Nonadiabatic entropy production for non-Markov dynamics
NASA Astrophysics Data System (ADS)
García-García, Reinaldo
2012-09-01
We extend the definition of nonadiabatic entropy production given for Markovian systems by Esposito and Van den Broeck [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.104.090601 104, 090601 (2010)], to arbitrary non-Markov ergodic dynamics. We also introduce a notion of stability characterizing non-Markovianity. For stable non-Markovian systems, the nonadiabatic entropy production satisfies an integral fluctuation theorem, leading to the second law of thermodynamics for transitions between nonequilibrium steady states. This quantity can also be written as a sum of products of generalized fluxes and forces, thus being suitable for thermodynamics. On the other hand, the generalized fluctuation-dissipation relation also holds, clarifying that the conditions for it to be satisfied are ergodicity and stability instead of Markovianity. We show that in spite of being counterintuitive, the stability criterion introduced in this work may be violated in non-Markovian systems even if they are ergodic, leading to a violation of the fluctuation theorem and the generalized fluctuation-dissipation relation. Stability represents then a necessary condition for the above properties to hold and explains why the generalized fluctuation-dissipation relation has remained elusive in the study of non-Markov systems exhibiting nonequilibrium steady states.
Non-Markov dissipative dynamics of electron transfer in a photosynthetic reaction center
NASA Astrophysics Data System (ADS)
Poddubnyy, V. V.; Glebov, I. O.; Eremin, V. V.
2014-02-01
We consider the dissipative dynamics of electron transfer in the photosynthetic reaction center of purple bacteria and propose a model where the transition between electron states arises only due to the interaction between a chromophore system and the protein environment and is not accompanied by the motion of nuclei of the reaction subsystem. We establish applicability conditions for the Markov approximation in the framework of this model and show that these conditions are not necessarily satisfied in the protein medium. We represent the spectral function of the "system+heat bath" interaction in the form of one or several Gaussian functions to study specific characteristics of non-Markov dynamics of the final state population, the presence of an induction period and vibrations. The consistency of the computational results obtained for non-Markov dynamics with experimental data confirms the correctness of the proposed approach.
Non-Markov stochastic processes satisfying equations usually associated with a Markov process
NASA Astrophysics Data System (ADS)
McCauley, J. L.
2012-04-01
There are non-Markov Ito processes that satisfy the Fokker-Planck, backward time Kolmogorov, and Chapman-Kolmogorov equations. These processes are non-Markov in that they may remember an initial condition formed at the start of the ensemble. Some may even admit 1-point densities that satisfy a nonlinear 1-point diffusion equation. However, these processes are linear, the Fokker-Planck equation for the conditional density (the 2-point density) is linear. The memory may be in the drift coefficient (representing a flow), in the diffusion coefficient, or in both. We illustrate the phenomena via exactly solvable examples. In the last section we show how such memory may appear in cooperative phenomena.
Markov and non-Markov processes in complex systems by the dynamical information entropy
NASA Astrophysics Data System (ADS)
Yulmetyev, R. M.; Gafarov, F. M.
1999-12-01
We consider the Markov and non-Markov processes in complex systems by the dynamical information Shannon entropy (DISE) method. The influence and important role of the two mutually dependent channels of entropy alternation (creation or generation of correlation) and anti-correlation (destroying or annihilation of correlation) have been discussed. The developed method has been used for the analysis of the complex systems of various natures: slow neutron scattering in liquid cesium, psychology (short-time numeral and pattern human memory and effect of stress on the dynamical taping-test), random dynamics of RR-intervals in human ECG (problem of diagnosis of various disease of the human cardio-vascular systems), chaotic dynamics of the parameters of financial markets and ecological systems.
Dynamical properties of non-Markovian stochastic differential equations
NASA Astrophysics Data System (ADS)
Hernández-Machado, A.; San Miguel, M.
1984-04-01
We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an Ornstein-Uhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.
Stochastic ice stream dynamics
NASA Astrophysics Data System (ADS)
Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca
2016-08-01
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.
Stochastic ice stream dynamics.
Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca
2016-08-01
Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution. PMID:27457960
Dynamics of Double Stochastic Operators
NASA Astrophysics Data System (ADS)
Saburov, Mansoor
2016-03-01
A double stochastic operator is a generalization of a double stochastic matrix. In this paper, we study the dynamics of double stochastic operators. We give a criterion for a regularity of a double stochastic operator in terms of absences of its periodic points. We provide some examples to insure that, in general, a trajectory of a double stochastic operator may converge to any interior point of the simplex.
Stochastic Quantum Gas Dynamics
NASA Astrophysics Data System (ADS)
Proukakis, Nick P.; Cockburn, Stuart P.
2010-03-01
We study the dynamics of weakly-interacting finite temperature Bose gases via the Stochastic Gross-Pitaevskii equation (SGPE). As a first step, we demonstrate [jointly with A. Negretti (Ulm, Germany) and C. Henkel (Potsdam, Germany)] that the SGPE provides a significantly better method for generating an equilibrium state than the number-conserving Bogoliubov method (except for low temperatures and small atom numbers). We then study [jointly with H. Nistazakis and D.J. Frantzeskakis (University of Athens, Greece), P.G.Kevrekidis (University of Massachusetts) and T.P. Horikis (University of Ioannina, Greece)] the dynamics of dark solitons in elongated finite temperature condensates. We demonstrate numerical shot-to-shot variations in soliton trajectories (S.P. Cockburn et al., arXiv:0909.1660.), finding individual long-lived trajectories as in experiments. In our simulations, these variations arise from fluctuations in the phase and density of the underlying medium. We provide a detailed statistical analysis, proposing regimes for the controlled experimental demonstration of this effect; we also discuss the extent to which simpler models can be used to mimic the features of ensemble-averaged stochastic trajectories.
Stochastic dynamics of dengue epidemics
NASA Astrophysics Data System (ADS)
de Souza, David R.; Tomé, Tânia; Pinho, Suani T. R.; Barreto, Florisneide R.; de Oliveira, Mário J.
2013-01-01
We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice versa, so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible, for any death rate of infected mosquitoes.
NonMarkov Ito Processes with 1- state memory
NASA Astrophysics Data System (ADS)
McCauley, Joseph L.
2010-08-01
A Markov process, by definition, cannot depend on any previous state other than the last observed state. An Ito process implies the Fokker-Planck and Kolmogorov backward time partial differential eqns. for transition densities, which in turn imply the Chapman-Kolmogorov eqn., but without requiring the Markov condition. We present a class of Ito process superficially resembling Markov processes, but with 1-state memory. In finance, such processes would obey the efficient market hypothesis up through the level of pair correlations. These stochastic processes have been mislabeled in recent literature as 'nonlinear Markov processes'. Inspired by Doob and Feller, who pointed out that the ChapmanKolmogorov eqn. is not restricted to Markov processes, we exhibit a Gaussian Ito transition density with 1-state memory in the drift coefficient that satisfies both of Kolmogorov's partial differential eqns. and also the Chapman-Kolmogorov eqn. In addition, we show that three of the examples from McKean's seminal 1966 paper are also nonMarkov Ito processes. Last, we show that the transition density of the generalized Black-Scholes type partial differential eqn. describes a martingale, and satisfies the ChapmanKolmogorov eqn. This leads to the shortest-known proof that the Green function of the Black-Scholes eqn. with variable diffusion coefficient provides the so-called martingale measure of option pricing.
Stochastic models of neuronal dynamics
Harrison, L.M; David, O; Friston, K.J
2005-01-01
Cortical activity is the product of interactions among neuronal populations. Macroscopic electrophysiological phenomena are generated by these interactions. In principle, the mechanisms of these interactions afford constraints on biologically plausible models of electrophysiological responses. In other words, the macroscopic features of cortical activity can be modelled in terms of the microscopic behaviour of neurons. An evoked response potential (ERP) is the mean electrical potential measured from an electrode on the scalp, in response to some event. The purpose of this paper is to outline a population density approach to modelling ERPs. We propose a biologically plausible model of neuronal activity that enables the estimation of physiologically meaningful parameters from electrophysiological data. The model encompasses four basic characteristics of neuronal activity and organization: (i) neurons are dynamic units, (ii) driven by stochastic forces, (iii) organized into populations with similar biophysical properties and response characteristics and (iv) multiple populations interact to form functional networks. This leads to a formulation of population dynamics in terms of the Fokker–Planck equation. The solution of this equation is the temporal evolution of a probability density over state-space, representing the distribution of an ensemble of trajectories. Each trajectory corresponds to the changing state of a neuron. Measurements can be modelled by taking expectations over this density, e.g. mean membrane potential, firing rate or energy consumption per neuron. The key motivation behind our approach is that ERPs represent an average response over many neurons. This means it is sufficient to model the probability density over neurons, because this implicitly models their average state. Although the dynamics of each neuron can be highly stochastic, the dynamics of the density is not. This means we can use Bayesian inference and estimation tools that have
Stochastics In Circumplanetary Dust Dynamics
NASA Astrophysics Data System (ADS)
Spahn, F.; Krivov, A. V.; Sremcevic, M.; Schwarz, U.; Kurths, J.
Charged dust grains in circumplanetary environments experience, beyond various de- terministic forces, also stochastic perturbations: E.g., fluctuations of the magnetic field, the charge of the grains etc. Here, we investigate the dynamics of a dust population in a circular orbit around the planet which is perturbed by a stochastic magnetic field B , modeled by an isotropi- cally Gaussian white noise. The resulting perturbation equations give rise to a modi- 2 fied diffusion of the inclinations and eccentricities x D [t +/- sin[2nt]/(2n)] (x - alias for eccentricity e and the inclination i, t - time). The diffusion coefficient is found to be D = [G]2/n, where the gyrofrequency and the orbital frequency are denoted by G, and n, respectively. This behavior has been checked by numerical experiments. We have chosen dust grains (1µm in radius) initially moving in circular orbits around a planet (Jupiter) and integrated numerically their trajectories over their typical lifetimes (100 years). The particles were exposed to a Gaussian fluctuating magnetic field B obeying the same statistical properties as in the analytical treatment. In this case, the theoretical 2 findings have been confirmed according to x D t with a diffusion coefficient of D G/n. 2 The theoretical studies showed the statistical properties of B being of decisive im- portance. To this aim, we analyzed the magnetic field data measured by the Galileo magnetometer at Jupiter and found almost Gaussian fluctuations of about 5 % of the mean field and exponentially decaying correlations. This results in a diffusion in the space of orbital elements of at least 1...5 % (variations of inclinations and eccentric- ity) over the lifetime of the dust grains. For smaller dusty motes stochastics might well dominate the dynamics.
Stochastic dynamics of cancer initiation
NASA Astrophysics Data System (ADS)
Foo, Jasmine; Leder, Kevin; Michor, Franziska
2011-02-01
Most human cancer types result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Once the first change (or changes) have arisen, tumorigenesis is initiated and the subsequent emergence of additional alterations drives progression to more aggressive and ultimately invasive phenotypes. Elucidation of the dynamics of cancer initiation is of importance for an understanding of tumor evolution and cancer incidence data. In this paper, we develop a novel mathematical framework to study the processes of cancer initiation. Cells at risk of accumulating oncogenic mutations are organized into small compartments of cells and proliferate according to a stochastic process. During each cell division, an (epi)genetic alteration may arise which leads to a random fitness change, drawn from a probability distribution. Cancer is initiated when a cell gains a fitness sufficiently high to escape from the homeostatic mechanisms of the cell compartment. To investigate cancer initiation during a human lifetime, a 'race' between this fitness process and the aging process of the patient is considered; the latter is modeled as a second stochastic Markov process in an aging dimension. This model allows us to investigate the dynamics of cancer initiation and its dependence on the mutational fitness distribution. Our framework also provides a methodology to assess the effects of different life expectancy distributions on lifetime cancer incidence. We apply this methodology to colorectal tumorigenesis while considering life expectancy data of the US population to inform the dynamics of the aging process. We study how the probability of cancer initiation prior to death, the time until cancer initiation, and the mutational profile of the cancer-initiating cell depends on the shape of the mutational fitness distribution and life expectancy of the population.
Rarefied gas dynamics using stochastic rotation dynamics
NASA Astrophysics Data System (ADS)
Tuzel, Erkan; Ihle, Thomas; Kroll, Daniel M.
2003-03-01
In the past two decades, Direct Simulation Monte Carlo (DSMC) has been the dominant predictive tool for rarefied gas dynamics. In the non-hydrodynamic regime, where continuum models fail, particle based methods have been used to model systems ranging from shuttle re-entry problems to mesoscopic flow in MEMS devices. A new method, namely stochastic rotation dynamics (SRD), which utilizes effective multiparticle collisions, will be described. It will be shown that it is possible to get the correct transport coefficients for Argon gas by tuning the collision parameters, namely the collision angle and collision probability. Simulation results comparing DSMC and SRD will be shown for equilibrium relaxation rates and Poiseuille flow. One important feature of SRD is that it coarse-grains the time scale, so that simulations in the transition regime are typically five to twenty times faster than for DSMC. Benchmarks as a function of Knudsen number will be given, and directions for further research will be discussed.
Variational principles for stochastic fluid dynamics
Holm, Darryl D.
2015-01-01
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.
Stochastic description of quantum Brownian dynamics
NASA Astrophysics Data System (ADS)
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
Immigration-extinction dynamics of stochastic populations
NASA Astrophysics Data System (ADS)
Meerson, Baruch; Ovaskainen, Otso
2013-07-01
How high should be the rate of immigration into a stochastic population in order to significantly reduce the probability of observing the population become extinct? Is there any relation between the population size distributions with and without immigration? Under what conditions can one justify the simple patch occupancy models, which ignore the population distribution and its dynamics in a patch, and treat a patch simply as either occupied or empty? We answer these questions by exactly solving a simple stochastic model obtained by adding a steady immigration to a variant of the Verhulst model: a prototypical model of an isolated stochastic population.
Automated Flight Routing Using Stochastic Dynamic Programming
NASA Technical Reports Server (NTRS)
Ng, Hok K.; Morando, Alex; Grabbe, Shon
2010-01-01
Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.
Stochastic solution to quantum dynamics
NASA Technical Reports Server (NTRS)
John, Sarah; Wilson, John W.
1994-01-01
The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.
Stochastic Resonance in Protein Folding Dynamics.
