stochastic fluctuations contribute to the appearance of complex behavior. The extracellular potassium concentration fed by surrounding activated neurons and the feeback to these neurons is modelled. Beside considering the local behavior, nucleation of spatially extended structures is studied. We find typical fronts and spirales as well as unusal patterns such as moving clusters and inverted waves. The boundary conditions of the considered system play an essential role in the formation process of such structures. We present methods to find expressions of the front velocity for discretely coupled bistable units as well as for the countinus front interacting with boundary values. Canonical bifurcation scenarios can be quantified. The feedback mechanism from the model for neuronal units can be generalized further. A two-state model is defined by two waiting time distributions representing excitable dynamics. We analyse the instantaneous and delayed response of the ensemble. In the case of delayed feedback a Hopf-bifurcation occur which lead to oscillations of the mean activity. In the last chapter the transport and diffusion of Brownian particles in a spatio-temporal oscillating potential is discussed. As a cause of nearly dispersionless transport synchronisations mechanisms can be identified. We find an estimation for parameter values which maximizes the effective diiffusion.
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Dean, David Stanley. "Stochastic dynamics." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318048.
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Almada, Monter Sergio Angel. "Scaling limit for the diffusion exit problem." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39518.
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A stochastic differential equation with vanishing martingale term is studied. Specifically, given a domain D, the asymptotic scaling properties of both the exit time from the domain and the exit distribution are considered under the additional (non-standard) hypothesis that the initial condition also has a scaling limit. Methods from dynamical systems are applied to get more complete estimates than the ones obtained by the probabilistic large deviation theory.
Two situations are completely analyzed. When there is a unique critical saddle point of the deterministic system (the system without random effects), and when the unperturbed system escapes the domain D in finite time. Applications to these results are in order. In particular, the study of 2-dimensional heteroclinic networks is closed with these results and shows the existence of possible asymmetries. Also, 1-dimensional diffusions conditioned to rare events are further studied using these results as building blocks.
The approach tries to mimic the well known linear situation. The original equation is smoothly transformed into a very specific non-linear equation that is treated as a singular perturbation of the original equation. The transformation provides a classification to all 2-dimensional systems with initial conditions close to a saddle point of the flow generated by the drift vector field. The proof then proceeds by estimates that propagate the small noise nature of the system through the non-linearity. Some proofs are based on geometrical arguments and stochastic pathwise expansions in noise intensity series.
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Lythe, Grant David. "Stochastic slow-fast dynamics." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338108.
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Restrepo, Juan M., and Shankar Venkataramani. "Stochastic longshore current dynamics." ELSEVIER SCI LTD, 2016. http://hdl.handle.net/10150/621938.
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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.
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Sanyal, Suman. "Stochastic dynamic equations." Diss., Rolla, Mo. : Missouri University of Science and Technology, 2008. http://scholarsmine.mst.edu/thesis/pdf/Sanyal_09007dcc80519030.pdf.
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Thesis (Ph. D.)--Missouri University of Science and Technology, 2008.Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed August 21, 2008) Includes bibliographical references (p. 124-131).
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Yilmaz, Bulent. "Stochastic Approach To Fusion Dynamics." Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608517/index.pdf.
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This doctoral study consists of two parts. In the first part, the quantum statistical effects on the formation process of the heavy ion fusion reactions have been investigated by using the c-number quantum Langevin equation approach. It has been shown that the quantum effects enhance the over-passing probability at low temperatures. In the second part, we have developed a simulation technique for the quantum noises which can be approximated by two-term exponential colored noise.
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De, Fabritiis Gianni. "Stochastic dynamics of mesoscopic fluids." Thesis, Queen Mary, University of London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268402.
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Stocks, Nigel Geoffrey. "Experiments in stochastic nonlinear dynamics." Thesis, Lancaster University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315224.
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Xie, Yan. "STOCHASTIC DYNAMICS OF GENE TRANSCRIPTION." UKnowledge, 2011. http://uknowledge.uky.edu/statistics_etds/2.
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Gene transcription in individual living cells is inevitably a stochastic and dynamic process. Little is known about how cells and organisms learn to balance the fidelity of transcriptional control and the stochasticity of transcription dynamics. In an effort to elucidate the contribution of environmental signals to this intricate balance, a Three State Model was recently proposed, and the transcription system was assumed to transit among three different functional states randomly.
In this work, we employ this model to demonstrate how the stochastic dynamics of gene transcription can be characterized by the three transition parameters. We compute the probability distribution of a zero transcript event and its conjugate, the distribution of the time durations in gene on or gene off periods, the transition frequency between system states, and the transcriptional bursting frequency. We also exemplify the mathematical results by the experimental data on prokaryotic and eukaryotic transcription.
The analysis reveals that no promoters will be definitely turned on to transcribe within a finite time period, no matter how strong the induction signals are applied, and how abundant the activators are available. Although stronger extrinsic signals could enhance promoter activation rate, the promoter creates an intrinsic ceiling that no signals could cross over in a finite time. Consequently, among a large population of isogenic cells, only a portion of the cells, but not the whole population, could be induced by environmental signals to express a particular gene within a finite time period. We prove that the gene on duration follows an exponential distribution, and the gene off intervals show a local maximum that is best described by assuming two sequential exponential process. The transition frequencies are determined by a system of stochastic differential equations, or equivalently, an iterative scheme of integral operators. We prove that for each positive integer n , there associates a unique time, called the peak instant, at which the nth transcript synthesis cycle since time zero proceeds most likely. These moments constitute a time series preserving the nature order of n.
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Naylor, Sarah Louise. "Stochastic dynamics in periodic potentials." Thesis, University of Nottingham, 2006. http://eprints.nottingham.ac.uk/10179/.
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This thesis describes the dynamics of both electrons and atoms in periodic potentials. In particular, it explores how such potentials can be used to realise a new type of quantum chaos in which the effective classical Hamiltonian originates from the intrinsically quantum nature of energy bands. Firstly, this study examines electron dynamics in a superlattice with an applied voltage and a tilted magnetic field. This system displays a rare type of chaos known as non-KAM (Kolmogorov-Arnold-Moser) chaos, which switches on abruptly when an applied perturbation reaches certain critical values. The onset of chaos in the system leads to the formation of complex patterns in phase space known as stochastic webs. The electron behaviour under these conditions is analysed both semiclassically and quantum mechanically, and the results compared to experimental studies. We show that the presence of stochastic webs strongly enhances electron transport. We calculate Wigner functions of the electron wavefunction at various times and show that, when compared to the Poincare sections, evidence of stochastic web formation is observed in the quantum mechanical phase space. Two designs of superlattice are studied and we show, in a full quantum mechanical analysis, that the design of the superlattice has a pronounced effect on the probability of inter-miniband tunnelling and hence the calculated and measured transport characteristics. Secondly, we explore the dynamics of an ultra-cold sodium atom falling through an optical lattice whilst confined in a harmonic gutter potential that is tilted at an angle to the lattice axis. We show this system is analogous to the case of an electron in a superlattice, and that the atomic dynamics show similar enhanced transport properties for certain trapping frequencies. We also find that in a full quantum mechanical calculation, the atomic wavepacket tends to fragment as the angle at which the gutter potential is tilted is increased. Finally, we examine the dynamics of a Bose-Einstein condensate falling through an optical lattice whilst confined in a harmonic gutter potential. We vary the strength of the interatomic interaction parameter to investigate the role of interactions in the system and find that, even for small tilt angles, the condensate wavefunction fragments. For large interaction parameters combined with large tilt angles, the wavefunction explodes catastrophically.