Davtyan, Aram; Platkov, Max; Gruebele, Martin; Papoian, Garegin A
2016-05-01
Although protein folding reactions are usually studied under static external conditions, it is likely that proteins fold in a locally fluctuating cellular environment in vivo. To mimic such behavior in in vitro experiments, the local temperature of the solvent can be modulated either harmonically or using correlated noise. In this study, coarse-grained molecular simulations are used to investigate these possibilities, and it is found that both periodic and correlated random fluctuations of the environment can indeed accelerate folding kinetics if the characteristic frequencies of the applied fluctuations are commensurate with the internal timescale of the folding reaction; this is consistent with the phenomenon of stochastic resonance observed in many other condensed-matter processes. To test this theoretical prediction, the folding dynamics of phosphoglycerate kinase under harmonic temperature fluctuations are experimentally probed using Förster resonance energy transfer fluorescence measurements. To analyze these experiments, a combination of theoretical approaches is developed, including stochastic simulations of folding kinetics and an analytical mean-field kinetic theory. The experimental observations are consistent with the theoretical predictions of stochastic resonance in phosphoglycerate kinase folding. When combined with an alternative experiment on the protein VlsE using a power spectrum analysis, elaborated in Dave et al., ChemPhysChem 2016, 10.1002/cphc.201501041, the overall data overwhelmingly point to the experimental confirmation of stochastic resonance in protein folding dynamics. PMID:26992148
Stochastic game dynamics under demographic fluctuations
Huang, Weini; Hauert, Christoph; Traulsen, Arne
2015-01-01
Frequency-dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency-dependent selection, the average fitness of the population may increase or decrease based on interactions between individuals within the population. This should be reflected in fluctuations of the population size even in constant environments. Here, we propose a stochastic model that naturally combines these two evolutionary ingredients by assuming frequency-dependent competition between different types in an individual-based model. In contrast to previous game theoretic models, the carrying capacity of the population, and thus the population size, is determined by pairwise competition of individuals mediated by evolutionary games and demographic stochasticity. In the limit of infinite population size, the averaged stochastic dynamics is captured by deterministic competitive Lotka–Volterra equations. In small populations, demographic stochasticity may instead lead to the extinction of the entire population. Because the population size is driven by fitness in evolutionary games, a population of cooperators is less prone to go extinct than a population of defectors, whereas in the usual systems of fixed size the population would thrive regardless of its average payoff. PMID:26150518
Stochastic game dynamics under demographic fluctuations.
Huang, Weini; Hauert, Christoph; Traulsen, Arne
2015-07-21
Frequency-dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency-dependent selection, the average fitness of the population may increase or decrease based on interactions between individuals within the population. This should be reflected in fluctuations of the population size even in constant environments. Here, we propose a stochastic model that naturally combines these two evolutionary ingredients by assuming frequency-dependent competition between different types in an individual-based model. In contrast to previous game theoretic models, the carrying capacity of the population, and thus the population size, is determined by pairwise competition of individuals mediated by evolutionary games and demographic stochasticity. In the limit of infinite population size, the averaged stochastic dynamics is captured by deterministic competitive Lotka-Volterra equations. In small populations, demographic stochasticity may instead lead to the extinction of the entire population. Because the population size is driven by fitness in evolutionary games, a population of cooperators is less prone to go extinct than a population of defectors, whereas in the usual systems of fixed size the population would thrive regardless of its average payoff. PMID:26150518
Stochastic rotation dynamics for nematic liquid crystals
Lee, Kuang-Wu Mazza, Marco G.
2015-04-28
We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified Ericksen-Leslie formulation of nematodynamics. We verify the applicability of this hybrid model by studying the equilibrium isotropic-nematic phase transition and nonequilibrium problems, such as the dynamics of topological defects and the rheology of sheared LCs. Our simulation results show that this hybrid model captures many essential aspects of LC physics at the mesoscopic scale, while preserving microscopic thermal fluctuations.
A stochastic evolutionary model for survival dynamics
NASA Astrophysics Data System (ADS)
Fenner, Trevor; Levene, Mark; Loizou, George
2014-09-01
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis, traditionally employed in clinical trials and reliability analysis in engineering. In our model, the only implicit assumption made is that the longer an actor has been in the system, the more likely it is to have failed. We derive a power-law distribution for the process and provide preliminary empirical evidence for the validity of the model from two well-known survival analysis data sets.
Stochastic hybrid modeling of intracellular calcium dynamics
NASA Astrophysics Data System (ADS)
Choi, TaiJung; Maurya, Mano Ram; Tartakovsky, Daniel M.; Subramaniam, Shankar
2010-10-01
Deterministic models of biochemical processes at the subcellular level might become inadequate when a cascade of chemical reactions is induced by a few molecules. Inherent randomness of such phenomena calls for the use of stochastic simulations. However, being computationally intensive, such simulations become infeasible for large and complex reaction networks. To improve their computational efficiency in handling these networks, we present a hybrid approach, in which slow reactions and fluxes are handled through exact stochastic simulation and their fast counterparts are treated partially deterministically through chemical Langevin equation. The classification of reactions as fast or slow is accompanied by the assumption that in the time-scale of fast reactions, slow reactions do not occur and hence do not affect the probability of the state. Our new approach also handles reactions with complex rate expressions such as Michaelis-Menten kinetics. Fluxes which cannot be modeled explicitly through reactions, such as flux of Ca2+ from endoplasmic reticulum to the cytosol through inositol 1,4,5-trisphosphate receptor channels, are handled deterministically. The proposed hybrid algorithm is used to model the regulation of the dynamics of cytosolic calcium ions in mouse macrophage RAW 264.7 cells. At relatively large number of molecules, the response characteristics obtained with the stochastic and deterministic simulations coincide, which validates our approach in the limit of large numbers. At low doses, the response characteristics of some key chemical species, such as levels of cytosolic calcium, predicted with stochastic simulations, differ quantitatively from their deterministic counterparts. These observations are ubiquitous throughout dose response, sensitivity, and gene-knockdown response analyses. While the relative differences between the peak-heights of the cytosolic [Ca2+] time-courses obtained from stochastic (mean of 16 realizations) and deterministic
Stochastic extinction dynamics of HIV-1
NASA Astrophysics Data System (ADS)
Schwartz, Ira; Forgoston, Eric; Weinberger, Leor
2012-02-01
We consider an HIV-1 within host model in which T cells are infected by the virus. Due to small numbers of molecules, stochastic effects play an important role in the dynamical outcomes in that two states are observed experimentally: a replication state in which the virus is active, or a dormant state leading to latency in which the virus becomes active after a delay. The two states are conjectured to be governed by the Tat gene protein transcription process, which does not possess two stable attractors. Rather, the active state is stable, while the dormant state is unstable. Therefore the dormant state can only be achieved through the dynamics of stochastic fluctuations in which noise organizes a path to dormancy. Here we use optimal path theory applied to a Tat gene stochastic model to show how random fluctuations generate the dormant state by deriving a path which optimizes the probability of achieving the dormant state. We explicitly show how the probability of achieving dormancy scales with the transition rate parameters.
Controlling statistical moments of stochastic dynamical networks
NASA Astrophysics Data System (ADS)
Bielievtsov, Dmytro; Ladenbauer, Josef; Obermayer, Klaus
2016-07-01
We consider a general class of stochastic networks and ask which network nodes need to be controlled, and how, to stabilize and switch between desired metastable (target) states in terms of the first and second statistical moments of the system. We first show that it is sufficient to directly interfere with a subset of nodes which can be identified using information about the graph of the network only. Then we develop a suitable method for feedback control which acts on that subset of nodes and preserves the covariance structure of the desired target state. Finally, we demonstrate our theoretical results using a stochastic Hopfield network and a global brain model. Our results are applicable to a variety of (model) networks and further our understanding of the relationship between network structure and collective dynamics for the benefit of effective control.
Controlling statistical moments of stochastic dynamical networks.
Bielievtsov, Dmytro; Ladenbauer, Josef; Obermayer, Klaus
2016-07-01
We consider a general class of stochastic networks and ask which network nodes need to be controlled, and how, to stabilize and switch between desired metastable (target) states in terms of the first and second statistical moments of the system. We first show that it is sufficient to directly interfere with a subset of nodes which can be identified using information about the graph of the network only. Then we develop a suitable method for feedback control which acts on that subset of nodes and preserves the covariance structure of the desired target state. Finally, we demonstrate our theoretical results using a stochastic Hopfield network and a global brain model. Our results are applicable to a variety of (model) networks and further our understanding of the relationship between network structure and collective dynamics for the benefit of effective control. PMID:27575147
Stochastic dynamic models and Chebyshev splines
Fan, Ruzong; Zhu, Bin; Wang, Yuedong
2015-01-01
In this article, we establish a connection between a stochastic dynamic model (SDM) driven by a linear stochastic differential equation (SDE) and a Chebyshev spline, which enables researchers to borrow strength across fields both theoretically and numerically. We construct a differential operator for the penalty function and develop a reproducing kernel Hilbert space (RKHS) induced by the SDM and the Chebyshev spline. The general form of the linear SDE allows us to extend the well-known connection between an integrated Brownian motion and a polynomial spline to a connection between more complex diffusion processes and Chebyshev splines. One interesting special case is connection between an integrated Ornstein–Uhlenbeck process and an exponential spline. We use two real data sets to illustrate the integrated Ornstein–Uhlenbeck process model and exponential spline model and show their estimates are almost identical. PMID:26045632
Langevin dynamics, entropic crowding, and stochastic cloaking.
Eliazar, Iddo
2011-12-01
We consider a pack of independent probes--within a spatially inhomogeneous thermal bath consisting of a vast number of randomly moving particles--which are subjected to an external force. The stochastic dynamics of the probes are governed by Langevin's equation. The probes attain a steady state distribution which, in general, is different than the concentration of the particles in the spatially inhomogeneous thermal bath. In this paper we explore the state of "entropic crowding" in which the probes' distribution and the particles' concentration coincide--thus yielding maximal relative entropies of one with respect to the other. Entropic crowding can be attained by two scenarios which are analyzed in detail: (i) "entropically crowding thermal baths"--in which the particles crowd uniformly around the probes; (ii) "entropically crowding Langevin forces"--in which the probes crowd uniformly amongst the particles. Entropic crowding is equivalent to the optimal stochastic cloaking of the probes within the spatially inhomogeneous thermal bath. PMID:22304065
Stochastic magnetization dynamics in single domain particles
NASA Astrophysics Data System (ADS)
Giordano, Stefano; Dusch, Yannick; Tiercelin, Nicolas; Pernod, Philippe; Preobrazhensky, Vladimir
2013-06-01
Magnetic particles are largely utilized in several applications ranging from magnetorheological fluids to bioscience and from nanothechnology to memories or logic devices. The behavior of each single particle at finite temperature (under thermal stochastic fluctuations) plays a central role in determining the response of the whole physical system taken into consideration. Here, the magnetization evolution is studied through the Landau-Lifshitz-Gilbert formalism and the non-equilibrium statistical mechanics is introduced with the Langevin and Fokker-Planck methodologies. As result of the combination of such techniques we analyse the stochastic magnetization dynamics and we numerically determine the convergence time, measuring the velocity of attainment of thermodynamic equilibrium, as function of the system temperature.
Hybrid Differential Dynamic Programming with Stochastic Search
NASA Technical Reports Server (NTRS)
Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob A.
2016-01-01
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.
Hybrid Differential Dynamic Programming with Stochastic Search
NASA Technical Reports Server (NTRS)
Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob
2016-01-01
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.
Simulating stochastic dynamics using large time steps.
Corradini, O; Faccioli, P; Orland, H
2009-12-01
We present an approach to investigate the long-time stochastic dynamics of multidimensional classical systems, in contact with a heat bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short- and long-time scales and both molecular dynamics or Monte Carlo (MC) simulations are generally inefficient. Using a field theoretic approach, we perform analytically the average over the short-time stochastic fluctuations. This way, we obtain an effective theory, which generates the same long-time dynamics of the original theory, but has a lower time-resolution power. Such an approach is used to develop an improved version of the MC algorithm, which is particularly suitable to investigate the dynamics of rare conformational transitions. In the specific case of molecular systems at room temperature, we show that elementary integration time steps used to simulate the effective theory can be chosen a factor approximately 100 larger than those used in the original theory. Our results are illustrated and tested on a simple system, characterized by a rugged energy landscape. PMID:20365123
Stochastic-dynamic Modelling of Morphodynamics
NASA Astrophysics Data System (ADS)
Eppel, D. P.; Kapitza, H.
The numerical prediction of coastal sediment motion over time spans of years and decades is hampered by the sediment's ability, when stirred by waves and currents, to often react not uniquely to the external forcing but rather to show some kind of internal dynamics whose characteristics are not directly linked to the external forcing. Analytical stability analyses of the sediment-water system indicate that instabilities of tidally forced sediment layers in shallow seas can occur on spatial scales smaller than and not related to the scales of the tidal components. The finite growth of these un- stable amplitides can be described in terms of Ginzburg-Landau equations. Examples are the formation of ripples, sand waves and sand dunes or the formation of shore- face connected ridges. Among others, analyses of time series of coastal profiles from Duck, South Carolina extending over several decades gave evidence for self-organized behaviour suggesting that some important sediment-water systems can be perceived as dissipative dynamical structures. The consequences of such behaviour for predicting morphodynamics has been pointed out: one would expect that there exist time horizons beyond which predictions in the traditional deterministic sense are not possible. One would have to look for statistical quantities containing information of some relevance such as phase-space densities of solutions, attractor sets and the like. This contribution is part of an effort to address the prediction problem of morphody- namics through process-oriented models containing stochastic parameterizations for bottom shear stresses, critical shear stresses, etc.; process-based models because they are directly related to the physical processes but in a stochastic form because it is known that the physical processes contain strong stochastic components. The final outcome of such a program would be the generation of an ensemble of solutions by Monte Carlo integrations of the stochastic model
The Stochastic Search Dynamics of Interneuron Migration
Britto, Joanne M.; Johnston, Leigh A.; Tan, Seong-Seng
2009-01-01
Abstract Migration is a dynamic process in which a cell searches the environment and translates acquired information into somal advancement. In particular, interneuron migration during development is accomplished by two distinct processes: the extension of neurites tipped with growth cones; and nucleus translocation, termed nucleokinesis. The primary purpose of our study is to investigate neurite branching and nucleokinesis using high-resolution time-lapse confocal microscopy and computational modeling. We demonstrate that nucleokinesis is accurately modeled by a spring-dashpot system and that neurite branching is independent of the nucleokinesis event, and displays the dynamics of a stochastic birth-death process. This is in contrast to traditional biological descriptions, which suggest a closer relationship between the two migratory mechanisms. Our models are validated on independent data sets acquired using two different imaging protocols, and are shown to be robust to alterations in guidance cues and cellular migratory mechanisms, through treatment with brain-derived neurotrophic factor, neurotrophin-4, and blebbistatin. We postulate that the stochastic branch dynamics exhibited by interneurons undergoing guidance-directed migration permit efficient exploration of the environment. PMID:19651028
Stochastic Event-Driven Molecular Dynamics
Donev, Aleksandar Garcia, Alejandro L.; Alder, Berni J.
2008-02-01
A novel Stochastic Event-Driven Molecular Dynamics (SEDMD) algorithm is developed for the simulation of polymer chains suspended in a solvent. SEDMD combines event-driven molecular dynamics (EDMD) with the Direct Simulation Monte Carlo (DSMC) method. The polymers are represented as chains of hard-spheres tethered by square wells and interact with the solvent particles with hard-core potentials. The algorithm uses EDMD for the simulation of the polymer chain and the interactions between the chain beads and the surrounding solvent particles. The interactions between the solvent particles themselves are not treated deterministically as in EDMD, rather, the momentum and energy exchange in the solvent is determined stochastically using DSMC. The coupling between the solvent and the solute is consistently represented at the particle level retaining hydrodynamic interactions and thermodynamic fluctuations. However, unlike full MD simulations of both the solvent and the solute, in SEDMD the spatial structure of the solvent is ignored. The SEDMD algorithm is described in detail and applied to the study of the dynamics of a polymer chain tethered to a hard-wall subjected to uniform shear. SEDMD closely reproduces results obtained using traditional EDMD simulations with two orders of magnitude greater efficiency. Results question the existence of periodic (cycling) motion of the polymer chain.
Stochastic dynamics of macromolecular-assembly networks.