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Herbert, Julian Richard. "Stochastic processes for parasite dynamics." Thesis, University College London (University of London), 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368164.
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Griffin, T. C. L. "Dynamics of stochastic nonsmooth systems." Thesis, University of Bristol, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411095.
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Swinburne, Thomas. "Stochastic dynamics of crystal defects." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/24878.
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The state of a deformed crystal is highly heterogeneous, with plasticity localised into linear and point defects such as dislocations, vacancies and interstitial clusters. The motion of these defects dictate a crystal's mechanical behaviour, but defect dynamics are complicated and correlated by external applied stresses, internal elastic interactions and the fundamentally stochastic influence of thermal vibrations. This thesis is concerned with establishing a rigorous, modern theory of the stochastic and dissipative forces on crystal defects, which remain poorly understood despite their importance in any temperature dependent micro-structural process such as the ductile to brittle transition and irradiation damage. From novel molecular dynamics simulations we parametrise an efficient, stochastic and discrete dislocation model that allows access to experimental time and length scales. Simulated trajectories of thermally activated dislocation motion are in excellent agreement with those measured experimentally. Despite these successes in coarse graining, we find existing theories unable to explain stochastic defect dynamics. To resolve this, we define crystal defects through projection operators, without any recourse to elasticity. By rigorous dimensional reduction we derive explicit analytical forms for the stochastic forces acting on crystal defects, allowing new quantitative insight into the role of thermal fluctuations in crystal plasticity.
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Zhitlukhin, Mikhail Valentinovich. "Stochastic dynamics of financial markets." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/stochastic-dynamics-of-financial-markets(4eb80d2a-e90a-4ab0-b9e2-ad930c8a4d94).html.
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This thesis provides a study on stochastic models of financial markets related to problems of asset pricing and hedging, optimal portfolio managing and statistical changepoint detection in trends of asset prices. Chapter 1 develops a general model of a system of interconnected stochastic markets associated with a directed acyclic graph. The main result of the chapter provides sufficient conditions of hedgeability of contracts in the model. These conditions are expressed in terms of consistent price systems, which generalise the notion of equivalent martingale measures. Using the general results obtained, a particular model of an asset market with transaction costs and portfolio constraints is studied. In the second chapter the problem of multi-period utility maximisation in the general market model is considered. The aim of the chapter is to establish the existence of systems of supporting prices, which play the role of Lagrange multipliers and allow to decompose a multi-period constrained utility maximisation problem into a family of single-period and unconstrained problems. Their existence is proved under conditions similar to those of Chapter 1.The last chapter is devoted to applications of statistical sequential methods for detecting trend changes in asset prices. A model where prices are driven by a geometric Gaussian random walk with changing mean and variance is proposed, and the problem of choosing the optimal moment of time to sell an asset is studied. The main theorem of the chapter describes the structure of the optimal selling moments in terms of the Shiryaev–Roberts statistic and the posterior probability process.
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Sato, Kenji. "Stochastic and Pseudostochastic Economic Dynamics." Kyoto University, 2012. http://hdl.handle.net/2433/157505.
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Siriwardena, Pathiranage Lochana Pabakara. "STOCHASTIC MODELS IN POPULATION DYNAMICS." OpenSIUC, 2014. https://opensiuc.lib.siu.edu/dissertations/908.
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This dissertation discusses the construction of some stochastic models for population dynamics with a variety of birth and death rate functions. A general model is constructed considering a fundamental growth rate function of the population while allowing random births and deaths in the population. Four stochastic discrete delay models and two non-delay models using the infinitesimal mean and variance given by birth and death rate functions have been produced and analyzed. In these constructions drift terms are in the form of logistic growth or logistic growth with delay. Logistic growth models are well known to biologists and economists. For each model, the existence and uniqueness of the global solution, non-negativeness of the solution is discussed, and for some models, boundedness of the path is also given. Persistence of the population and the boundary behavior have also been discussed through the hitting times. Here, a new method to analyze the hitting times for a specific class of stochastic delay models is presented. This work is related to and also extends the work of Edward Allen, Linda Allen and Bernt Oksendal in population dynamics.
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Sehl, Mary Elizabeth. "Stochastic dynamics of cancer stem cells." Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=2023755671&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Perelló, Josep 1974. "Correlated Stochastic Dynamics in Financial Markets." Doctoral thesis, Universitat de Barcelona, 2001. http://hdl.handle.net/10803/1787.
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Thesis investigates the dynamics of financial markets. Nowadays, this is one of the emergent fields in physics and requires a multidisciplinary approach. The thesis studies the first work made by the financial mathematicians and presents those in a more comprehensible form for a physicist. Option pricing is perhaps most complete problem. Until very recently, stochastic differential equations theory was solely applied to finance by mathematicians. The thesis reviews the theory of Black-Scholes and pays attention to questions that had not interested too much to the mathematicians but that are of importance from a physicist point of view. Among other things, thesis derives the so-called Black-Scholes option price following the rules used by physicists (Stratonovich). Mathematicians have been using Itô convention for deriving this price and thesis founds that both approaches are equivalent. Thesis also focus on the martingale option pricing which directly relates the stock probability density to the option price. The thesis optimizes the martingale method to implement it in cases where only the characteristic function is known.
The study of the correlations observed in markets conform the second block of the thesis. Good knowledge of correlations is essential to perform predictions. In this sense, two diffusive models are presented. First model proposes a market described by a singular two-dimensional process driven by an Ornstein-Uhlenbeck process where noise source is Gaussian and white. The model correctly describes the volatility as a function of time by considering the memory effects in the stock price changes. This model gives reason of the market inefficiencies due to the absence of liquidity or any other type of market interties. These correlations appear to have a a long range persistence in the option price and entails a remarkable influence in the risk due to holding an option. The second model is a stochastic volatility model. In this case, prices are described by a two-dimensional process with two Gaussian white noise sources and where volatility follows an Ornstein-Uhlenbeck process. Their statistical properties are studied and these describe most of the empirical market properties such as the leverage effect.
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Li, Na. "Stochastic Models of Stock Market Dynamics." Thesis, Uppsala universitet, Analys och tillämpad matematik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-144307.
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Dobay, Maria Pamela. "Dynamics of stochastic membrane rupture events." Diss., lmu, 2012. http://nbn-resolving.de/urn:nbn:de:bvb:19-154957.
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Perelló, Palou Josep. "Correlated Stochastic Dynamics in Financial Markets." Doctoral thesis, Universitat de Barcelona, 2001. http://hdl.handle.net/10803/1787.
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Thesis investigates the dynamics of financial markets. Nowadays, this is one of the emergent fields in physics and requires a multidisciplinary approach. The thesis studies the first work made by the financial mathematicians and presents those in a more comprehensible form for a physicist. Option pricing is perhaps most complete problem. Until very recently, stochastic differential equations theory was solely applied to finance by mathematicians. The thesis reviews the theory of Black-Scholes and pays attention to questions that had not interested too much to the mathematicians but that are of importance from a physicist point of view. Among other things, thesis derives the so-called Black-Scholes option price following the rules used by physicists (Stratonovich). Mathematicians have been using Itô convention for deriving this price and thesis founds that both approaches are equivalent. Thesis also focus on the martingale option pricing which directly relates the stock probability density to the option price. The thesis optimizes the martingale method to implement it in cases where only the characteristic function is known. The study of the correlations observed in markets conform the second block of the thesis. Good knowledge of correlations is essential to perform predictions. In this sense, two diffusive models are presented. First model proposes a market described by a singular two-dimensional process driven by an Ornstein-Uhlenbeck process where noise source is Gaussian and white. The model correctly describes the volatility as a function of time by considering the memory effects in the stock price changes. This model gives reason of the market inefficiencies due to the absence of liquidity or any other type of market interties. These correlations appear to have a a long range persistence in the option price and entails a remarkable influence in the risk due to holding an option. The second model is a stochastic volatility model. In this case, prices are described by a two-dimensional process with two Gaussian white noise sources and where volatility follows an Ornstein-Uhlenbeck process. Their statistical properties are studied and these describe most of the empirical market properties such as the leverage effect.
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Jatuviriyapornchai, Watthanan. "Population dynamics and stochastic particle systems." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/99427/.
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Condensation is a special class of phase transition which has been observed throughout the natural and social sciences. The understanding of dynamics towards condensation on a mathematically rigorous level is currently a major research topic. Starting the system from homogeneous initial conditions, the time evolution of the condensed phase often exhibits an interesting coarsening phenomenon of mass transport between cluster sites. In this thesis, we study the coarsening dynamics in several condensing stochastic particle systems. First, we consider the single site dynamics in general stochastic particle systems of misanthrope type with bounded rates on a complete graph. In the limit of diverging system size, we establish convergence to a Markovian non-linear birth death chain, described by a mean-field equation also known from exchange-driven growth processes. Conservation of mass in the particle system leads to conservation of the first moment for the limiting dynamics, and to non-uniqueness of stationary measures. The proof is based on a coupling to branching processes via the graphical construction and establishing uniqueness of the solution for the limit dynamics. As particularly interesting examples we discuss the dynamics of two models that exhibit a condensation transition and their connection to exchange-driven growth processes. The first model is the zero-range process with bounded jump rates. It is well known that zero-range processes with decreasing jump rates exhibit a condensation transition under certain conditions. The mean-field limit of the single site dynamics leads to a non-linear birth death chain describing the coarsening behaviour. We introduce a size-biased version of the single site process, which provides an effective tool to analyse the dynamics of the condensed phase without finite size effects. The second model is the inclusion process, which has unbounded jump rates and also exhibits the condensation phenomenon. However, in this case, the mean-field equation is derived differently, and the single site process is in the form of a standard birth death chain. In addition to the site and size-biased processes, we derive some exact results on the system through duality. We compute the time dependent covariance using the self-duality of inclusion processes and a two-particle dual process. Our results are based on exact computations and are corroborated by detailed simulation data, which contribute to a rigorous understanding of the approach to stationarity in the thermodynamic limit of diverging system size and particle number.
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Ridden, Sonya. "Stochastic models of stem cell dynamics." Thesis, University of Southampton, 2016. https://eprints.soton.ac.uk/401863/.
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There is a growing body of evidence to suggest that stem cell populations from both the embryo and the adult are heterogeneous in their gene expression patterns. However, the underlying mechanisms are not well understood. This thesis explores cell-to-cell variability in both multipotent and pluripotent stem cell populations using mathematical models to provide a theoretical framework to understand the collective dynamics of stem cell populations. In the first part of the thesis we investigate the possibility that fluctuations in the transcription factor Nanog { which is central to the embryonic stem cell transcriptional regulatory network (ESCTRN) { regulate population variability by controlling important feedback mechanisms. Our analyses reveal the ESC TRN is rich in feedback, with global feedback structure critically dependent on Nanog, Oct4 and Sox2, which collectively participate in over two thirds of all feedback loops. Using a general measure of feedback centrality we show that removal of Nanog severely compromises the global feedback structure of the ESC TRN. These analyses indicate that Nanog fluctuations regulate population heterogeneity by transiently activating different regulatory subnetworks, driving transitions between a Nanog-expressing, feedback-rich, robust and self-perpetuating pluripotent state and a Nanog-diminished, feedback-sparse and differentiation-sensitive state. The majority of studies characterising heterogeneity in Nanog expression have used live-cell fluorescent reporter strategies. However, recent evidence suggests that these reporters may not give a faithful reflection of endogenous Nanog expression because the introduction of the reporter construct can perturb the kinetics of the underlying regulatory network. To investigate the role of Nanog further we therefore sought to model in detail the dynamics of Nanog expression in heterozygous fluorescent knock-in reporter cell lines. We develop chemical master equation, chemical Langevin equation and reaction rate equation models of the reporter system to determine how this might disturb normal Nanog transcriptional control. Our analyses indicate that the reporter construct can weaken the strength of autoactivatory feedback loops that are central to Nanog regulation, and thereby qualitatively perturbs endogenous Nanog dynamics. These results question the efficacy of commonly used reporter strategies and therefore have important implications for the design and use of synthetic reporters in general, not just for Nanog. In the second part of this thesis we consider the dynamics of populations of multipotent adult hematopoietic stem cells (HSCs). It is known that fluctuations within individual HSCs allow them to transit stochastically between functionally distinct metastable states, while the overall population distribution of expression remains stable. To investigate the relationship between single cell and population-level dynamics we propose a theoretical framework that views cellular multipotency as an instance of maximum entropy statistical inference, in which an underlying ergodic stochastic process gives rise to robust variability within the cell population. We illustrate this view by analysing expression fluctuations of the stem cell surface marker Sca1 in mouse HSCs and find that the observed dynamics naturally lie close to a critical state, thereby producing a diverse population that is able to respond rapidly to environmental changes. Although we focus on Sca1 dynamics, comparable expression fluctuations are known to generate functional diversity in other mammalian stem cell systems, including in pluripotent stem cells. Thus, the generation of ergodic expression fluctuations may be a generic way in which cell populations maintain robust multilineage differentiation potential under environmental uncertainty.
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Ferreira, Brigham Marco Paulo. "Nonstationary Stochastic Dynamics of Neuronal Membranes." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066111/document.