NASA Astrophysics Data System (ADS)
Saiz, Leonor; Vilar, Jose
2006-03-01
The formation and regulation of macromolecular complexes provides the backbone of most cellular processes, including gene regulation and signal transduction. The inherent complexity of assembling macromolecular structures makes current computational methods strongly limited for understanding how the physical interactions between cellular components give rise to systemic properties of cells. Here we present a stochastic approach to study the dynamics of networks formed by macromolecular complexes in terms of the molecular interactions of their components [1]. Exploiting key thermodynamic concepts, this approach makes it possible to both estimate reaction rates and incorporate the resulting assembly dynamics into the stochastic kinetics of cellular networks. As prototype systems, we consider the lac operon and phage λ induction switches, which rely on the formation of DNA loops by proteins [2] and on the integration of these protein-DNA complexes into intracellular networks. This cross-scale approach offers an effective starting point to move forward from network diagrams, such as those of protein-protein and DNA-protein interaction networks, to the actual dynamics of cellular processes. [1] L. Saiz and J.M.G. Vilar, submitted (2005). [2] J.M.G. Vilar and L. Saiz, Current Opinion in Genetics & Development, 15, 136-144 (2005).
Irreversible thermodynamics in multiscale stochastic dynamical systems
NASA Astrophysics Data System (ADS)
Santillán, Moisés; Qian, Hong
2011-04-01
This work extends the results of a recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We investigate whether and in what way the thermodynamic structure is invariant in a multiscale stochastic system, that is, whether the relations between thermodynamic functions of state and process variables remain unchanged when the system is viewed at different time scales and resolutions. Our results show that the dynamics on a fast time scale contribute an entropic term to the internal energy function uS(x) for the slow dynamics. Based on the conditional free energy uS(x), we can then treat the slow dynamics as if the fast dynamics is nonexistent. Furthermore, we show that the free energy, which characterizes the spontaneous organization in a system without detailed balance, is invariant with or without the fast dynamics: The fast dynamics is assumed to reach stationarity instantaneously on the slow time scale; it has no effect on the system’s free energy. The same cannot be said for the entropy and the internal energy, both of which contain the same contribution from the fast dynamics. We also investigate the consequences of time-scale separation in connection to the concepts of quasi-stationarity and steady adiabaticity introduced in the phenomenological steady-state thermodynamics.
Irreversible thermodynamics in multiscale stochastic dynamical systems.
Santillán, Moisés; Qian, Hong
2011-04-01
This work extends the results of a recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We investigate whether and in what way the thermodynamic structure is invariant in a multiscale stochastic system, that is, whether the relations between thermodynamic functions of state and process variables remain unchanged when the system is viewed at different time scales and resolutions. Our results show that the dynamics on a fast time scale contribute an entropic term to the internal energy function u(S)(x) for the slow dynamics. Based on the conditional free energy u(S)(x), we can then treat the slow dynamics as if the fast dynamics is nonexistent. Furthermore, we show that the free energy, which characterizes the spontaneous organization in a system without detailed balance, is invariant with or without the fast dynamics: The fast dynamics is assumed to reach stationarity instantaneously on the slow time scale; it has no effect on the system's free energy. The same cannot be said for the entropy and the internal energy, both of which contain the same contribution from the fast dynamics. We also investigate the consequences of time-scale separation in connection to the concepts of quasi-stationarity and steady adiabaticity introduced in the phenomenological steady-state thermodynamics. PMID:21599138
Method to describe stochastic dynamics using an optimal coordinate.
Krivov, Sergei V
2013-12-01
A general method to describe the stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems: the determination of an optimal coordinate for the description of stochastic dynamics; the reconstruction of time from an ensemble of stochastic trajectories; and the decomposition of stationary stochastic dynamics into eigenmodes which do not decay exponentially with time. The problems are solved by introducing additive eigenvectors which are transformed by a stochastic matrix in a simple way - every component is translated by a constant distance. Such solutions have peculiar properties. For example, an optimal coordinate for stochastic dynamics with detailed balance is a multivalued function. An optimal coordinate for a random walk on a line corresponds to the conventional eigenvector of the one-dimensional Dirac equation. The equation for the optimal coordinate in a slowly varying potential reduces to the Hamilton-Jacobi equation for the action function. PMID:24483410
Nonlinear and Stochastic Dynamics in the Heart
Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.
2014-01-01
In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems. PMID:25267872
Wolbachia spread dynamics in stochastic environments.
Hu, Linchao; Huang, Mugen; Tang, Moxun; Yu, Jianshe; Zheng, Bo
2015-12-01
Dengue fever is a mosquito-borne viral disease with 100 million people infected annually. A novel strategy for dengue control uses the bacterium Wolbachia to invade dengue vector Aedes mosquitoes. As the impact of environmental heterogeneity on Wolbachia spread dynamics in natural areas has been rarely quantified, we develop a model of differential equations for which the environmental conditions switch randomly between two regimes. We find some striking phenomena that random regime transitions could drive Wolbachia to extinction from certain initial states confirmed Wolbachia fixation in homogeneous environments, and mosquito releasing facilitates Wolbachia invasion more effectively when the regimes transit frequently. By superimposing the phase spaces of the ODE systems defined in each regime, we identify the threshold curves below which Wolbachia invades the whole population, which extends the theory of threshold infection frequency to stochastic environments. PMID:26428255
Stochastic dynamics for idiotypic immune networks
NASA Astrophysics Data System (ADS)
Barra, Adriano; Agliari, Elena
2010-12-01
In this work we introduce and analyze the stochastic dynamics obeyed by a model of an immune network recently introduced by the authors. We develop Fokker-Planck equations for the single lymphocyte behavior and coarse grained Langevin schemes for the averaged clone behavior. After showing agreement with real systems (as a short path Jerne cascade), we suggest, both with analytical and numerical arguments, explanations for the generation of (metastable) memory cells, improvement of the secondary response (both in the quality and quantity) and bell shaped modulation against infections as a natural behavior. The whole emerges from the model without being postulated a-priori as it often occurs in second generation immune networks: so the aim of the work is to present some out-of-equilibrium features of this model and to highlight mechanisms which can replace a-priori assumptions in view of further detailed analysis in theoretical systemic immunology.
Predicting stochastic gene expression dynamics in single cells.
Mettetal, Jerome T; Muzzey, Dale; Pedraza, Juan M; Ozbudak, Ertugrul M; van Oudenaarden, Alexander
2006-05-01
Fluctuations in protein numbers (noise) due to inherent stochastic effects in single cells can have large effects on the dynamic behavior of gene regulatory networks. Although deterministic models can predict the average network behavior, they fail to incorporate the stochasticity characteristic of gene expression, thereby limiting their relevance when single cell behaviors deviate from the population average. Recently, stochastic models have been used to predict distributions of steady-state protein levels within a population but not to predict the dynamic, presteady-state distributions. In the present work, we experimentally examine a system whose dynamics are heavily influenced by stochastic effects. We measure population distributions of protein numbers as a function of time in the Escherichia coli lactose uptake network (lac operon). We then introduce a dynamic stochastic model and show that prediction of dynamic distributions requires only a few noise parameters in addition to the rates that characterize a deterministic model. Whereas the deterministic model cannot fully capture the observed behavior, our stochastic model correctly predicts the experimental dynamics without any fit parameters. Our results provide a proof of principle for the possibility of faithfully predicting dynamic population distributions from deterministic models supplemented by a stochastic component that captures the major noise sources. PMID:16648266
Stochastic Terminal Dynamics in Epithelial Cell Intercalation
NASA Astrophysics Data System (ADS)
Eule, Stephan; Metzger, Jakob; Reichl, Lars; Kong, Deqing; Zhang, Yujun; Grosshans, Joerg; Wolf, Fred
2015-03-01
We found that the constriction of epithelial cell contacts during intercalation in germ band extension in Drosophila embryos follows intriguingly simple quantitative laws. The mean contact length < L > follows < L > (t) ~(T - t) α , where T is the finite collapse time; the time dependent variance of contact length is proportional to the square of the mean; finally the time dependent probability density of the contact lengths remains close to Gaussian during the entire process. These observations suggest that the dynamics of contact collapse can be captured by a stochastic differential equation analytically tractable in small noise approximation. Here, we present such a model, providing an effective description of the non-equilibrium statistical mechanics of contact collapse. All model parameters are fixed by measurements of time dependent mean and variance of contact lengths. The model predicts the contact length covariance function that we obtain in closed form. The contact length covariance function closely matches experimental observations suggesting that the model well captures the dynamics of contact collapse.
Extended Plefka expansion for stochastic dynamics
NASA Astrophysics Data System (ADS)
Bravi, B.; Sollich, P.; Opper, M.
2016-05-01
We propose an extension of the Plefka expansion, which is well known for the dynamics of discrete spins, to stochastic differential equations with continuous degrees of freedom and exhibiting generic nonlinearities. The scenario is sufficiently general to allow application to e.g. biochemical networks involved in metabolism and regulation. The main feature of our approach is to constrain in the Plefka expansion not just first moments akin to magnetizations, but also second moments, specifically two-time correlations and responses for each degree of freedom. The end result is an effective equation of motion for each single degree of freedom, where couplings to other variables appear as a self-coupling to the past (i.e. memory term) and a coloured noise. This constitutes a new mean field approximation that should become exact in the thermodynamic limit of a large network, for suitably long-ranged couplings. For the analytically tractable case of linear dynamics we establish this exactness explicitly by appeal to spectral methods of random matrix theory, for Gaussian couplings with arbitrary degree of symmetry.
Collisionally induced stochastic dynamics of fast ions in solids
Burgdoerfer, J.
1989-01-01
Recent developments in the theory of excited state formation in collisions of fast highly charged ions with solids are reviewed. We discuss a classical transport theory employing Monte-Carlo sampling of solutions of a microscopic Langevin equation. Dynamical screening by the dielectric medium as well as multiple collisions are incorporated through the drift and stochastic forces in the Langevin equation. The close relationship between the extrinsically stochastic dynamics described by the Langevin and the intrinsic stochasticity in chaotic nonlinear dynamical systems is stressed. Comparison with experimental data and possible modification by quantum corrections are discussed. 49 refs., 11 figs.
Identification and stochastic control of helicopter dynamic modes
NASA Technical Reports Server (NTRS)
Molusis, J. A.; Bar-Shalom, Y.
1983-01-01
A general treatment of parameter identification and stochastic control for use on helicopter dynamic systems is presented. Rotor dynamic models, including specific applications to rotor blade flapping and the helicopter ground resonance problem are emphasized. Dynamic systems which are governed by periodic coefficients as well as constant coefficient models are addressed. The dynamic systems are modeled by linear state variable equations which are used in the identification and stochastic control formulation. The pure identification problem as well as the stochastic control problem which includes combined identification and control for dynamic systems is addressed. The stochastic control problem includes the effect of parameter uncertainty on the solution and the concept of learning and how this is affected by the control's duel effect. The identification formulation requires algorithms suitable for on line use and thus recursive identification algorithms are considered. The applications presented use the recursive extended kalman filter for parameter identification which has excellent convergence for systems without process noise.
Extending Newtonian Dynamics to Include Stochastic Processes
NASA Technical Reports Server (NTRS)
Zak, Michail
2009-01-01
A paper presents further results of continuing research reported in several previous NASA Tech Briefs articles, the two most recent being Stochastic Representations of Chaos Using Terminal Attractors (NPO-41519), [Vol. 30, No. 5 (May 2006), page 57] and Physical Principle for Generation of Randomness (NPO-43822) [Vol. 33, No. 5 (May 2009), page 56]. This research focuses upon a mathematical formalism for describing post-instability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism involves fictitious control forces that couple the equations of motion of the system with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These stabilizing forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in configuration space (ordinary three-dimensional space as commonly perceived) is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. As a result, the post-instability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable.
A dynamic localization model with stochastic backscatter
NASA Astrophysics Data System (ADS)
Carati, Daniele; Ghosal, Sandip
1994-12-01
The modeling of subgrid scales in large-eddy simulation (LES) has been rationalized by the introduction of the dynamic localization procedure. This method allows one to compute rather than prescribe the unknown coefficients in the subgrid-scale model. Formally, the LES equations are supposed to be obtained by applying to the Navier-Stokes equations a 'grid filter' operation. Though the subgrid stress itself is unknown, an identity between subgrid stresses generated by different filters has been derived. Although preliminary tests of the Dynamic Localization Model (DLM) with k-equation have been satisfactory, the use of a negative eddy viscosity to describe backscatter is probably a crude representation of the physics of reverse transfer of energy. Indeed, the model is fully deterministic. Knowing the filtered velocity field and the subgrid-scale energy, the subgrid stress is automatically determined. We know that the LES equations cannot be fully deterministic since the small scales are not resolved. This stems from an important distinction between equilibrium hydrodynamics and turbulence. In equilibrium hydrodynamics, the molecular motions are also not resolved. However, there is a clear separation of scale between these unresolved motions and the relevant hydrodynamic scales. The result of molecular motions can then be separated into an average effect (the molecular viscosity) and some fluctuations. Due to the large number of molecules present in a box with size of the order of the hydrodynamic scale, the ratio between fluctuations and the average effect should be very small (as a result of the 'law of large numbers'). For that reason, the hydrodynamic balance equations are usually purely deterministic. In turbulence, however, there is no clear separation of scale between small and large eddies. In that case, the fluctuations around a deterministic eddy viscosity term could be significant. An eddy noise would then appear through a stochastic term in the subgrid
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 Dynamics Underlying Cognitive Stability and Flexibility
Ueltzhöffer, Kai; Armbruster-Genç, Diana J. N.; Fiebach, Christian J.
2015-01-01
dopaminergic modulation of cognitive flexibility. These results show that stochastic dynamical systems can implement the basic computations underlying cognitive stability and flexibility and explain neurobiological bases of individual differences. PMID:26068119
Stochastic Dynamics Underlying Cognitive Stability and Flexibility.
Ueltzhöffer, Kai; Armbruster-Genç, Diana J N; Fiebach, Christian J
2015-06-01
dopaminergic modulation of cognitive flexibility. These results show that stochastic dynamical systems can implement the basic computations underlying cognitive stability and flexibility and explain neurobiological bases of individual differences. PMID:26068119
Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings
Kadtke, J.B.; Bulsara, A.
1997-12-01
These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)
Analysing Dynamical Behavior of Cellular Networks via Stochastic Bifurcations
Zakharova, Anna; Kurths, Jürgen; Vadivasova, Tatyana; Koseska, Aneta
2011-01-01
The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types. PMID:21647432
Analysis of the non-Markov parameter in continuous-time signal processing
NASA Astrophysics Data System (ADS)
Varghese, J. J.; Bellette, P. A.; Weegink, K. J.; Bradley, A. P.; Meehan, P. A.
2014-02-01
The use of statistical complexity metrics has yielded a number of successful methodologies to differentiate and identify signals from complex systems where the underlying dynamics cannot be calculated. The Mori-Zwanzig framework from statistical mechanics forms the basis for the generalized non-Markov parameter (NMP). The NMP has been used to successfully analyze signals in a diverse set of complex systems. In this paper we show that the Mori-Zwanzig framework masks an elegantly simple closed form of the first NMP, which, for C1 smooth autocorrelation functions, is solely a function of the second moment (spread) and amplitude envelope of the measured power spectrum. We then show that the higher-order NMPs can be constructed in closed form in a modular fashion from the lower-order NMPs. These results provide an alternative, signal processing-based perspective to analyze the NMP, which does not require an understanding of the Mori-Zwanzig generating equations. We analyze the parametric sensitivity of the zero-frequency value of the first NMP, which has been used as a metric to discriminate between states in complex systems. Specifically, we develop closed-form expressions for three instructive systems: band-limited white noise, the output of white noise input to an idealized all-pole filter,f and a simple harmonic oscillator driven by white noise. Analysis of these systems shows a primary sensitivity to the decay rate of the tail of the power spectrum.