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Les neurones interagissent à travers leur potentiel de membrane qui a en général une évolution temporelle complexe due aux nombreuses entrées synaptiques irrégulières reçues. Cette évolution est mieux décrite en termes probabilistes, en raison de ces entrées irrégulières ou «bruit synaptique». L'évolution temporelle du potentiel de membrane est stochastique mais aussi déterministe: stochastique, car conduite par des entrées synaptiques qui arrivent de façon aléatoire dans le temps, et déterministe, car un neurone biologique a une évolution temporelle très similaire quand soumis à une même séquence d'entrées synaptiques. Nous étudions les propriétés statistiques d'un modèle simplifié de neurone soumis à des entrées à taux variable d'où en résulte l'évolution non-stationnaire du potentiel de membrane. Nous considérons un modèle passif de membrane neuronale, sans mécanisme de décharge neuronale, soumis à des entrées à courant ou à conductance sous la forme d'un processus de «shot noise». Les fluctuations du potentiel de membrane sont aussi modélisées par un processus stochastique similaire, de «shot noise» filtré. Nous avons analysé les propriétés statistiques de ces processus dans le cadre des transformations de processus ponctuels de Poisson. Des propriétés de ces transformations sont dérivées les statistiques non-stationnaires du processus. Nous obtenons ainsi des expressions analytiques exactes pour les moments et cumulants du processus filtré dans le cas général des taux d'entrée variables. Ce travail ouvre de nombreuses perspectives pour l'analyse de neurones dans les conditions in vivo, en présence d'entrées synaptiques intenses et bruitéesNeurons interact through their membrane potential that generally has a complex time evolution due to numerous irregular synaptic inputs received. This complex time evolution is best described in probabilistic terms due to this irregular or "noisy" activity. The time evolution of the membrane potential is therefore both stochastic and deterministic: it is stochastic since it is driven by random input arrival times, but also deterministic, since subjecting a biological neuron to the same sequence of input arrival times often results in very similar membrane potential traces. In this thesis, we investigated key statistical properties of a simplified neuron model under nonstationary input from other neurons that results in nonstationary evolution of membrane potential statistics. We considered a passive neuron model without spiking mechanism that is driven by input currents or conductances in the form of shot noise processes. Under such input, membrane potential fluctuations can be modeled as filtered shot noise currents or conductances. We analyzed the statistical properties of these filtered processes in the framework of Poisson Point Processes transformations. The key idea is to express filtered shot noise as a transformation of random input arrival times and to apply the properties of these transformations to derive its nonstationary statistics. Using this formalism we derive exact analytical expressions, and useful approximations, for the mean and joint cumulants of the filtered process in the general case of variable input rate. This work opens many perspectives for analyzing neurons under in vivo conditions, in the presence of intense and noisy synaptic inputs
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Brett, Tobias Stefan. "Stochastic population dynamics with delay reactions." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/stochastic-population-dynamics-with-delay-reactions(61982a13-b969-4d8d-904b-21c289c813f2).html.
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All real-world populations are composed of a finite number of individuals. Due to the intrinsically random nature of interactions between individuals, the dynamics of finite-sized populations are stochastic processes. Additionally, for many types of interaction not all effects occur instantaneously. Instead there are delays before effects are felt. The centrepiece of this thesis is a method of analytically studying stochastic population dynamics with delay reactions. Dynamics with delay reactions are non-Markovian, meaning many of the widely used techniques to study stochastic processes break down. It is not always possible to formulate the master equation, which is a common starting point for analysis of stochastic effects in population dynamics. We follow an alternative method, and derive an exact functional integral approach which is capable of capturing the effects of both stochasticity and delay in the same modelling framework. Our work builds on previous techniques developed in statistical physics, in particular the Martin-Siggia-Rose-Janssen-de Dominicis functional integral. The functional integral approach does not rely on an particular constraints on the population dynamics, for example the choice of delay distribution. Functional integrals can not in general be solved exactly. We show how the functional integral can be used to derive the deterministic, chemical Langevin, and linear-noise approximations for stochastic dynamics with delay. In the later chapters we extend Gillespie’s approximate method of studying stochastic dynamics with delay reactions, which can be used to derive the chemical Langevin equation, by-pass the functional integral. We also derive an extension to the functional integral approach so that it also covers systems with interruptible delay reactions. To demonstrate the applicability of our results we consider various models of population dynamics, arising from ecology, epidemiology, developmental biology, and chemistry. Our analytical calculations are found to provide excellent agreement with exact numerical simulations.
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Challenger, Joseph Daniel. "The stochastic dynamics of biochemical systems." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/the-stochastic-dynamics-of-biochemical-systems(bdc0634e-12d7-49c8-a587-041483c54498).html.
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The topic of this thesis is the stochastic dynamics of biochemical reaction systems. The importance of the intrinsic fluctuations in these systems has become more widely appreciated in recent years, and should be accounted for when modelling such systems mathematically. These models are described as continuous time Markov processes and their dynamics defined by a master equation. Analytical progress is made possible by the use of the van Kampen system-size expansion, which splits the dynamics into a macroscopic component plus stochastic corrections, statistics for which can then be obtained. In the first part of this thesis, the terms obtained from the expansion are written down for an arbitrary model, enabling the expansion procedure to be automated and implemented in the software package COPASI. This means that the fluctuation analysis may be used in tandem with other tools in COPASI, in particular parameter scanning and optimisation. This scheme is then extended so that models involving multiple compartments (e.g. cells) may be studied. This increases the range of models that can be evaluated in this fashion. The second part of this thesis also concerns these multi-compartment models, and examines how oscillations can synchronise across a population of cells. This has been observed in many biochemical processes, such as yeast glycolysis. However, the vast majority of modelling of such systems has used the deterministic framework, which ignores the effect of fluctuations. It is now widely known that the type of models studied here can exhibit sustained temporal oscillations when formulated stochastically, despite no such oscillations being found in the deterministic version of the model. Using the van Kampen expansion as a starting point, multi-cell models are studied, to see how stochastic oscillations in one cell may influence, and be influenced by, oscillations in neighbouring cells. Analytical expressions are found, indicating whether or not the oscillations will synchronise across multiple cells and, if synchronisation does occur, whether the oscillations synchronise in phase, or with a phase lag.
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Constable, George William Albert. "Fast timescales in stochastic population dynamics." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/fast-timescales-in-stochastic-population-dynamics(2e9cace8-e615-44ec-818e-26b96aaa6459).html.
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In this thesis, I present two methods of fast variable elimination in stochastic systems. Their application to models of population dynamics from ecology, epidemiology and population genetics, is explored. In each application, care is taken to develop the models at the microscale, in terms of interactions between individuals. Such an approach leads to well-defined stochastic systems for finite population sizes. These systems are then approximated at the mesoscale, and expressed as stochastic differential equations. It is in this setting the elimination techniques are developed. In each model a deterministically stable state is assumed to exist, about which the system is linearised. The eigenvalues of the system's Jacobian are used to identify the existence of a separation of timescales. The fast and slow directions are then given locally by the associated eigenvectors. These are used as approximations for the fast and slow directions in the full non-linear system. The general aim is then to remove these fast degrees of freedom and thus arrive at an approximate, reduced-variable description of the dynamics on a slow subspace of the full system. In the first of the methods introduced, the conditioning method, the noise of the system is constrained so that it cannot leave the slow subspace. The technique is applied to an ecological model and a susceptible-exposed-infectious-recovered epidemiological model, in both instances providing a reduced system which preserves the behaviour of the full model to high precision. The second method is referred to as the projection matrix method. It isolates the components of the noise on the slow subspace to provide its reduced description. The method is applied to a generalised Moran model of population genetics on islands, between which there is migration. The model is successfully reduced from a system in as many variables as there are islands, to an effective description in a single variable. The same methodology is later applied to the Lotka-Volterra competition model, which is found under certain conditions to behave as a Moran model. In both cases the agreement between the reduced system and stochastic simulations of the full model is excellent. It is stressed that the ideas behind both the conditioning and projection matrix methods are simple, their application systematic, and the results in very good agreement with simulations for a range of parameter values. When the methods are compared however, the projection matrix method is found in general to provide better results.
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Black, Andrew James. "The stochastic dynamics of epidemic models." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/the-stochastic-dynamics-of-epidemic-models(196cf4a1-2db2-4696-bc64-64fb28cb0b7d).html.