Stochastic population dynamics under resource constraints
NASA Astrophysics Data System (ADS)
Gavane, Ajinkya S.; Nigam, Rahul
2016-06-01
This paper investigates the population growth of a certain species in which every generation reproduces thrice over a period of predefined time, under certain constraints of resources needed for survival of population. We study the survival period of a species by randomizing the reproduction probabilities within a window at same predefined ages and the resources are being produced by the working force of the population at a variable rate. This randomness in the reproduction rate makes the population growth stochastic in nature and one cannot predict the exact form of evolution. Hence we study the growth by running simulations for such a population and taking an ensemble averaged over 500 to 5000 such simulations as per the need. While the population reproduces in a stochastic manner, we have implemented a constraint on the amount of resources available for the population. This is important to make the simulations more realistic. The rate of resource production then is tuned to find the rate which suits the survival of the species. We also compute the mean life time of the species corresponding to different resource production rate. Study for these outcomes in the parameter space defined by the reproduction probabilities and rate of resource production is carried out.
Discriminating chaotic and stochastic dynamics through the permutation spectrum test
Kulp, C. W.; Zunino, L.
2014-09-01
In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism.
Path sampling with stochastic dynamics: Some new algorithms
Stoltz, Gabriel . E-mail: stoltz@cermics.enpc.fr
2007-07-01
We propose here some new sampling algorithms for path sampling in the case when stochastic dynamics are used. In particular, we present a new proposal function for equilibrium sampling of paths with a Monte-Carlo dynamics (the so-called 'brownian tube' proposal). This proposal is based on the continuity of the dynamics with respect to the random forcing, and generalizes all previous approaches when stochastic dynamics are used. The efficiency of this proposal is demonstrated using some measure of decorrelation in path space. We also discuss a switching strategy that allows to transform ensemble of paths at a finite rate while remaining at equilibrium, in contrast with the usual Jarzynski like switching. This switching is very interesting to sample constrained paths starting from unconstrained paths, or to perform simulated annealing in a rigorous way.
Discriminating chaotic and stochastic dynamics through the permutation spectrum test.
Kulp, C W; Zunino, L
2014-09-01
In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism. PMID:25273196
Approximation of stochastic equilibria for dynamic systems with colored noise
Bashkirtseva, Irina
2015-03-10
We consider nonlinear dynamic systems forced by colored noise. Using first approximation systems, we study dynamics of deviations of stochastic solutions from stable deterministic equilibria. Equations for the stationary second moments of deviations of random states are derived. An application of the elaborated theory to Van der Pol system driven by colored noise is given. A dependence of the dispersion on the time correlation of the colored noise is studied.
Quantum mechanics emerging from stochastic dynamics of virtual particles
NASA Astrophysics Data System (ADS)
Tsekov, Roumen
2016-03-01
It is shown how quantum mechanics emerges from the stochastic dynamics of force carriers. It is demonstrated that the Moyal equation corresponds to dynamic correlations between the real particle momentum and the virtual particle position, which are not present in classical mechanics. This new concept throws light on the physical meaning of quantum theory, showing that the Planck constant square is a second-second position-momentum cross-cumulant.
A dynamical stochastic coupled model for financial markets
NASA Astrophysics Data System (ADS)
Govindan, T. E.; Ibarra-Valdez, Carlos; Ruiz de Chávez, J.
2007-07-01
A model coupling a deterministic dynamical system which represents trading, with a stochastic one that represents asset prices evolution is presented. Both parts of the model have connections with well established dynamic models in mathematical economics and finance. The main objective is to represent the double feedback between trading dynamics (the demand/supply interaction) and price dynamics (assumed as largely random). We present the model, and address to some extent existence and uniqueness, continuity with respect to initial conditions and stability of solutions. The non-Lipschitz case is briefly considered as well.
Stochastic heart-rate model can reveal pathologic cardiac dynamics
NASA Astrophysics Data System (ADS)
Kuusela, Tom
2004-03-01
A simple one-dimensional Langevin-type stochastic difference equation can simulate the heart-rate fluctuations in a time scale from minutes to hours. The model consists of a deterministic nonlinear part and a stochastic part typical of Gaussian noise, and both parts can be directly determined from measured heart-rate data. Data from healthy subjects typically exhibit the deterministic part with two or more stable fixed points. Studies of 15 congestive heart-failure subjects reveal that the deterministic part of pathologic heart dynamics has no clear stable fixed points. Direct simulations of the stochastic model for normal and pathologic cases can produce statistical parameters similar to those of real subjects. Results directly indicate that pathologic situations simplify the heart-rate control system.
Stochastic Dynamics with Correct Sampling for Constrained Systems.
Peters, E A J F; Goga, N; Berendsen, H J C
2014-10-14
In this paper we discuss thermostatting using stochastic methods for molecular simulations where constraints are present. For so-called impulsive thermostats, like the Andersen thermostat, the equilibrium temperature will differ significantly from the imposed temperature when a limited number of particles are picked and constraints are applied. We analyze this problem and give two rigorous solutions for it. A correct general treatment of impulsive stochastic thermostatting, including pairwise dissipative particle dynamics and stochastic forcing in the presence of constraints, is given and it is shown that the constrained canonical distribution is sampled rigorously. We discuss implementation issues such as second order Trotter expansions. The method is shown to rigorously maintain the correct temperature for the case of extended simple point charge (SPC/E) water simulations. PMID:26588119
Stochastic Evaluation of Riparian Vegetation Dynamics in River Channels
NASA Astrophysics Data System (ADS)
Miyamoto, H.; Kimura, R.; Toshimori, N.
2013-12-01
Vegetation overgrowth in sand bars and floodplains has been a serious problem for river management in Japan. From the viewpoints of flood control and ecological conservation, it would be necessary to accurately predict the vegetation dynamics for a long period of time. In this study, we have developed a stochastic model for predicting the dynamics of trees in floodplains with emphasis on the interaction with flood impacts. The model consists of the following four processes in coupling ecohydrology with biogeomorphology: (i) stochastic behavior of flow discharge, (ii) hydrodynamics in a channel with vegetation, (iii) variation of riverbed topography and (iv) vegetation dynamics on the floodplain. In the model, the flood discharge is stochastically simulated using a Poisson process, one of the conventional approaches in hydrological time-series generation. The model for vegetation dynamics includes the effects of tree growth, mortality by flood impacts, and infant tree invasion. To determine the model parameters, vegetation conditions have been observed mainly before and after flood impacts since 2008 at a field site located between 23.2-24.0 km from the river mouth in Kako River, Japan. This site is one of the vegetation overgrowth locations in Kako River floodplains, where the predominant tree species are willows and bamboos. In this presentation, sensitivity of the vegetation overgrowth tendency is investigated in Kako River channels. Through the Monte Carlo simulation for several cross sections in Kako River, responses of the vegetated channels are stochastically evaluated in terms of the changes of discharge magnitude and channel geomorphology. The expectation and standard deviation of vegetation areal ratio are compared in the different channel cross sections for different river discharges and relative floodplain heights. The result shows that the vegetation status changes sensitively in the channels with larger discharge and insensitive in the lower floodplain
Dynamic option pricing with endogenous stochastic arbitrage
NASA Astrophysics Data System (ADS)
Contreras, Mauricio; Montalva, Rodrigo; Pellicer, Rely; Villena, Marcelo
2010-09-01
Only few efforts have been made in order to relax one of the key assumptions of the Black-Scholes model: the no-arbitrage assumption. This is despite the fact that arbitrage processes usually exist in the real world, even though they tend to be short-lived. The purpose of this paper is to develop an option pricing model with endogenous stochastic arbitrage, capable of modelling in a general fashion any future and underlying asset that deviate itself from its market equilibrium. Thus, this investigation calibrates empirically the arbitrage on the futures on the S&P 500 index using transaction data from September 1997 to June 2009, from here a specific type of arbitrage called “arbitrage bubble”, based on a t-step function, is identified and hence used in our model. The theoretical results obtained for Binary and European call options, for this kind of arbitrage, show that an investment strategy that takes advantage of the identified arbitrage possibility can be defined, whenever it is possible to anticipate in relative terms the amplitude and timespan of the process. Finally, the new trajectory of the stock price is analytically estimated for a specific case of arbitrage and some numerical illustrations are developed. We find that the consequences of a finite and small endogenous arbitrage not only change the trajectory of the asset price during the period when it started, but also after the arbitrage bubble has already gone. In this context, our model will allow us to calibrate the B-S model to that new trajectory even when the arbitrage already started.
Traffic jam dynamics in stochastic cellular automata
Nagel, K. |; Schreckenberg, M.
1995-09-01
Simple models for particles hopping on a grid (cellular automata) are used to simulate (single lane) traffic flow. Despite their simplicity, these models are astonishingly realistic in reproducing start-stop-waves and realistic fundamental diagrams. One can use these models to investigate traffic phenomena near maximum flow. A so-called phase transition at average maximum flow is visible in the life-times of jams. The resulting dynamic picture is consistent with recent fluid-dynamical results by Kuehne/Kerner/Konhaeuser, and with Treiterer`s hysteresis description. This places CA models between car-following models and fluid-dynamical models for traffic flow. CA models are tested in projects in Los Alamos (USA) and in NRW (Germany) for large scale microsimulations of network traffic.
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. PMID:26707373
Dynamic maintenance of stochastic molecular clusters on cell membranes
NASA Astrophysics Data System (ADS)
Mugler, Andrew; Wehrens, Martijn; Ten Wolde, Pieter Rein
2015-03-01
Clustering of molecules on cell membranes is a widely observed phenomenon. A key example is the oncoprotein Ras. Maintenance of Ras clusters has been linked to proper Ras signaling. Yet, the mechanism by which Ras clusters are maintained remains unclear. Recently it was discovered that activated Ras promotes further Ras activation. We show using particle-based simulation that this positive feedback link is sufficient to produce persistent clusters of active Ras molecules via a dynamic nucleation mechanism. The cluster statistics are consistent with experimental observations. Interestingly, our model does not support a Turing regime of macroscopic reaction-diffusion patterning. This means that the clustering we observe is a purely stochastic effect, arising from the coupling of the positive feedback network with the discrete nature of individual molecules. These findings underscore the importance of stochastic and dynamic properties of reaction diffusion systems for biological behavior.
Stochastic dynamics of a delayed bistable system with multiplicative noise
Dung, Nguyen Tien E-mail: dungnt@fpt.edu.vn
2014-05-15
In this paper we investigate the properties of a delayed bistable system under the effect of multiplicative noise. We first prove the existence and uniqueness of the positive solution and show that its moments are uniformly bounded. Then, we study stochastic dynamics of the solution in long time, the lower and upper bounds for the paths and an estimate for the average value are provided.
Nonperturbative stochastic dynamics driven by strongly correlated colored noise
NASA Astrophysics Data System (ADS)
Jing, Jun; Li, Rui; You, J. Q.; Yu, Ting
2015-02-01
We propose a quantum model consisting of two remote qubits interacting with two correlated colored noises and establish an exact stochastic Schrödinger equation for this open quantum system. It is shown that the quantum dynamics of the qubit system is profoundly modulated by the mutual correlation between baths and the bath memory capability through dissipation and fluctuation. We report a physical effect on generating inner correlation and entanglement of two distant qubits arising from the strong bath-bath correlation.
Stochastic Mean-Field Dynamics For Nuclear Collisions
Ayik, Sakir
2008-11-11
We discuss a stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. For small amplitude fluctuations, this approach gives a result for the dispersion of a one-body observable that is identical to the result obtained previously through a variational approach. Furthermore, it incorporates one-body dissipation and fluctuation mechanisms in accordance with quantal fluctuation-dissipation relation.
NASA Astrophysics Data System (ADS)
Juriev, D. V.
1996-02-01
The results of investigating the stochastic properties of the long-term behavior of a continuously observed (and interactively controlled) quantum-field top are reported. Applications for interactively controlled stochastic dynamic computer-graphics systems are discussed.
A dynamic model for the Lagrangian stochastic dispersion coefficient
Pesmazoglou, I.; Navarro-Martinez, S.; Kempf, A. M.
2013-12-15
A stochastic sub-grid model is often used to accurately represent particle dispersion in turbulent flows using large eddy simulations. Models of this type have a free parameter, the dispersion coefficient, which is not universal and is strongly grid-dependent. In the present paper, a dynamic model for the evaluation of the coefficient is proposed and validated in decaying homogeneous isotropic turbulence. The grid dependence of the static coefficient is investigated in a turbulent mixing layer and compared to the dynamic model. The dynamic model accurately predicts dispersion statistics and resolves the grid-dependence. Dispersion statistics of the dynamically calculated constant are more accurate than any static coefficient choice for a number of grid spacings. Furthermore, the dynamic model produces less numerical artefacts than a static model and exhibits smaller sensitivity in the results predicted for different particle relaxation times.
Indirect Identification of Linear Stochastic Systems with Known Feedback Dynamics
NASA Technical Reports Server (NTRS)
Huang, Jen-Kuang; Hsiao, Min-Hung; Cox, David E.
1996-01-01
An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall closed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open-loop plant dynamics from the identified closed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.
Effects of stochastic noise on dynamical decoupling procedures
NASA Astrophysics Data System (ADS)
Bernád, J. Z.; Frydrych, H.
2014-06-01
Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap between fidelity improvements achieved in practice compared to theoretical predictions. We propose a model for imperfect dynamical decoupling based on a stochastic Ito differential equation which could explain the observed gap. We discuss the impact of our model on the time evolution of various quantum systems in finite- and infinite-dimensional Hilbert spaces. Analytical results are given for the limit of continuous control, whereas we present numerical simulations and upper bounds for the case of finite control.
Time-Reversal Test for Stochastic Quantum Dynamics
NASA Astrophysics Data System (ADS)
Dowling, Mark R.; Drummond, Peter D.; Davis, Matthew J.; Deuar, Piotr
2005-04-01
The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultracold atomic Bose-Einstein condensates to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal test. We apply this test to a simulation of the evolution of a quantum anharmonic oscillator with up to 6.022×1023 (Avogadro’s number) of particles. This system is realizable as a Bose-Einstein condensate in an optical lattice, for which the time-reversal procedure could be implemented experimentally.
Stochastic description of pilus retraction dynamics
NASA Astrophysics Data System (ADS)
Lindén, Martin; Johansson, Emil; Jonsson, Ann-Beth
2005-03-01
Motility of certain gram-negative bacteria is mediated by retraction of type IV pili surface filaments, which are essential for infectivity. Type IV pili are helical filaments with 4 nm periodicity and 5 subunits per turn. The retraction is powered by a strong molecular motor protein, PilT, producing very high forces in excess of 100 pN[1]. One possible explanation for the high forces are that several ATP are hydrolyzed to retract each subunit.We consider a widely used class of discrete hopping models, which has been used to describe well-known motor proteins such as kinesin[2] and myosin[3]. The model describes recent experimental measurements[1] on Neisseria gonorrhoeae well, and makes several interesting predictions for the randomness of the retraction dynamics.1. Maier et al, PNAS 101:10961 (2004)2. M. E. Fisher and A. B. Kolomeisky, PNAS 98:7748 (2001)3. A. B. Kolomeisky and M. E. Fisher, Biophys. J. 84:1650 (2003)
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
NASA Astrophysics Data System (ADS)
Romanczuk, P.; Bär, M.; Ebeling, W.; Lindner, B.; Schimansky-Geier, L.