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This thesis is concerned with quantifying the dynamical role of stochasticity in models of recurrent epidemics. Although the simulation of stochastic models can accurately capture the qualitative epidemic patterns of childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns. The novel aspect of this thesis is the use of analytic methods to quantify the results from simulations. All the models are formulated as continuous time Markov processes, the temporal evolutions of which is described by a master equation. This is expanded in the inverse system size, which decomposes the full stochastic dynamics into a macroscopic part, described by deterministic equations, plus a stochastic fluctuating part. The first part examines the inclusion of non-exponential latent and infectious periods into the the standard susceptible-infectious-recovered model. The method of stages is used to formulate the problem as a Markov process and thus derive a power spectrum for the stochastic oscillations. This model is used to understand the dynamics of whooping cough, which we show to be the mixture of an annual limit cycle plus resonant stochastic oscillations. This limit cycle is generated by the time-dependent external forcing, but we show that the spectrum is close to that predicted by the unforced model. It is demonstrated that adding distributed infectious periods only changes the frequency and amplitude of the stochastic oscillations---the basic mechanisms remain the same. In the final part of this thesis, the effect of seasonal forcing is studied with an analysis of the full time-dependent master equation. The comprehensive nature of this approach allows us to give a coherent picture of the dynamics which unifies past work, but which also provides a systematic method for predicting the periods of oscillations seen in measles epidemics. In the pre-vaccination regime the dynamics are dominated by a period doubling bifurcation, which leads to large biennial oscillations in the deterministic dynamics. Vaccination is shown to move the system away from the biennial limit cycle and into a region where there is an annual limit cycle and stochastic oscillations, similar to whooping cough. Finite size effects are investigated and found to be of considerable importance for measles dynamics, especially in the biennial regime.
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Orr, Genevieve Beth. "Dynamics and algorithms for stochastic search /." Full text open access at:, 1995. http://content.ohsu.edu/u?/etd,197.
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Garofalo, Marco. "Dynamics of numerical stochastic perturbation theory." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31086.
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Numerical Stochastic Perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice quantum field theory. The standard algorithm based on the Langevin equation, however, suffers from several limitations which in practice restrict the potential of this technique: first of all it is not exact, a sequence of simulations with finer and finer discretization of the relevant equations have to be performed in order to extrapolate away the systematic errors in the results; and, secondly, the numerical simulations suffer from critical slowing down as the continuum limit of the theory is approached. In this thesis I investigate some alternative methods which improve upon the standard approach. In particular, I present a formulation of Numerical Stochastic Perturbation theory based on the Generalised Hybrid Molecular Dynamics algorithm and a study of the recently proposed Instantaneous Stochastic Perturbation Theory. The viability of these methods is investigated in φ4 theory.
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Wang, Shi'an. "Stochastic Dynamic Model of Urban Traffic and Optimum Management of Its Flow and Congestion." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37254.
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There are a lot more roads being built periodically in most of the countries with the advancement of modern society. In order to promote the overall traffic flow quality within different cities, city traffic management has been playing a more and more essential role during the last few decades. In recent years, a significantly increasing attention has been paid to the management of traffic flow in major cities all over the world.
In this thesis, we develop a stochastic dynamic model for urban traffic along with physical constraints characteristic of intersections equipped with traffic light. We assume that the incoming traffic to each stream in an intersection is amenable to the Poisson random process with variable intensity (mean). We introduce expressions for traffic throughput, congestion as well as operator's waiting time for the typical intersection in a city and hereafter define an appropriate objective functional. Afterwards, we formulate an optimization problem and propose the sequential (or recursive) algorithm based on the principle of optimality (dynamic programming) due to Bellman. The solution if implemented is expected to improve throughput, reduce congestion, and promote driver's satisfaction. Because the dynamic programming method is computationally quite intensive, we consider the scenario that one unit traffic stream stands for a specific number of vehicles which actually depends on the volume of traffic flow through the intersection.
The system is simulated with inputs described by several distinct nonhomogeneous Poisson processes. For example, we apply the typical traffic arrival rate in Canada with morning peak hour at around 7:30 AM and afternoon peak hour at around 4:30 PM whilst it is also applied with morning rush hour at about 8:00 AM and afternoon rush hour at about 6:00 PM like in China. In the meanwhile, we also present a group of numerical results for the traffic arrival rates that have shorter morning peak-hour period but longer afternoon rush hour period. This may occasionally happen when there are some social activities or big events in the afternoon. In addition, another series of experiments are carried out to illustrate the feasibility of the proposed dynamic model based on the traffic arrival rates with only one peak-hour throughout the whole day. The system is simulated with a series of experiments and the optimization problem is solved by dynamic programming based on the proposed algorithm which gives us the optimal feedback control law. More specifically, the results show that both the optimal traffic light timing allocated for each stream and the congestion broadcast level (CBL) of each road segment during each time segment are found. Accordingly, the corresponding optimal cost can be found for any given initial condition. It is reasonably believed that this stochastic dynamic model would be potentially applicable for real time adaptive traffic control system.
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Kuhlbrodt, Till. "Stability and variability of open-ocean deep convection in deterministic and stochastic simple models." Phd thesis, [S.l. : s.n.], 2002. http://pub.ub.uni-potsdam.de/2002/0033/kuhlb.pdf.
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Pensuwon, Wanida. "Stochastic dynamic hierarchical neural networks." Thesis, University of Hertfordshire, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366030.
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Rué, Queralt Pau. "Transient and stochastic dynamics in cellular processes." Doctoral thesis, Universitat Politècnica de Catalunya, 2013. http://hdl.handle.net/10803/128333.
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This Thesis studies different cellular and cell population processes driven by non-linear and stochastic dynamics.
The problems addressed here gravitate around the concepts of transient dynamics and relaxation from a perturbed to a steady state. In this regard, in all processes studied, stochastic fluctuations, either intrinsically present in or externally applied to these systems play an important and constructive role, by either driving the systems out of equilibrium, interfering with the underlying deterministic laws, or establishing suitable levels of heterogeneity.
The first part of the Thesis is committed the analysis of genetically regulated transient cellular processes. Here, we analyse, from a theoretical standpoint, three genetic circuits with pulsed excitable dynamics. We show that all circuits can work in two different excitable regimes, in contrast to what was previously speculated.
We also study how, in the presence of molecular noise, these excitable circuits can generate periodic polymodal pulses due to the combination of two noise induced phenomena: stabilisation of an unstable spiral point and coherence resonance.
We also studied an excitable genetic mechanism for the regulation of the transcriptional fluctuations observed in some pluripotency factors in Embryonic Stem cells. In the embryo, pluripotency is a transient cellular state and the exit of cells from it seems to be associated with transcriptional fluctuations.
In regard to pluripotency control, we also propose a novel mechanism based on the post-translational regulation of a small set of four pluripotency factors. We have validated the theoretical model, based on the formation of binary complexes among these factors, with quantitative experimental data at the single-cell level. The model suggests that the pluripotency state does not depend on the cellular levels of a single factor, but rather on the equilibrium of correlations between the different proteins. In addition, the model is able to anticipate the phenotype of several mutant cell types and suggests that the regulatory function of the protein interactions is to buffer the transcriptional activity of Oc4, a key pluripotency factor.
In the second part of the Thesis we studied the behaviour of a computational cell signalling network of the human fibroblast in the presence of external fluctuations and signals. The results obtained here indicate that the network responds in a nontrivial manner to background chatter, both intrinsically and in the presence of external periodic signals. We show that these responses are consequence of the rerouting of the signal to different network information-transmission paths that emerge as noise is modulated.