2012-03-01
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
Cycles, stochasticity and density dependence in pink salmon population dynamics.
Krkosek, Martin; Hilborn, Ray; Peterman, Randall M; Quinn, Thomas P
2011-07-01
Complex dynamics of animal populations often involve deterministic and stochastic components. A fascinating example is the variation in magnitude of 2-year cycles in abundances of pink salmon (Oncorhynchus gorbuscha) stocks along the North Pacific rim. Pink salmon have a 2-year anadromous and semelparous life cycle, resulting in odd- and even-year lineages that occupy the same habitats but are reproductively isolated in time. One lineage is often much more abundant than the other in a given river, and there are phase switches in dominance between odd- and even-year lines. In some regions, the weak line is absent and in others both lines are abundant. Our analysis of 33 stocks indicates that these patterns probably result from stochastic perturbations of damped oscillations owing to density-dependent mortality caused by interactions between lineages. Possible mechanisms are cannibalism, disease transmission, food depletion and habitat degradation by which one lineage affects the other, although no mechanism has been well-studied. Our results provide comprehensive empirical estimates of lagged density-dependent mortality in salmon populations and suggest that a combination of stochasticity and density dependence drives cyclical dynamics of pink salmon stocks. PMID:21147806
Condition-dependent mate choice: A stochastic dynamic programming approach.
Frame, Alicia M; Mills, Alex F
2014-09-01
We study how changing female condition during the mating season and condition-dependent search costs impact female mate choice, and what strategies a female could employ in choosing mates to maximize her own fitness. We address this problem via a stochastic dynamic programming model of mate choice. In the model, a female encounters males sequentially and must choose whether to mate or continue searching. As the female searches, her own condition changes stochastically, and she incurs condition-dependent search costs. The female attempts to maximize the quality of the offspring, which is a function of the female's condition at mating and the quality of the male with whom she mates. The mating strategy that maximizes the female's net expected reward is a quality threshold. We compare the optimal policy with other well-known mate choice strategies, and we use simulations to examine how well the optimal policy fares under imperfect information. PMID:24996205
Generic modes of consensus formation in stochastic language dynamics
NASA Astrophysics Data System (ADS)
Blythe, R A
2009-02-01
We introduce a class of stochastic models for the dynamics of two linguistic variants that are competing to become the single, shared convention within an unstructured community of speakers. Different instances of the model are distinguished by the way agents handle variability in the language (i.e., multiple forms for the same meaning). The class of models includes as special cases two previously studied models of language dynamics, the Naming Game, in which agents tend to standardize on variants that they have encountered most frequently, and the Utterance Selection Model, in which agents tend to preserve variability by uniform sampling of a pool of utterances. We reduce the full complexities of the dynamics to a single-coordinate stochastic model which allows the probability and time taken for speakers to reach consensus on a single variant to be calculated for large communities. This analysis suggests that in the broad class of models considered, consensus is formed in one of three generic ways, according to whether agents tend to eliminate, accentuate or sample neutrally the variability in the language. These different regimes are observed in simulations of the full dynamics, and for which the simplified model in some cases makes good quantitative predictions. We use these results, along with comparisons with related models, to conjecture the likely behaviour of more general models, and further make use of empirical data to argue that in reality, biases away from neutral sampling behaviour are likely to be small.
Dynamic Stochastic Superresolution of sparsely observed turbulent systems
Branicki, M.; Majda, A.J.
2013-05-15
Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum
Stochastic dynamics and mechanosensitivity of myosin II minifilaments
NASA Astrophysics Data System (ADS)
Albert, Philipp J.; Erdmann, Thorsten; Schwarz, Ulrich S.
2014-09-01
Tissue cells are in a state of permanent mechanical tension that is maintained mainly by myosin II minifilaments, which are bipolar assemblies of tens of myosin II molecular motors contracting actin networks and bundles. Here we introduce a stochastic model for myosin II minifilaments as two small myosin II motor ensembles engaging in a stochastic tug-of-war. Each of the two ensembles is described by the parallel cluster model that allows us to use exact stochastic simulations and at the same time to keep important molecular details of the myosin II cross-bridge cycle. Our simulation and analytical results reveal a strong dependence of myosin II minifilament dynamics on environmental stiffness that is reminiscent of the cellular response to substrate stiffness. For small stiffness, minifilaments form transient crosslinks exerting short spikes of force with negligible mean. For large stiffness, minifilaments form near permanent crosslinks exerting a mean force which hardly depends on environmental elasticity. This functional switch arises because dissociation after the power stroke is suppressed by force (catch bonding) and because ensembles can no longer perform the power stroke at large forces. Symmetric myosin II minifilaments perform a random walk with an effective diffusion constant which decreases with increasing ensemble size, as demonstrated for rigid substrates with an analytical treatment.
Two-strain competition in quasineutral stochastic disease dynamics.
Kogan, Oleg; Khasin, Michael; Meerson, Baruch; Schneider, David; Myers, Christopher R
2014-10-01
We develop a perturbation method for studying quasineutral competition in a broad class of stochastic competition models and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic susceptible-infected-susceptible (SIS) model. Here we extend previous results due to Parsons and Quince [Theor. Popul. Biol. 72, 468 (2007)], Parsons et al. [Theor. Popul. Biol. 74, 302 (2008)], and Lin, Kim, and Doering [J. Stat. Phys. 148, 646 (2012)]. The second model, a two-strain generalization of the stochastic susceptible-infected-recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of subpopulation sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the subpopulations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population. PMID:25375480
Stochastic Polynomial Dynamic Models of the Yeast Cell Cycle
NASA Astrophysics Data System (ADS)
Mitra, Indranil; Dimitrova, Elena; Jarrah, Abdul S.
2010-03-01
In the last decade a new holistic approach for tackling biological problems, systems biology, which takes into account the study of the interactions between the components of a biological system to predict function and behavior has emerged. The reverse-engineering of biochemical networks from experimental data have increasingly become important in systems biology. Based on Boolean networks, we propose a time-discrete stochastic framework for the reverse engineering of the yeast cell cycle regulatory network from experimental data. With a suitable choice of state set, we have used powerful tools from computational algebra, that underlie the reverse-engineering algorithm, avoiding costly enumeration strategies. Stochasticity is introduced by choosing at each update step a random coordinate function for each variable, chosen from a probability space of update functions. The algorithm is based on a combinatorial structure known as the Gr"obner fans of a polynomial ideal which identifies the underlying network structure and dynamics. The model depicts a correct dynamics of the yeast cell cycle network and reproduces the time sequence of expression patterns along the biological cell cycle. Our findings indicate that the methodolgy has high chance of success when applied to large and complex systems to determine the dynamical properties of corresponding networks.
Stochastic cellular automata model for wildland fire spread dynamics
NASA Astrophysics Data System (ADS)
Maduro Almeida, Rodolfo; Macau, Elbert E. N.
2011-03-01
A stochastic cellular automata model for wildland fire spread under flat terrain and no-wind conditions is proposed and its dynamics is characterized and analyzed. One of three possible states characterizes each cell: vegetation cell, burning cell and burnt cell. The dynamics of fire spread is modeled as a stochastic event with an effective fire spread probability S which is a function of three probabilities that characterize: the proportion of vegetation cells across the lattice, the probability of a burning cell becomes burnt, and the probability of the fire spread from a burning cell to a neighboring vegetation cell. A set of simulation experiments is performed to analyze the effects of different values of the three probabilities in the fire pattern. Monte-Carlo simulations indicate that there is a critical line in the model parameter space that separates the set of parameters which a fire can propagate from those for which it cannot propagate. Finally, the relevance of the model is discussed under the light of computational experiments that illustrate the capability of the model catches both the dynamical and static qualitative properties of fire propagation.
Stochastic Dynamics of DC and AC Driven Dislocation Kinks
NASA Astrophysics Data System (ADS)
Vardanyan, A.; Kteyan, A.
2013-02-01
Dynamics of a pinned dislocation kink controlled by the acting DC and AC forces is studied analytically. The motion of the kink, described by sine-Gordon (sG) equation, is explored within the framework of McLaughlin-Scott perturbation theory. Assuming weakness of the acting AC force, the equation of motion of the dislocation kink in the pinning potential is linearized. Based on the equations derived, we study stochastic behavior of the kink, and determine the probability of its depinning. The dependencies of the depinning probability on DC and AC forces are analyzed in detail.
Synaptic Size Dynamics as an Effectively Stochastic Process
Statman, Adiel; Kaufman, Maya; Minerbi, Amir; Ziv, Noam E.; Brenner, Naama
2014-01-01
Long-term, repeated measurements of individual synaptic properties have revealed that synapses can undergo significant directed and spontaneous changes over time scales of minutes to weeks. These changes are presumably driven by a large number of activity-dependent and independent molecular processes, yet how these processes integrate to determine the totality of synaptic size remains unknown. Here we propose, as an alternative to detailed, mechanistic descriptions, a statistical approach to synaptic size dynamics. The basic premise of this approach is that the integrated outcome of the myriad of processes that drive synaptic size dynamics are effectively described as a combination of multiplicative and additive processes, both of which are stochastic and taken from distributions parametrically affected by physiological signals. We show that this seemingly simple model, known in probability theory as the Kesten process, can generate rich dynamics which are qualitatively similar to the dynamics of individual glutamatergic synapses recorded in long-term time-lapse experiments in ex-vivo cortical networks. Moreover, we show that this stochastic model, which is insensitive to many of its underlying details, quantitatively captures the distributions of synaptic sizes measured in these experiments, the long-term stability of such distributions and their scaling in response to pharmacological manipulations. Finally, we show that the average kinetics of new postsynaptic density formation measured in such experiments is also faithfully captured by the same model. The model thus provides a useful framework for characterizing synapse size dynamics at steady state, during initial formation of such steady states, and during their convergence to new steady states following perturbations. These findings show the strength of a simple low dimensional statistical model to quantitatively describe synapse size dynamics as the integrated result of many underlying complex processes
Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics*
Ao, P.
2011-01-01
The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann–Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach: One is based on Feynman–Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium. PMID:21949462
Dynamic stochastic optimization models for air traffic flow management
NASA Astrophysics Data System (ADS)
Mukherjee, Avijit
This dissertation presents dynamic stochastic optimization models for Air Traffic Flow Management (ATFM) that enables decisions to adapt to new information on evolving capacities of National Airspace System (NAS) resources. Uncertainty is represented by a set of capacity scenarios, each depicting a particular time-varying capacity profile of NAS resources. We use the concept of a scenario tree in which multiple scenarios are possible initially. Scenarios are eliminated as possibilities in a succession of branching points, until the specific scenario that will be realized on a particular day is known. Thus the scenario tree branching provides updated information on evolving scenarios, and allows ATFM decisions to be re-addressed and revised. First, we propose a dynamic stochastic model for a single airport ground holding problem (SAGHP) that can be used for planning Ground Delay Programs (GDPs) when there is uncertainty about future airport arrival capacities. Ground delays of non-departed flights can be revised based on updated information from scenario tree branching. The problem is formulated so that a wide range of objective functions, including non-linear delay cost functions and functions that reflect equity concerns can be optimized. Furthermore, the model improves on existing practice by ensuring efficient use of available capacity without necessarily exempting long-haul flights. Following this, we present a methodology and optimization models that can be used for decentralized decision making by individual airlines in the GDP planning process, using the solutions from the stochastic dynamic SAGHP. Airlines are allowed to perform cancellations, and re-allocate slots to remaining flights by substitutions. We also present an optimization model that can be used by the FAA, after the airlines perform cancellation and substitutions, to re-utilize vacant arrival slots that are created due to cancellations. Finally, we present three stochastic integer programming
Stochastic dynamics of bionanosystems: Multiscale analysis and specialized ensembles
NASA Astrophysics Data System (ADS)
Pankavich, S.; Miao, Y.; Ortoleva, J.; Shreif, Z.; Ortoleva, P.
2008-06-01
An approach for simulating bionanosystems such as viruses and ribosomes is presented. This calibration-free approach is based on an all-atom description for bionanosystems, a universal interatomic force field, and a multiscale perspective. The supramillion-atom nature of these bionanosystems prohibits the use of a direct molecular dynamics approach for phenomena such as viral structural transitions or self-assembly that develop over milliseconds or longer. A key element of these multiscale systems is the cross-talk between, and consequent strong coupling of processes over many scales in space and time. Thus, overall nanoscale features of these systems control the relative probability of atomistic fluctuations, while the latter mediate the average forces and diffusion coefficients that induce the dynamics of these nanoscale features. This feedback loop is overlooked in typical coarse-grained methods. We elucidate the role of interscale cross-talk and overcome bionanosystem simulation difficulties with (1) automated construction of order parameters (OPs) describing suprananometer scale structural features, (2) construction of OP-dependent ensembles describing the statistical properties of atomistic variables that ultimately contribute to the entropies driving the dynamics of the OPs, and (3) the derivation of a rigorous equation for the stochastic dynamics of the OPs. As the OPs capture hydrodynamic modes in the host medium, ``long-time tails'' in the correlation functions yielding the generalized diffusion coefficients do not emerge. Since the atomic-scale features of the system are treated statistically, several ensembles are constructed that reflect various experimental conditions. Attention is paid to the proper use of the Gibbs hypothesized equivalence of long-time and ensemble averages to accommodate the varying experimental conditions. The theory provides a basis for a practical, quantitative bionanosystem modeling approach that preserves the cross
Stochastic Simulation of Biomolecular Networks in Dynamic Environments.
Voliotis, Margaritis; Thomas, Philipp; Grima, Ramon; Bowsher, Clive G
2016-06-01
Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate-using decision-making by a large population of quorum sensing bacteria-that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits. PMID:27248512
Outbreak and Extinction Dynamics in a Stochastic Ebola Model
NASA Astrophysics Data System (ADS)
Nieddu, Garrett; Bianco, Simone; Billings, Lora; Forgoston, Eric; Kaufman, James
A zoonotic disease is a disease that can be passed between animals and humans. In many cases zoonotic diseases can persist in the animal population even if there are no infections in the human population. In this case we call the infected animal population the reservoir for the disease. Ebola virus disease (EVD) and SARS are both notable examples of such diseases. There is little work devoted to understanding stochastic disease extinction and reintroduction in the presence of a reservoir. Here we build a stochastic model for EVD and explicitly consider the presence of an animal reservoir. Using a master equation approach and a WKB ansatz, we determine the associated Hamiltonian of the system. Hamilton's equations are then used to numerically compute the 12-dimensional optimal path to extinction, which is then used to estimate mean extinction times. We also numerically investigate the behavior of the model for dynamic population size. Our results provide an improved understanding of outbreak and extinction dynamics in diseases like EVD.