Finally, we also study the cell population dynamics during the formation of microbial biofilms, wrinkled pellicles of bacteria glued by an extracellular matrix that are one of the simplest cases of self-organised multicellular structures. In this Thesis we develop a spatiotemporal model of cellular growth and death that accounts for the experimentally observed patterns of massive bacterial death that precede wrinkle formation in biofilms. These localised patterns focus mechanical forces during biofilm expansion and trigger the formation of the characteristic ridges. In this sense, the proposed model suggests that the death patterns emerge from the mobility changes in bacteria due to the production of extracellular matrix and the spatially inhomogeneous cellular growth. An important prediction of the model is that matrix productions is crucial for the appearance of the patterns and, therefore for winkle formation. We have also experimentally validated validated this prediction with matrix deficient bacterial strains, which show neither death patterns nor wrinkles.En aquesta Tesi s’estudien diferents processos intracel·lulars i de poblacions cel·lulars regits per dinàmica estocàstica i no lineal. El problemes biològics tractats graviten al voltant el concepte de dinàmica transitòria i de relaxació d’un estat dinàmic pertorbat a l’estat estacionari. En aquest sentit, en tots els processos estudiats, les fluctuacions estocàstiques, presents intrínsecament o aplicades de forma externa, hi tenen un paper constructiu, ja sigui empenyent els sistemes fora de l’equilibri, interferint amb les lleis deterministes subjacents, o establint els nivells d’heterogeneïtat necessaris. La primera part de la Tesi es dedica a l’estudi de processos cel·lulars transitoris regulats genèticament. En ella analitzem des d’un punt de vista teòric tres circuits genètics de control de polsos excitables i, contràriament al que s’havia especulat anteriorment, establim que tots ells poden treballar en dos tipus de règim excitable. Analitzem també com, en presència de soroll molecular, aquests circuits excitables poden generar polsos periòdics i multimodals degut a la combinació de dos fenòmens induïts per soroll: l’estabilització estocàstica d’estats inestables i la ressonància de coherència. D’altra banda, estudiem com un mecanisme genètic excitable pot ser el responsable de regular a nivell transcripcional les fluctuacions que s’observen experimentalment en alguns factors de pluripotència en cèl·lules mare embrionàries. En l’embrió, la pluripotència és un estat cel·lular transitori i la sortida de les cèl·lules d’aquest sembla que està associada a fluctuacions transcripcionals. En relació al control de la pluripotència, presentem també un nou mecanisme basat en la regulació post-traduccional d’un petit conjunt de 4 factors de pluripotència. El model teòric proposat, basat en la formació de complexos entre els diferents factors de pluripotència, l’hem validat mitjançant experiments quantitatius en cèl·lules individuals. El model postula que l’estat de pluripotència no depèn dels nivells cel·lulars d’un únic factor, sinó d’un equilibri de correlacions entre diverses proteïnes. A més, prediu el fenotip de cèl·lules mutants i suggereix que la funció reguladora de les interaccions entre les quatre proteïnes és la d’esmorteir l’activitat transcripcional d’Oct4, un dels principals factors de pluripotència. En el segon apartat de la Tesi estudiem el comportament d’una xarxa computacional de senyalització cel·lular de fibroblast humà en presència de senyals externs fluctuants i cíclics. Els resultats obtinguts mostren que la xarxa respon de forma no trivial a les fluctuacions ambientals, fins i tot en presència d’una senyal externa. Diferents nivells de soroll permeten modular la resposta de la xarxa, mitjançant la selecció de rutes alternatives de transmissió de la informació. Finalment, estudiem la dinàmica de poblacions cel·lulars durant la formació de biofilms, pel·lícules arrugades d’aglomerats de bacteris que conformen un dels exemples més simples d’estructures multicel·lulars autoorganitzades. En aquesta Tesi presentem un model espai-temporal de creixement i mort cel·lular motivat per l’evidència experimental sobre l’aparició de patrons de mort massiva de bacteris previs a la formació de les arrugues dels biofilms. Aquests patrons localitzats concentren les forces mecàniques durant l’expansió del biofilm i inicien la formació de les arrugues característiques. En aquest sentit, el model proposat explica com es formen els patrons de mort a partir dels canvis de mobilitat dels bacteris deguts a la producció de matriu extracel·lular combinats amb un creixement espacialment heterogeni. Una important predicció del model és que la producció de matriu és un procés clau per a l’aparició dels patrons i, per tant de les arrugues. En aquest aspecte, els nostres resultats experimentals en bacteris mutants que no produeixen components essencials de la matriu, confirmen les prediccions.
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Erdmann, Thorsten. "Stochastic dynamics of adhesion clusters under force." Phd thesis, [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=97610492X.
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Martí, Ortega Daniel. "Neural stochastic dynamics of perceptual decision making." Doctoral thesis, Universitat Pompeu Fabra, 2008. http://hdl.handle.net/10803/7552.
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Models computacionals basats en xarxes a gran escala d'inspiració neurobiològica permeten descriure els correlats neurals de la decisió observats en certes àrees corticals com una transició entre atractors de la xarxa cortical. L'estimulació provoca un canvi en el paisatge d'atractors que afavoreix la transició entre l'atractor neutre inicial a un dels atractors associats a les eleccions categòriques. El soroll present en el sistema introdueix indeterminació en les transicions. En aquest treball mostrem l'existència de dos mecanismes de decisió qualitativament diferents, cadascun amb signatures psicofísiques diferenciades. El mecanisme que apareix a baixes intensitats, induït exclusivament pel soroll, dóna lloc a temps de decisió distribuïts asimètricament, amb una mitjana dictada per l'amplitud del soroll.A més, tant els temps de decisió com el rendiment psicofísic són funcions decreixents de l'estimulació externa. També proposem dos mètodes, un basat en l'aproximació macroscòpica i un altre en la teoria de la varietat central, que simplifiquen la descripció de sistemes estocàstics multistables.Computational models based on large-scale, neurobiologically-inspired networks describe the decision-related activity observed in some cortical areas as a transition between attractors of the cortical network. Stimulation induces a change in the attractor configuration and drives the system out from its initial resting attractor to one of the existing attractors associated with the categorical choices. The noise present in the system renders transitions random. We show that there exist two qualitatively different mechanisms for decision, each with distinctive psychophysical signatures. The decision mechanism arising at low inputs, entirely driven by noise, leads to skewed distributions of decision times, with a mean governed by the amplitude of the noise. Moreover, both decision times and performances are monotonically decreasing functions of the overall external stimulation. We also propose two methods, one based on the macroscopic approximation and one based on center manifold theory, to simplify the description of multistable stochastic neural systems.
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Dammer, Stephan M. "Stochastic many-particle systems with irreversible dynamics." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974953334.
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Dammer, Stephan Markus. "Stochastic many-particle systems with irreversible dynamics." Gerhard-Mercator-Universitaet Duisburg, 2005. http://www.ub.uni-duisburg.de/ETD-db/theses/available/duett-01282005-115619/.