Stochasticity and universal dynamics in communicating cellular populations
NASA Astrophysics Data System (ADS)
Noorbakhsh, Javad; Mehta, Pankaj; Allyson Sgro Collaboration; David Schwab Collaboration; Troy Mestler Collaboration; Thomas Gregor Collaboration
2014-03-01
A fundamental problem in biology is to understand how biochemical networks within individual cells coordinate and control population-level behaviors. Our knowledge of these biochemical networks is often incomplete, with little known about the underlying kinetic parameters. Here, we present a general modeling approach for overcoming these challenges based on universality. We apply our approach to study the emergence of collective oscillations of the signaling molecule cAMP in populations of the social amoebae Dictyostelium discoideum and show that a simple two-dimensional dynamical system can reproduce signaling dynamics of single cells and successfully predict novel population-level behaviors. We reduce all the important parameters of our model to only two and will study its behavior through a phase diagram. This phase diagram determines conditions under which cells are quiet or oscillating either coherently or incoherently. Furthermore it allows us to study the effect of different model components such as stochasticity, multicellularity and signal preprocessing. A central finding of our model is that Dictyostelium exploit stochasticity within biochemical networks to control population level behaviors.
Stochastic Simulation of Biomolecular Networks in Dynamic Environments
Voliotis, Margaritis; Thomas, Philipp; Grima, Ramon; Bowsher, Clive G.
2016-01-01
Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate—using decision-making by a large population of quorum sensing bacteria—that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits. PMID:27248512
Stochasticity and Spatial Interaction Govern Stem Cell Differentiation Dynamics
NASA Astrophysics Data System (ADS)
Smith, Quinton; Stukalin, Evgeny; Kusuma, Sravanti; Gerecht, Sharon; Sun, Sean X.
2015-07-01
Stem cell differentiation underlies many fundamental processes such as development, tissue growth and regeneration, as well as disease progression. Understanding how stem cell differentiation is controlled in mixed cell populations is an important step in developing quantitative models of cell population dynamics. Here we focus on quantifying the role of cell-cell interactions in determining stem cell fate. Toward this, we monitor stem cell differentiation in adherent cultures on micropatterns and collect statistical cell fate data. Results show high cell fate variability and a bimodal probability distribution of stem cell fraction on small (80-140 μm diameter) micropatterns. On larger (225-500 μm diameter) micropatterns, the variability is also high but the distribution of the stem cell fraction becomes unimodal. Using a stochastic model, we analyze the differentiation dynamics and quantitatively determine the differentiation probability as a function of stem cell fraction. Results indicate that stem cells can interact and sense cellular composition in their immediate neighborhood and adjust their differentiation probability accordingly. Blocking epithelial cadherin (E-cadherin) can diminish this cell-cell contact mediated sensing. For larger micropatterns, cell motility adds a spatial dimension to the picture. Taken together, we find stochasticity and cell-cell interactions are important factors in determining cell fate in mixed cell populations.
Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings
NASA Astrophysics Data System (ADS)
Cunha, Americo; Soize, Christian; Sampaio, Rubens
2015-11-01
This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bit-rock interaction model are taken into account using a parametric probabilistic approach. Numerical simulations have shown that the mechanical system of interest has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits.
Assessing predictability of a hydrological stochastic-dynamical system
NASA Astrophysics Data System (ADS)
Gelfan, Alexander
2014-05-01
The water cycle includes the processes with different memory that creates potential for predictability of hydrological system based on separating its long and short memory components and conditioning long-term prediction on slower evolving components (similar to approaches in climate prediction). In the face of the Panta Rhei IAHS Decade questions, it is important to find a conceptual approach to classify hydrological system components with respect to their predictability, define predictable/unpredictable patterns, extend lead-time and improve reliability of hydrological predictions based on the predictable patterns. Representation of hydrological systems as the dynamical systems subjected to the effect of noise (stochastic-dynamical systems) provides possible tool for such conceptualization. A method has been proposed for assessing predictability of hydrological system caused by its sensitivity to both initial and boundary conditions. The predictability is defined through a procedure of convergence of pre-assigned probabilistic measure (e.g. variance) of the system state to stable value. The time interval of the convergence, that is the time interval during which the system losses memory about its initial state, defines limit of the system predictability. The proposed method was applied to assess predictability of soil moisture dynamics in the Nizhnedevitskaya experimental station (51.516N; 38.383E) located in the agricultural zone of the central European Russia. A stochastic-dynamical model combining a deterministic one-dimensional model of hydrothermal regime of soil with a stochastic model of meteorological inputs was developed. The deterministic model describes processes of coupled heat and moisture transfer through unfrozen/frozen soil and accounts for the influence of phase changes on water flow. The stochastic model produces time series of daily meteorological variables (precipitation, air temperature and humidity), whose statistical properties are similar
Stochastic queueing-theory approach to human dynamics
NASA Astrophysics Data System (ADS)
Walraevens, Joris; Demoor, Thomas; Maertens, Tom; Bruneel, Herwig
2012-02-01
Recently, numerous studies have shown that human dynamics cannot be described accurately by exponential laws. For instance, Barabási [Nature (London)NATUAS0028-083610.1038/nature03459 435, 207 (2005)] demonstrates that waiting times of tasks to be performed by a human are more suitably modeled by power laws. He presumes that these power laws are caused by a priority selection mechanism among the tasks. Priority models are well-developed in queueing theory (e.g., for telecommunication applications), and this paper demonstrates the (quasi-)immediate applicability of such a stochastic priority model to human dynamics. By calculating generating functions and by studying them in their dominant singularity, we prove that nonexponential tails result naturally. Contrary to popular belief, however, these are not necessarily triggered by the priority selection mechanism.
Dynamic, stochastic, and topological aspects of polyrhythmic performance.
Jagacinski, R J; Peper, C E; Beek, P J
2000-12-01
Previous research on polyrhythmic performance can be broadly summarized in terms of 2 classes of models: timekeeper models and nonlinear dynamical models. In the former approach, research has been focused on patterns of covariance among time intervals, and in the latter approach, the concentration has been on pattern (in)stability and the spatiotemporal properties of oscillating limbs. It is suggested that one can achieve a more comprehensive theory that incorporates the strengths of each of these approaches by endowing timekeeper models with nonlinear dynamics or by endowing nonlinear oscillator models with stochastic variability. Additionally, those models are complemented by a topological description of performance based on knot theory. Knot theory provides a new index of difficulty for polyrhythmic tapping, a spatial interpretation of transitions between different stable rhythms, and a possible instantiation of N. A. Bernstein's (1967a) notion of a topological motor program. PMID:11114226
Stochastic dynamics of melt ponds and sea ice-albedo climate feedback
NASA Astrophysics Data System (ADS)
Sudakov, Ivan
Evolution of melt ponds on the Arctic sea surface is a complicated stochastic process. We suggest a low-order model with ice-albedo feedback which describes stochastic dynamics of melt ponds geometrical characteristics. The model is a stochastic dynamical system model of energy balance in the climate system. We describe the equilibria in this model. We conclude the transition in fractal dimension of melt ponds affects the shape of the sea ice albedo curve.
Stochastic dynamics of particles trapped in turbulent flows
NASA Astrophysics Data System (ADS)
Machicoane, N.; López-Caballero, M.; Fiabane, L.; Pinton, J.-F.; Bourgoin, M.; Burguete, J.; Volk, R.
2016-02-01
The long-time dynamics of large particles trapped in two nonhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different spatial symmetries and temporal behaviors. Because large particles are less and less sensitive to flow fluctuations as their size increases, we observe the emergence of a slow dynamics corresponding to back-and-forth motions between two attractors, and a super-slow regime synchronized with flow reversals when they exist. Such dynamics is substantially reproduced by a one-dimensional stochastic model of an overdamped particle trapped in a two-well potential, forced by a colored noise. An extended model is also proposed that reproduces observed dynamics and trapping without potential barrier: the key ingredient is the ratio between the time scales of the noise correlation and the particle dynamics. A total agreement with experiments requires the introduction of spatially nonhomogeneous fluctuations and a suited confinement strength.
Two-strain competition in quasineutral stochastic disease dynamics
NASA Astrophysics Data System (ADS)
Kogan, Oleg; Khasin, Michael; Meerson, Baruch; Schneider, David; Myers, Christopher R.
2014-10-01
We develop a perturbation method for studying quasineutral competition in a broad class of stochastic competition models and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic susceptible-infected-susceptible (SIS) model. Here we extend previous results due to Parsons and Quince [Theor. Popul. Biol. 72, 468 (2007), 10.1016/j.tpb.2007.04.002], Parsons et al. [Theor. Popul. Biol. 74, 302 (2008), 10.1016/j.tpb.2008.09.001], and Lin, Kim, and Doering [J. Stat. Phys. 148, 646 (2012), 10.1007/s10955-012-0479-9]. The second model, a two-strain generalization of the stochastic susceptible-infected-recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of subpopulation sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the subpopulations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.
Stochastic-Dynamic Earthquake Models and Tsunami Generation
NASA Astrophysics Data System (ADS)
Oglesby, D. D.; Geist, E. L.
2013-12-01
Dynamic models are now understood to provide physically plausible faulting scenarios for ground motion prediction, but their use in tsunami hazard analysis is in its infancy. Typical tsunami model generation methods rely on kinematic or dislocation models of the earthquake source, in which the seismic moment, rupture path, and slip distribution are assumed a priori, typically based on models of prior earthquakes, aftershock distributions, and/or some sort of stochastic slip model. However, such models are not guaranteed to be consistent with any physically plausible faulting scenario and may span a range of parameter space far outside of what is physically realistic. In contrast, in dynamic models the earthquake rupture and slip process (including the final size of the earthquake, the spatiotemporal evolution of slip, and the rupture path on complex fault geometry) are calculated results of the models. Utilizing the finite element method, a self-affine stochastic stress field, and a shallow-water hydrodynamic code, we calculate a suite of dynamic slip models and near-source tsunamis from a megathrust/splay fault system motivated by the geometry in the Nankai region of Japan. Different stress realizations produce different spatial patterns of slip, including different partitioning between the megathrust and splay segments. Because the final moment from different stress realizations can differ, and because partitioning of slip between fault segments has a first-order effect on the surface deformation and tsunami generation, the modeled near-source tsunamis are also highly variable. Models whose stress amplitudes have been scaled to produce equivalent seismic moments (but with the same spatial variability and relative fault strength as the previous unscaled models) have less variability in tsunami amplitude in regions far from the fault, but greater variability in amplitude in the near-fault region.
Nonequilibrium dynamics of stochastic point processes with refractoriness
Deger, Moritz; Cardanobile, Stefano; Rotter, Stefan; Helias, Moritz; Atay, Fatihcan M.
2010-08-15
Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze nonstationary renewal processes.
Nonequilibrium dynamics of stochastic point processes with refractoriness
NASA Astrophysics Data System (ADS)
Deger, Moritz; Helias, Moritz; Cardanobile, Stefano; Atay, Fatihcan M.; Rotter, Stefan
2010-08-01
Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze nonstationary renewal processes.
Stochastic fire-diffuse-fire model with realistic cluster dynamics
NASA Astrophysics Data System (ADS)
Calabrese, Ana; Fraiman, Daniel; Zysman, Daniel; Ponce Dawson, Silvina
2010-09-01
Living organisms use waves that propagate through excitable media to transport information. Ca2+ waves are a paradigmatic example of this type of processes. A large hierarchy of Ca2+ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, Ca2+ release occurs trough inositol 1,4,5-trisphosphate receptors (IP3Rs) which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of IP3R ’s that replicates the experimental observations reported in [D. Fraiman , Biophys. J. 90, 3897 (2006)10.1529/biophysj.105.075911]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the IP3 concentration is increased.
Stochastic Approximation of Dynamical Exponent at Quantum Critical Point
NASA Astrophysics Data System (ADS)
Suwa, Hidemaro; Yasuda, Shinya; Todo, Synge
We have developed a unified finite-size scaling method for quantum phase transitions that requires no prior knowledge of the dynamical exponent z. During a quantum Monte Carlo simulation, the temperature is automatically tuned by the Robbins-Monro stochastic approximation method, being proportional to the lowest gap of the finite-size system. The dynamical exponent is estimated in a straightforward way from the system-size dependence of the temperature. As a demonstration of our novel method, the two-dimensional S = 1 / 2 quantum XY model, or equivalently the hard-core boson system, in uniform and staggered magnetic fields is investigated in the combination of the world-line quantum Monte Carlo worm algorithm. In the absence of a uniform magnetic field, we obtain the fully consistent result with the Lorentz invariance at the quantum critical point, z = 1 . Under a finite uniform magnetic field, on the other hand, the dynamical exponent becomes two, and the mean-field universality with effective dimension (2+2) governs the quantum phase transition. We will discuss also the system with random magnetic fields, or the dirty boson system, bearing a non-trivial dynamical exponent.Reference: S. Yasuda, H. Suwa, and S. Todo Phys. Rev. B 92, 104411 (2015); arXiv:1506.04837
Partial synchronization in stochastic dynamical networks with switching communication channels
NASA Astrophysics Data System (ADS)
Huang, Chi; Ho, Daniel W. C.; Lu, Jianquan; Kurths, Jürgen
2012-06-01
In this paper, the partial synchronization problem of stochastic dynamical networks (SDNs) is investigated. Unlike the existing models, the SDN considered in this paper suffers from a class of communication constraint—only part of nodes' states can be transmitted. Thus, less nodes' states can be used to synchronize the SDN, which makes the analysis of the synchronization problem much harder. A set of channel matrices are introduced to reflect such kind of constraint. Furthermore, due to unpredictable environmental changes, the channel matrices can switch among some communication modes. The switching considered here is governed by a Markov process. To overcome the difficulty, a regrouping method is employed to derive our main results. The obtained conditions guarantee that partial synchronization can be achieved for SDNs under switching communication constraint. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results and how the communication constraint influences synchronization result.
Stochastic-Dynamical Modeling of Space Time Rainfall
NASA Technical Reports Server (NTRS)
Georgankakos, Konstantine P.
1997-01-01
The focus of this research work is the elucidation of the physical origins of the observed extreme-rainfall variability over tropical oceans. The quantitative results of this work may be used to establish links between deterministic models of the mesoscale and synoptic scale with statistical descriptions of the temporal variability of local tropical oceanic rainfall. In addition, they may be used to quantify the influence of measurement error in large-scale forcing and cloud scale observations on the accuracy of local rainfall variability inferences, important for hydrologic studies. A simple statistical-dynamical model, suitable for use in repetitive Monte Carlo experiments, is formulated as a diagnostic tool for this purpose. Stochastic processes with temporal structure and parameters estimated from observed large-scale data represent large-scale forcing.
The stochastic dynamics of tethered microcantilevers in a viscous fluid
NASA Astrophysics Data System (ADS)
Robbins, Brian A.; Radiom, Milad; Ducker, William A.; Walz, John Y.; Paul, Mark R.
2014-10-01
We explore and quantify the coupled dynamics of a pair of micron scale cantilevers immersed in a viscous fluid that are also directly tethered to one another at their tips by a spring force. The spring force, for example, could represent the molecular stiffness or elasticity of a biomolecule or material tethered between the cantilevers. We use deterministic numerical simulations with the fluctuation-dissipation theorem to compute the stochastic dynamics of the cantilever pair for the conditions of experiment when driven only by Brownian motion. We validate our approach by comparing directly with experimental measurements in the absence of the tether which shows excellent agreement. Using numerical simulations, we quantify the correlated dynamics of the cantilever pair over a range of tether stiffness. Our results quantify the sensitivity of the auto- and cross-correlations of equilibrium fluctuations in cantilever displacement to the stiffness of the tether. We show that the tether affects the magnitude of the correlations which can be used in a measurement to probe the properties of an attached tethering substance. For the configurations of current interest using micron scale cantilevers in water, we show that the magnitude of the fluid coupling between the cantilevers is sufficiently small such that the influence of the tether can be significant. Our results show that the cross-correlation is more sensitive to tether stiffness than the auto-correlation indicating that a two-cantilever measurement has improved sensitivity when compared with a measurement using a single cantilever.
The stochastic dynamics of tethered microcantilevers in a viscous fluid
Robbins, Brian A.; Paul, Mark R.; Radiom, Milad; Ducker, William A.; Walz, John Y.
2014-10-28
We explore and quantify the coupled dynamics of a pair of micron scale cantilevers immersed in a viscous fluid that are also directly tethered to one another at their tips by a spring force. The spring force, for example, could represent the molecular stiffness or elasticity of a biomolecule or material tethered between the cantilevers. We use deterministic numerical simulations with the fluctuation-dissipation theorem to compute the stochastic dynamics of the cantilever pair for the conditions of experiment when driven only by Brownian motion. We validate our approach by comparing directly with experimental measurements in the absence of the tether which shows excellent agreement. Using numerical simulations, we quantify the correlated dynamics of the cantilever pair over a range of tether stiffness. Our results quantify the sensitivity of the auto- and cross-correlations of equilibrium fluctuations in cantilever displacement to the stiffness of the tether. We show that the tether affects the magnitude of the correlations which can be used in a measurement to probe the properties of an attached tethering substance. For the configurations of current interest using micron scale cantilevers in water, we show that the magnitude of the fluid coupling between the cantilevers is sufficiently small such that the influence of the tether can be significant. Our results show that the cross-correlation is more sensitive to tether stiffness than the auto-correlation indicating that a two-cantilever measurement has improved sensitivity when compared with a measurement using a single cantilever.
Stochastic approximation of dynamical exponent at quantum critical point
NASA Astrophysics Data System (ADS)
Yasuda, Shinya; Suwa, Hidemaro; Todo, Synge
2015-09-01
We have developed a unified finite-size scaling method for quantum phase transitions that requires no prior knowledge of the dynamical exponent z . During a quantum Monte Carlo simulation, the temperature is automatically tuned by the Robbins-Monro stochastic approximation method, being proportional to the lowest gap of the finite-size system. The dynamical exponent is estimated in a straightforward way from the system-size dependence of the temperature. As a demonstration of our novel method, the two-dimensional S =1 /2 quantum X Y model in uniform and staggered magnetic fields is investigated in the combination of the world-line quantum Monte Carlo worm algorithm. In the absence of a uniform magnetic field, we obtain the fully consistent result with the Lorentz invariance at the quantum critical point, z =1 , i.e., the three-dimensional classical X Y universality class. Under a finite uniform magnetic field, on the other hand, the dynamical exponent becomes two, and the mean-field universality with effective dimension (2 +2 ) governs the quantum phase transition.
Kryvohuz, Maksym; Mukamel, Shaul
2015-06-01
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. PMID:26049450
Kryvohuz, Maksym Mukamel, Shaul
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.
Second Cancers After Fractionated Radiotherapy: Stochastic Population Dynamics Effects
NASA Technical Reports Server (NTRS)
Sachs, Rainer K.; Shuryak, Igor; Brenner, David; Fakir, Hatim; Hahnfeldt, Philip
2007-01-01
When ionizing radiation is used in cancer therapy it can induce second cancers in nearby organs. Mainly due to longer patient survival times, these second cancers have become of increasing concern. Estimating the risk of solid second cancers involves modeling: because of long latency times, available data is usually for older, obsolescent treatment regimens. Moreover, modeling second cancers gives unique insights into human carcinogenesis, since the therapy involves administering well characterized doses of a well studied carcinogen, followed by long-term monitoring. In addition to putative radiation initiation that produces pre-malignant cells, inactivation (i.e. cell killing), and subsequent cell repopulation by proliferation can be important at the doses relevant to second cancer situations. A recent initiation/inactivation/proliferation (IIP) model characterized quantitatively the observed occurrence of second breast and lung cancers, using a deterministic cell population dynamics approach. To analyze ifradiation-initiated pre-malignant clones become extinct before full repopulation can occur, we here give a stochastic version of this I I model. Combining Monte Carlo simulations with standard solutions for time-inhomogeneous birth-death equations, we show that repeated cycles of inactivation and repopulation, as occur during fractionated radiation therapy, can lead to distributions of pre-malignant cells per patient with variance >> mean, even when pre-malignant clones are Poisson-distributed. Thus fewer patients would be affected, but with a higher probability, than a deterministic model, tracking average pre-malignant cell numbers, would predict. Our results are applied to data on breast cancers after radiotherapy for Hodgkin disease. The stochastic IIP analysis, unlike the deterministic one, indicates: a) initiated, pre-malignant cells can have a growth advantage during repopulation, not just during the longer tumor latency period that follows; b) weekend
Deterministic and Stochastic Descriptions of Gene Expression Dynamics
NASA Astrophysics Data System (ADS)
Marathe, Rahul; Bierbaum, Veronika; Gomez, David; Klumpp, Stefan
2012-09-01
A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of unregulated (constitutive) gene expression and compare different mathematical descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error made by models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.
A Stochastic Fractional Dynamics Model of Rainfall Statistics
NASA Astrophysics Data System (ADS)
Kundu, Prasun; Travis, James
2013-04-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.
Dynamics of the stochastic Lorenz chaotic system with long memory effects
Zeng, Caibin Yang, Qigui
2015-12-15
Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.
Stochastic Rotation Dynamics simulations of wetting multi-phase flows
NASA Astrophysics Data System (ADS)
Hiller, Thomas; Sanchez de La Lama, Marta; Brinkmann, Martin
2016-06-01
Multi-color Stochastic Rotation Dynamics (SRDmc) has been introduced by Inoue et al. [1,2] as a particle based simulation method to study the flow of emulsion droplets in non-wetting microchannels. In this work, we extend the multi-color method to also account for different wetting conditions. This is achieved by assigning the color information not only to fluid particles but also to virtual wall particles that are required to enforce proper no-slip boundary conditions. To extend the scope of the original SRDmc algorithm to e.g. immiscible two-phase flow with viscosity contrast we implement an angular momentum conserving scheme (SRD+mc). We perform extensive benchmark simulations to show that a mono-phase SRDmc fluid exhibits bulk properties identical to a standard SRD fluid and that SRDmc fluids are applicable to a wide range of immiscible two-phase flows. To quantify the adhesion of a SRD+mc fluid in contact to the walls we measure the apparent contact angle from sessile droplets in mechanical equilibrium. For a further verification of our wettability implementation we compare the dewetting of a liquid film from a wetting stripe to experimental and numerical studies of interfacial morphologies on chemically structured surfaces.
Stability analysis of associative memory network composed of stochastic neurons and dynamic synapses
Katori, Yuichi; Otsubo, Yosuke; Okada, Masato; Aihara, Kazuyuki
2013-01-01
We investigate the dynamical properties of an associative memory network consisting of stochastic neurons and dynamic synapses that show short-term depression and facilitation. In the stochastic neuron model used in this study, the efficacy of the synaptic transmission changes according to the short-term depression or facilitation mechanism. We derive a macroscopic mean field model that captures the overall dynamical properties of the stochastic model. We analyze the stability and bifurcation structure of the mean field model, and show the dependence of the memory retrieval performance on the noise intensity and parameters that determine the properties of the dynamic synapses, i.e., time constants for depressing and facilitating processes. The associative memory network exhibits a variety of dynamical states, including the memory and pseudo-memory states, as well as oscillatory states among memory patterns. This study provides comprehensive insight into the dynamical properties of the associative memory network with dynamic synapses. PMID:23440567
Summing over trajectories of stochastic dynamics with multiplicative noise
Tang, Ying Ao, Ping; Yuan, Ruoshi
2014-07-28
We demonstrate that previous path integral formulations for the general stochastic interpretation generate incomplete results exemplified by the geometric Brownian motion. We thus develop a novel path integral formulation for the overdamped Langevin equation with multiplicative noise. The present path integral leads to the corresponding Fokker-Planck equation, and naturally generates a normalized transition probability in examples. Our result solves the inconsistency of the previous path integral formulations for the general stochastic interpretation, and can have wide applications in chemical and physical stochastic processes.
Sabass, Benedikt; Schwarz, Ulrich S
2010-05-19
In migrating cells, retrograde flow of the actin cytoskeleton is related to traction at adhesion sites located at the base of the lamellipodium. The coupling between the moving cytoskeleton and the stationary adhesions is mediated by the continuous association and dissociation of molecular bonds. We introduce a simple model for the competition between the stochastic dynamics of elastic bonds at the moving interface and relaxation within the moving actin cytoskeleton represented by an internal viscous friction coefficient. Using exact stochastic simulations and an analytical mean field theory, we show that the stochastic bond dynamics lead to biphasic friction laws as observed experimentally. At low internal dissipation, stochastic bond dynamics lead to a regime of irregular stick-and-slip motion. High internal dissipation effectively suppresses cooperative effects among bonds and hence stabilizes the adhesion. PMID:21386438
Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics
NASA Astrophysics Data System (ADS)
Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc
2016-03-01
We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.
Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics.
Arampatzis, Georgios; Katsoulakis, Markos A; Rey-Bellet, Luc
2016-03-14
We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications. PMID:26979681
The Dynamical Behaviors in a Stochastic SIS Epidemic Model with Nonlinear Incidence
Rifhat, Ramziya; Ge, Qing; Teng, Zhidong
2016-01-01
A stochastic SIS-type epidemic model with general nonlinear incidence and disease-induced mortality is investigated. It is proved that the dynamical behaviors of the model are determined by a certain threshold value R~0. That is, when R~0<1 and together with an additional condition, the disease is extinct with probability one, and when R~0>1, the disease is permanent in the mean in probability, and when there is not disease-related death, the disease oscillates stochastically about a positive number. Furthermore, when R~0>1, the model admits positive recurrence and a unique stationary distribution. Particularly, the effects of the intensities of stochastic perturbation for the dynamical behaviors of the model are discussed in detail, and the dynamical behaviors for the stochastic SIS epidemic model with standard incidence are established. Finally, the numerical simulations are presented to illustrate the proposed open problems. PMID:27418943
Stochastic rotation dynamics simulation of electro-osmosis
NASA Astrophysics Data System (ADS)
Ceratti, Davide R.; Obliger, Amaël; Jardat, Marie; Rotenberg, Benjamin; Dahirel, Vincent
2015-09-01
Stochastic Rotation Dynamics (SRD) is a mesoscale simulation technique that captures hydrodynamic couplings in simple and complex fluids. It can be used in various hydrodynamic regimes and it is not restricted to specific geometries. We show here that SRD using the collisional coupling approach to capture momentum transfer between the semi-implicit solvent and the explicit counterions, is able to describe electro-kinetic effects, i.e. coupled electrostatic and hydrodynamic phenomena occurring at charged solid-liquid interfaces. The method is first validated for electro-osmosis in the simple case of a slit pore without added salt, for which an analytical solution of the Helmholtz-Smoluchowski theory is known, in a physical regime where this mean-field theory is valid. We then discuss the predictions of SRD for electro-osmosis beyond the range of validity of the Helmholtz-Smoluchowski (or Poisson-Nernst-Planck) theory, in particular due to ion-ion correlations at the surface, to charge localisation on discrete sites at the solid surface and to surface charge heterogeneity, that all contribute to a reduction of the electro-osmotic flow. In order to disentangle these last two aspects, we also investigate at the mean-field level a simple system with alternate charged and neutral stripes, using lattice-Boltzmann electro-kinetics simulations. Overall, this work opens new perspectives for the use of SRD as a generic mesoscopic simulation method for soft matter problems, in particular under confinement, since in practice many interfaces between fluids and solids are charged.
Complex Population Dynamics in Mussels Arising from Density-Linked Stochasticity
Wootton, J. Timothy; Forester, James D.
2013-01-01
Population fluctuations are generally attributed to the deterministic consequences of strong non-linear interactions among organisms, or the effects of random stochastic environmental variation superimposed upon the deterministic skeleton describing population change. Analysis of the population dynamics of the mussel Mytilus californianus taken in 16 plots over 18-years found no evidence that these processes explained observed strong fluctuations. Instead, population fluctuations arose because environmental stochasticity varied with abundance, which we term density-linked stochasticity. This phenomenon arises from biologically relevant mechanisms: recruitment variation and transmission of disturbance among neighboring individuals. Density-linked stochasticity is probably present frequently in populations, as it arises naturally from several general ecological processes, including stage structure variation with density, ontogenetic niche shifts, and local transmission of stochastic perturbations. More thoroughly characterizing and interpreting deviations from the mean behavior of a system will lead to better ecological prediction and improved insight into the important processes affecting populations and ecosystems. PMID:24086617
Stochastic expression dynamics of a transcription factor revealed by single-molecule noise analysis.
Hensel, Zach; Feng, Haidong; Han, Bo; Hatem, Christine; Wang, Jin; Xiao, Jie
2012-08-01
Gene expression is inherently stochastic; precise gene regulation by transcription factors is important for cell-fate determination. Many transcription factors regulate their own expression, suggesting that autoregulation counters intrinsic stochasticity in gene expression. Using a new strategy, cotranslational activation by cleavage (CoTrAC), we probed the stochastic expression dynamics of cI, which encodes the bacteriophage λ repressor CI, a fate-determining transcription factor. CI concentration fluctuations influence both lysogenic stability and induction of bacteriophage λ. We found that the intrinsic stochasticity in cI expression was largely determined by CI expression level irrespective of autoregulation. Furthermore, extrinsic, cell-to-cell variation was primarily responsible for CI concentration fluctuations, and negative autoregulation minimized CI concentration heterogeneity by counteracting extrinsic noise and introducing memory. This quantitative study of transcription factor expression dynamics sheds light on the mechanisms cells use to control noise in gene regulatory networks. PMID:22751020
Fully nonlinear dynamics of stochastic thin-film dewetting.
Nesic, S; Cuerno, R; Moro, E; Kondic, L
2015-12-01
The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows materials nanostructuring. Often, it is crucial to be able to control the evolution, and to produce patterns characterized by regularly spaced droplets. While thermal fluctuations are expected to play a role in the dewetting process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution that involve droplet formation. Within a stochastic lubrication framework, we show that thermal noise substantially influences the process of droplets formation. Stochastic systems feature a smaller number of droplets with a larger variability in size and space distribution, when compared to their deterministic counterparts. Finally, we discuss the influence of stochasticity on droplet coarsening for asymptotically long times. PMID:26764623
Fully nonlinear dynamics of stochastic thin-film dewetting
NASA Astrophysics Data System (ADS)
Nesic, S.; Cuerno, R.; Moro, E.; Kondic, L.
2015-12-01
The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows materials nanostructuring. Often, it is crucial to be able to control the evolution, and to produce patterns characterized by regularly spaced droplets. While thermal fluctuations are expected to play a role in the dewetting process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution that involve droplet formation. Within a stochastic lubrication framework, we show that thermal noise substantially influences the process of droplets formation. Stochastic systems feature a smaller number of droplets with a larger variability in size and space distribution, when compared to their deterministic counterparts. Finally, we discuss the influence of stochasticity on droplet coarsening for asymptotically long times.