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In this thesis, several stochastic models are investigated, which are subjected to irreversible dynamics. Motivation for the presented work stems, on the one hand, from particular physical systems under consideration, which are modeled by the studied stochastic processes. Besides that, the models discussed in this thesis are, on the other hand, generally interesting from the point of view of statistical physics, since they describe systems far from thermodynamic equilibrium. Interesting properties to be encountered are, e.g., dynamical scaling behavior or continuous phase transitions. The first issue to be addressed, is the investigation of irreversibly aggregating systems, where the main emphasis is laid on aggregation of monopolarly charged clusters suspended in a fluid. For this purpose, rate equations are analyzed and Brownian dynamics simulations are performed. It is shown that the system crosses over from power-law cluster growth to sub-logarithmic cluster growth. Asymptotically, the cluster size distribution evolves towards a universal scaling form, which implies a 'self-focussing' of the size distribution. Another emphasis of this thesis is the investigation of nonequilibrium critical phenomena, in particular, the study of phase transitions into absorbing states (states that may be reached irreversibly). To this end, the continuous nonequilibrium phase transition of directed percolation, which serves as a paradigm for absorbing-state phase transitions, is analyzed by a novel approach. Despite the lack of a partition function for directed percolation, this novel approach follows the ideas of Yang-Lee theory of equilibrium statistical mechanics, by investigating the complex roots of the survival probability. Stochastic models such as directed percolation mimic spreading processes, e.g., the spreading of an infectious disease. The effect of long-time memory, which is not included in directed percolation and which corresponds to immunization in epidemic spreading, is investigated through an appropriate model. This model includes dynamical percolation (perfect immunization) as a special case, as well as directed percolation (no immunization). The critical behavior of this model is studied by means of Monte Carlo simulations, in particular for weak immunization. A further generalization is investigated, which allows spontaneous mutations and different species of spreading agents (pathogens). Restricting the analysis to perfect immunization and two spatial dimensions, it is shown by Monte Carlo simulations, that immunization leads to a crossover from dynamical to directed percolation. Other properties of this model are discussed in detail.
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Sulstarova, Astrit. "Sovereign debt dynamics in a stochastic environment /." Genève : Inst. Univ. de Hautes Etudes Internat, 2008. http://www.gbv.de/dms/zbw/569461138.pdf.
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Meadows, Brian K. "Spatiotemporal dynamics of stochastic and chaotic arrays." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/30747.
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Liang, Gechun. "A functional approach to backward stochastic dynamics." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:afb9af6f-c79c-4204-838d-2a4872c1c796.
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In this thesis, we consider a class of stochastic dynamics running backwards, so called backward stochastic differential equations (BSDEs) in the literature. We demonstrate BSDEs can be reformulated as functional differential equations defined on path spaces, and therefore solving BSDEs is equivalent to solving the associated functional differential equations. With such observation we can solve BSDEs on general filtered probability space satisfying the usual conditions, and in particular without the requirement of the martingale representation. We further solve the above functional differential equations numerically, and propose a numerical scheme based on the time discretization and the Picard iteration. This in turn also helps us solve the associated BSDEs numerically. In the second part of the thesis, we consider a class of BSDEs with quadratic growth (QBSDEs). By using the functional differential equation approach introduced in this thesis and the idea of the Cole-Hopf transformation, we first solve the scalar case of such QBSDEs on general filtered probability space satisfying the usual conditions. For a special class of QBSDE systems (not necessarily scalar) in Brownian setting, we do not use such Cole-Hopf transformation at all, and instead introduce the weak solution method, which is to use the strong solutions of forward backward stochastic differential equations (FBSDEs) to construct the weak solutions of such QBSDE systems. Finally we apply the weak solution method to a specific financial problem in the credit risk setting, where we modify the Merton's structural model for credit risk by using the idea of indifference pricing. The valuation and the hedging strategy are characterized by a class of QBSDEs, which we solve by the weak solution method.
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Mitrovic, Djordje. "Stochastic optimal control with learned dynamics models." Thesis, University of Edinburgh, 2011. http://hdl.handle.net/1842/4783.
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The motor control of anthropomorphic robotic systems is a challenging computational task mainly because of the high levels of redundancies such systems exhibit. Optimality principles provide a general strategy to resolve such redundancies in a task driven fashion. In particular closed loop optimisation, i.e., optimal feedback control (OFC), has served as a successful motor control model as it unifies important concepts such as costs, noise, sensory feedback and internal models into a coherent mathematical framework. Realising OFC on realistic anthropomorphic systems however is non-trivial: Firstly, such systems have typically large dimensionality and nonlinear dynamics, in which case the optimisation problem becomes computationally intractable. Approximative methods, like the iterative linear quadratic gaussian (ILQG), have been proposed to avoid this, however the transfer of solutions from idealised simulations to real hardware systems has proved to be challenging. Secondly, OFC relies on an accurate description of the system dynamics, which for many realistic control systems may be unknown, difficult to estimate, or subject to frequent systematic changes. Thirdly, many (especially biologically inspired) systems suffer from significant state or control dependent sources of noise, which are difficult to model in a generally valid fashion. This thesis addresses these issues with the aim to realise efficient OFC for anthropomorphic manipulators. First we investigate the implementation of OFC laws on anthropomorphic hardware. Using ILQG we optimally control a high-dimensional anthropomorphic manipulator without having to specify an explicit inverse kinematics, inverse dynamics or feedback control law. We achieve this by introducing a novel cost function that accounts for the physical constraints of the robot and a dynamics formulation that resolves discontinuities in the dynamics. The experimental hardware results reveal the benefits of OFC over traditional (open loop) optimal controllers in terms of energy efficiency and compliance, properties that are crucial for the control of modern anthropomorphic manipulators. We then propose a new framework of OFC with learned dynamics (OFC-LD) that, unlike classic approaches, does not rely on analytic dynamics functions but rather updates the internal dynamics model continuously from sensorimotor plant feedback. We demonstrate how this approach can compensate for unknown dynamics and for complex dynamic perturbations in an online fashion. A specific advantage of a learned dynamics model is that it contains the stochastic information (i.e., noise) from the plant data, which corresponds to the uncertainty in the system. Consequently one can exploit this information within OFC-LD in order to produce control laws that minimise the uncertainty in the system. In the domain of antagonistically actuated systems this approach leads to improved motor performance, which is achieved by co-contracting antagonistic actuators in order to reduce the negative effects of the noise. Most importantly the shape and source of the noise is unknown a priory and is solely learned from plant data. The model is successfully tested on an antagonistic series elastic actuator (SEA) that we have built for this purpose. The proposed OFC-LD model is not only applicable to robotic systems but also proves to be very useful in the modelling of biological motor control phenomena and we show how our model can be used to predict a wide range of human impedance control patterns during both, stationary and adaptation tasks.
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RODRIGUEZ, CARLOS ENRIQUE OLIVARES. "EFFECTIVE STOCHASTIC DYNAMICS OF SIMPLIFIED PROTEIN SEQUENCES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=23611@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
As proteínas e outros peptídeos são cadeias de aminoácidos que desempenham funções biológicas específicas dentro de um organismo. A funcionalidade dessas estruturas depende da sua organização tridimensional, portanto é importante determinar quais são os fatores que controlam o bom enovelamento. Se a sequência é conhecida em principio poder-se-ia predizer sua estrutura 3D mediante uma dinâmica molecular de todos os átomos da sequência e das moléculas de água circundantes, mas é claro que esse tipo de simulação é inviável com os recursos computacionais atuais. Alternativamente, consideramos modelos simplificados que levem em conta somente as características principais de cada monômero e das partículas do meio. Efetuamos simulações de dinâmica molecular, considerando interações do tipo Lennard Jones entre monômeros (distinguindo entre monômeros polares e hidrofóbicos) e adicionalmente incorporando uma força estocástica (Langevin) para complementar a influência do meio aquoso. Consideramos diversas sequências lineares, simétricas e de comprimento fixo, evoluindo no espaço bi ou tridimensional. Como resultado destas simulações, podemos descrever a evolução temporal no espaço de conformações mediante variáveis efetivas ou coordenadas de reação, tais como o raio de giro, a distância entre as extremidades ou o número de contatos entre monômeros não ligados. Da análise das séries temporais dessas variáveis efetivas, extraímos os coeficientes que permitem construir seja a equação diferencial estocástica do movimento das variáveis efetivas ou a equação de Fokker-Planck associada. Estas equações para um número reduzido de graus de liberdade permitem, em princípio, obter informações sobre mudanças conformacionais, difíceis de acessar na descrição completa no espaço de fases original, de alta dimensionalidade. Discutimos as vantagens e limitações desta abordagem.
Proteins and other peptides are aminoacid chains that perform specific biological functions within an organism. The functionality of these structures depends on their three-dimensional organization, so it is important to determine what are the factors that control the proper folding. If the sequence is known, in principle it would be possible to predict its 3D structure by means of molecular dynamics of all atoms of the sequence and the surrounding water molecules, but it is clear that this type of simulation is not feasible with the current computational resources. Alternatively, we consider simplified models that take into account only the main characteristics of each monomer and the particles of the medium. We have performed molecular dynamics simulations, considering the LennardJones-like interactions between monomers (distinguishing between polar and hydrophobic monomers) and additionally incorporating a stochastic (Langevin) force to complement the influence of the aqueous medium. We considered several linear sequences, symmetric, with fixed-length, evolving in the tri or bi-dimensional space. As a result of these simulations, we can describe the temporal evolution in the space of conformations through effective variables or reaction coordinates, such as gyration radius, distance between ends or number of contacts between unbound monomers. From the analysis of the time series of the effective variables, we extract the coefficients that allow to build the stochastic differential equation of motion of the effective variables or its associated Fokker-Planck equation. These equations for a limited number of degrees of freedom provide, in principle, information on conformational changes, which are difficult to access in the description of the original, high dimensional, phase. We discuss the advantages and limitations of this approach.
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Geffert, Paul Matthias. "Nonequilibrium dynamics of piecewise-smooth stochastic systems." Thesis, Queen Mary, University of London, 2018. http://qmro.qmul.ac.uk/xmlui/handle/123456789/46783.
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Piecewise-smooth stochastic systems have attracted a lot of interest in the last decades in engineering science and mathematics. Many investigations have focused only on one-dimensional problems. This thesis deals with simple two-dimensional piecewise-smooth stochastic systems in the absence of detailed balance. We investigate the simplest example of such a system, which is a pure dry friction model subjected to coloured Gaussian noise. The nite correlation time of the noise establishes an additional dimension in the phase space and gives rise to a non-vanishing probability current. Our investigation focuses on stick-slip transitions, which can be related to a critical value of the noise correlation time. Analytical insight is provided by applying the uni ed coloured noise approximation. Afterwards, we extend our previous model by adding viscous friction and a constant force. Then we perform a similar analysis as for the pure dry friction case. With parameter values close to the deterministic stick-slip transition, we observe a non-monotonic behaviour of the probability of sticking by increasing the correlation time of the noise. As the eigenvalue spectrum is not accessible for the systems with coloured noise, we consider the eigenvalue problem of a dry friction model with displacement, velocity and Gaussian white noise. By imposing periodic boundary conditions on the displacement and using a Fourier ansatz, we can derive an eigenvalue equation, which has a similar form in comparison to the known one-dimensional problem for the velocity only. The eigenvalue analysis is done for the case without a constant force and with a constant force separately. Finally, we conclude our ndings and provide an outlook on related open problems.
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Von, Gottberg friedrich K. (Friedrich Klemens). "Stochastic dynamics simulations of surfactant self-assembly." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/42642.
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Cao, Jiarui. "Dynamics of condensation in stochastic particle systems." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/77674/.
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Condensation is a special class of phase transition which has been observed throughout the natural and social sciences. The understanding of the critical behaviour of such systems is a very active area of current research, in particular a mathematical description of the formation and time evolution of the condensate. In this thesis we study these phenomena in several models. In particular we focus on the recently introduced inclusion process, and we compare it with related classical mass transport models such as zero range processes. We first give a brief review of relevant definitions and properties of interacting particle systems, in particular recent literatures on the condensation and stationary behaviour of a large class of interacting particle systems with stationary product measures, which forms the theoretical basis of this thesis. The second part of this thesis is on the dynamics of condensation in the inclusion process on a one-dimensional periodic lattice in the thermodynamic limit. This generalises recent results which were limited to finite lattices and symmetric dynamics. Our main focus is firstly on totally asymmetric dynamics which have not been studied before, which we compare to exact solutions for symmetric systems. We identify all the relevant dynamical regimes and corresponding time scales as a function of the system size, including a coarsening regime where clusters move on the lattice and exchange particles, leading to a growing average cluster size. After establishing the general approach to study dynamics of condensation in totally asymmetric processes, we extend the results to more general partially asymmetric cases as well as higher dimensional cases. In the third part of this thesis we derive some preliminary exact results on symmetric systems through duality, which recovers heuristic results in previous chapter and allows us to treat coarsening in the infinite lattice directly.
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Dickson, Scott M. "Stochastic neural network dynamics : synchronisation and control." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/16508.
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Biological brains exhibit many interesting and complex behaviours. Understanding of the mechanisms behind brain behaviours is critical for continuing advancement in fields of research such as artificial intelligence and medicine. In particular, synchronisation of neuronal firing is associated with both improvements to and degeneration of the brain's performance; increased synchronisation can lead to enhanced information-processing or neurological disorders such as epilepsy and Parkinson's disease. As a result, it is desirable to research under which conditions synchronisation arises in neural networks and the possibility of controlling its prevalence. Stochastic ensembles of FitzHugh-Nagumo elements are used to model neural networks for numerical simulations and bifurcation analysis. The FitzHugh-Nagumo model is employed because of its realistic representation of the flow of sodium and potassium ions in addition to its advantageous property of allowing phase plane dynamics to be observed. Network characteristics such as connectivity, configuration and size are explored to determine their influences on global synchronisation generation in their respective systems. Oscillations in the mean-field are used to detect the presence of synchronisation over a range of coupling strength values. To ensure simulation efficiency, coupling strengths between neurons that are identical and fixed with time are investigated initially. Such networks where the interaction strengths are fixed are referred to as homogeneously coupled. The capacity of controlling and altering behaviours produced by homogeneously coupled networks is assessed through the application of weak and strong delayed feedback independently with various time delays. To imitate learning, the coupling strengths later deviate from one another and evolve with time in networks that are referred to as heterogeneously coupled. The intensity of coupling strength fluctuations and the rate at which coupling strengths converge to a desired mean value are studied to determine their impact upon synchronisation performance. The stochastic delay differential equations governing the numerically simulated networks are then converted into a finite set of deterministic cumulant equations by virtue of the Gaussian approximation method. Cumulant equations for maximal and sub-maximal connectivity are used to generate two-parameter bifurcation diagrams on the noise intensity and coupling strength plane, which provides qualitative agreement with numerical simulations. Analysis of artificial brain networks, in respect to biological brain networks, are discussed in light of recent research in sleep theory.
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Shen, Tongye. "Fluctuations and stochastic dynamics in molecular biophysics /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2002. http://wwwlib.umi.com/cr/ucsd/fullcit?p3061634.
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