Extension of Nelson's stochastic quantization to finite temperature using thermo field dynamics
NASA Astrophysics Data System (ADS)
Kobayashi, K.; Yamanaka, Y.
2011-08-01
We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schrödinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature.
Mathematical framework for the analysis of dynamic stochastic systems with the RAVEN code
Rabiti, C.; Mandelli, D.; Alfonsi, A.; Cogliati, J.; Kinoshita, R.
2013-07-01
RAVEN (Reactor Analysis and Virtual control Environment) is a software code under development at Idaho National Laboratory aimed at performing probabilistic risk assessment and uncertainty quantification using RELAP-7, for which it acts also as a simulation controller. In this paper we will present the equations characterizing a dynamic stochastic system and we will then discuss the behavior of each stochastic term and how it is accounted for in the RAVEN software design. Moreover we will present preliminary results of the implementation. (authors)
Stochastic Cascade Dynamical Downscaling of Precipitation over Complex Terrain
NASA Astrophysics Data System (ADS)
Posadas, A.; Duffaut, L. E.; Jones, C.; Carvalho, L. V.; Carbajal, M.; Heidinger, H.; Quiroz, R.
2013-12-01
spatial and temporal variability of rainfall between the rainfall fields obtained from the rain gauge network and those generated by the simulation model. The potential advantages of this methodology are discussed.Stochastic Cascade Dynamical Downscaling of Precipitation over Complex Terrain
Dynamics of the 2001 UK Foot and Mouth Epidemic: Stochastic Dispersal in a Heterogeneous Landscape
NASA Astrophysics Data System (ADS)
Keeling, Matt J.; Woolhouse, Mark E. J.; Shaw, Darren J.; Matthews, Louise; Chase-Topping, Margo; Haydon, Dan T.; Cornell, Stephen J.; Kappey, Jens; Wilesmith, John; Grenfell, Bryan T.
2001-10-01
Foot-and-mouth is one of the world's most economically important livestock diseases. We developed an individual farm-based stochastic model of the current UK epidemic. The fine grain of the epidemiological data reveals the infection dynamics at an unusually high spatiotemporal resolution. We show that the spatial distribution, size, and species composition of farms all influence the observed pattern and regional variability of outbreaks. The other key dynamical component is long-tailed stochastic dispersal of infection, combining frequent local movements with occasional long jumps. We assess the history and possible duration of the epidemic, the performance of control strategies, and general implications for disease dynamics in space and time.
NASA Astrophysics Data System (ADS)
Volchenkov, D.
2009-03-01
Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magneto-hydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications.
A Hierarchical Latent Stochastic Differential Equation Model for Affective Dynamics
ERIC Educational Resources Information Center
Oravecz, Zita; Tuerlinckx, Francis; Vandekerckhove, Joachim
2011-01-01
In this article a continuous-time stochastic model (the Ornstein-Uhlenbeck process) is presented to model the perpetually altering states of the core affect, which is a 2-dimensional concept underlying all our affective experiences. The process model that we propose can account for the temporal changes in core affect on the latent level. The key…
Time Evolution of the Dynamical Variables of a Stochastic System.
ERIC Educational Resources Information Center
de la Pena, L.
1980-01-01
By using the method of moments, it is shown that several important and apparently unrelated theorems describing average properties of stochastic systems are in fact particular cases of a general law; this method is applied to generalize the virial theorem and the fluctuation-dissipation theorem to the time-dependent case. (Author/SK)
Activity of Excitatory Neuron with Delayed Feedback Stimulated with Poisson Stream is Non-Markov
NASA Astrophysics Data System (ADS)
Vidybida, Alexander K.
2015-09-01
For a class of excitatory spiking neuron models with delayed feedback fed with a Poisson stochastic process, it is proven that the stream of output interspike intervals cannot be presented as a Markov process of any order.
NASA Astrophysics Data System (ADS)
Fontanela, F.; Silva, O. M.; Lenzi, A.; Ritto, T. G.
2016-08-01
The analysis of household compressor's components is typically evaluated by using mathematical-mechanical models, and many decisions are taken based on simulations. However, such an investigation is usually performed in a deterministic framework, which cannot consider manufacturing variabilities and epistemic uncertainties. In this paper, a stochastic structural model that considers data and model uncertainties is developed for a discharge pipe connected to a hermetic compressor's shell. An experimental test rig is constructed to test each part separately, and an identification strategy is proposed to fit the stochastic model to experimental results. Finally, the impact of the uncertainties in each structural component on the dynamical responses of the whole system is investigated. It turns out that: (1) the proposed stochastic dynamical model presented very good results when compared to the experimental responses, and (2) uncertainties in the discharge pipe model play an important role in the coupled system dynamics.
NASA Astrophysics Data System (ADS)
Hidalgo, J.; Seoane, L. F.; Cortés, J. M.; Muñoz, M. A.
2013-01-01
We review the mechanism of stochastic amplification of fluctuations in the context of fast cortical oscillations observed during up-states both in vitro and in vivo. For this purpose, we employ minimalistic models based on short-time synaptic depression with or without synaptic facilitation and compare results with empirical observations. The phenomenon of stochastic amplification of fluctuations is shown to be relevant and robust against different regulatory mechanisms and model specificities. In particular, by introducing synaptic facilitation as a possible manner to dynamically tune the synaptic efficacy, we show that, beyond resonancy details, the mechanism responsible for stochastic amplification is robust and persists along a wide range in the synaptic parameters space. In passing, we explain why a similar stochastic amplification cannot possibly be observed in cortical down-states.
Nonlinear dynamics of accretion disks with stochastic viscosity
Cowperthwaite, Philip S.; Reynolds, Christopher S.
2014-08-20
We present a nonlinear numerical model for a geometrically thin accretion disk with the addition of stochastic nonlinear fluctuations in the viscous parameter. These numerical realizations attempt to study the stochastic effects on the disk angular momentum transport. We show that this simple model is capable of reproducing several observed phenomenologies of accretion-driven systems. The most notable of these is the observed linear rms-flux relationship in the disk luminosity. This feature is not formally captured by the linearized disk equations used in previous work. A Fourier analysis of the dissipation and mass accretion rates across disk radii show coherence for frequencies below the local viscous frequency. This is consistent with the coherence behavior observed in astrophysical sources such as Cygnus X-1.
Midpoint numerical technique for stochastic Landau-Lifshitz-Gilbert dynamics
NASA Astrophysics Data System (ADS)
D'Aquino, M.; Serpico, C.; Coppola, G.; Mayergoyz, I. D.; Bertotti, G.
2006-04-01
The implicit midpoint time-integration technique is applied to the stochastic Landau-Lifshitz-Gilbert (LLG) equation. The numerical scheme converges to the Stratonovich solution in the limit of vanishing time step. It preserves the magnetization magnitude and the main energy balance properties of the LLG equation independently of the time step. The numerical technique is then applied to the study of superparamagnetic state in a small spheroidal particle, and the numerical results are compared with the theory.
Predicting stochastic community dynamics in grasslands under the assumption of competitive symmetry.
Lohier, Théophile; Jabot, Franck; Weigelt, Alexandra; Schmid, Bernhard; Deffuant, Guillaume
2016-06-21
Community dynamics is influenced by multiple ecological processes such as environmental spatiotemporal variation, competition between individuals and demographic stochasticity. Quantifying the respective influence of these various processes and making predictions on community dynamics require the use of a dynamical framework encompassing these various components. We here demonstrate how to adapt the framework of stochastic community dynamics to the peculiarities of herbaceous communities, by using a short temporal resolution adapted to the time scale of competition between herbaceous plants, and by taking into account the seasonal drops in plant aerial biomass following winter, harvesting or consumption by herbivores. We develop a hybrid inference method for this novel modelling framework that both uses numerical simulations and likelihood computations. Applying this methodology to empirical data from the Jena biodiversity experiment, we find that environmental stochasticity has a larger effect on community dynamics than demographic stochasticity, and that both effects are generally smaller than observation errors at the plot scale. We further evidence that plant intrinsic growth rates and carrying capacities are moderately predictable from plant vegetative height, specific leaf area and leaf dry matter content. We do not find any trade-off between demographical components, since species with larger intrinsic growth rates tend to also have lower demographic and environmental variances. Finally, we find that our model is able to make relatively good predictions of multi-specific community dynamics based on the assumption of competitive symmetry. PMID:27060673
Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids
Donev, A; Alder, B J; Garcia, A L
2008-02-26
A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.
Benderskii, V. A.; Kats, E. I.
2013-01-15
The quantum dynamics problem for a 1D chain consisting of 2N + 1 sites (N Much-Greater-Than 1) with the interaction of nearest neighbors and an impurity site at the middle differing in energy and in coupling constant from the sites of the remaining chain is solved analytically. The initial excitation of the impurity is accompanied by the propagation of excitation over the chain sites and with the emergence of Loschmidt echo (partial restoration of the impurity site population) in the recurrence cycles with a period proportional to N. The echo consists of the main (most intense) component modulated by damped oscillations. The intensity of oscillations increases with increasing cycle number and matrix element C of the interaction of the impurity site n = 0 with sites n = {+-}1 (0 < C {<=} 1; for the remaining neighboring sites, the matrix element is equal to unity). Mixing of the components of echo from neighboring cycles induces a transition from the regular to stochastic evolution. In the regular evolution region, the wave packet propagates over the chain at a nearly constant group velocity, embracing a number of sites varying periodically with time. In the stochastic regime, the excitation is distributed over a number of sites close to 2N, with the populations varying irregularly with time. The model explains qualitatively the experimental data on ballistic propagation of the vibrational energy in linear chains of CH{sub 2} fragments and predicts the possibility of a nondissipative energy transfer between reaction centers associated with such chains.
Craven, Galen T; Popov, Alexander V; Hernandez, Rigoberto
2015-04-21
The dynamical properties of a system of soft rods governed by stochastic hard collisions (SHCs) have been determined over a varying range of softness using molecular dynamics simulations in one dimension and analytic theory. The SHC model allows for interpenetration of the system's constituent particles in the simulations, generating overlapping clustering behavior analogous to the spatial structures observed in systems governed by deterministic bounded potentials. Through variation of an assigned softness parameter δ, the limiting ranges of intermolecular softness are bridged, connecting the limiting ensemble behavior from hard to ideal (completely soft). Various dynamical and structural observables are measured from simulation and compared to developed theoretical values. The spatial properties are found to be well predicted by theories developed for the deterministic penetrable-sphere model with a transformation from energetic to probabilistic arguments. While the overlapping spatial structures are complex, the dynamical properties can be adequately approximated through a theory built on impulsive interactions with Enskog corrections. Our theory suggests that as the softness of interaction is varied toward the ideal limit, correlated collision processes are less important to the energy transfer mechanism, and Markovian processes dominate the evolution of the configuration space ensemble. For interaction softness close to hard limit, collision processes are highly correlated and overlapping spatial configurations give rise to entanglement of single-particle trajectories. PMID:25903909
Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties
Craven, Galen T.; Popov, Alexander V.; Hernandez, Rigoberto
2015-04-21
The dynamical properties of a system of soft rods governed by stochastic hard collisions (SHCs) have been determined over a varying range of softness using molecular dynamics simulations in one dimension and analytic theory. The SHC model allows for interpenetration of the system’s constituent particles in the simulations, generating overlapping clustering behavior analogous to the spatial structures observed in systems governed by deterministic bounded potentials. Through variation of an assigned softness parameter δ, the limiting ranges of intermolecular softness are bridged, connecting the limiting ensemble behavior from hard to ideal (completely soft). Various dynamical and structural observables are measured from simulation and compared to developed theoretical values. The spatial properties are found to be well predicted by theories developed for the deterministic penetrable-sphere model with a transformation from energetic to probabilistic arguments. While the overlapping spatial structures are complex, the dynamical properties can be adequately approximated through a theory built on impulsive interactions with Enskog corrections. Our theory suggests that as the softness of interaction is varied toward the ideal limit, correlated collision processes are less important to the energy transfer mechanism, and Markovian processes dominate the evolution of the configuration space ensemble. For interaction softness close to hard limit, collision processes are highly correlated and overlapping spatial configurations give rise to entanglement of single-particle trajectories.
NASA Astrophysics Data System (ADS)
Guiaş, Flavius
2009-01-01
We present a stochastic approach for the simulation of coagulation-diffusion dynamics in the gelation regime. The method couples the mass flow algorithm for coagulation processes with a stochastic variant of the diffusion-velocity method in a discretized framework. The simulation of the stochastic processes occurs according to an optimized implementation of the principle of grouping the possible events. A full simulation of a particle system driven by coagulation-diffusion dynamics is performed with a high degree of accuracy. This allows a qualitative and quantitative analysis of the behaviour of the system. The performance of the method becomes more evident especially in the gelation regime, where the computations become usually very time consuming.
Zunino, L; Soriano, M C; Rosso, O A
2012-10-01
In this paper we introduce a multiscale symbolic information-theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems. More precisely, we show that the multiscale complexity-entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system's dynamics. Numerical simulations obtained from the well-known and widely used Mackey-Glass oscillator operating in a high-dimensional chaotic regime were used as test beds. The effect of an increased amount of observational white noise was carefully examined. The results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles. Finally, several experimental and natural time series were analyzed in order to show the applicability of this scale-dependent symbolic approach in practical situations. PMID:23214666
Stochastically averaged master equation for a quantum-dynamic system interacting with a thermal bath
NASA Astrophysics Data System (ADS)
Petrov, E. G.; Teslenko, V. I.; Goychuk, I. A.
1994-05-01
The methods of nonequilibrium density-matrix and coarse-temporal conception are used to obtain the kinetic equation for the parameters γnm(t)=Sp[ρ^(t)||n>
NASA Astrophysics Data System (ADS)
Murphy, Shane; Scala, Antonio; Lorito, Stefano; Herrero, Andre; Festa, Gaetano; Nielsen, Stefan; Trasatti, Elisa; Tonini, Roberto; Romano, Fabrizio; Molinari, Irene
2016-04-01
Stochastic slip modelling based on general scaling features with uniform slip probability over the fault plane is commonly employed in tsunami and seismic hazard. However, dynamic rupture effects driven by specific fault geometry and frictional conditions can potentially control the slip probability. Unfortunately dynamic simulations can be computationally intensive, preventing their extensive use for hazard analysis. The aim of this study is to produce a computationally efficient stochastic model that incorporates slip features observed in dynamic simulations. Dynamic rupture simulations are performed along a transect representing an average along-depth profile on the Tohoku subduction interface. The surrounding media, effective normal stress and friction law are simplified. Uncertainty in the nucleation location and pre-stress distribution are accounted for by using randomly located nucleation patches and stochastic pre-stress distributions for 500 simulations. The 1D slip distributions are approximated as moment magnitudes on the fault plane based on empirical scaling laws with the ensemble producing a magnitude range of 7.8 - 9.6. To measure the systematic spatial slip variation and its dependence on earthquake magnitude we introduce the concept of the Slip Probability density Function (SPF). We find that while the stochastic SPF is magnitude invariant, the dynamically derived SPF is magnitude-dependent and shows pronounced slip amplification near the surface for M > 8.6 events. To incorporate these dynamic features in the stochastic source models, we sub-divide the dynamically derived SPFs into 0.2 magnitude bins and compare them with the stochastic SPF in order to generate a depth and magnitude dependent transfer function. Applying this function to the traditional stochastic slip distribution allows for an approximated but efficient incorporation of regionally specific dynamic features in a modified source model, to be used specifically when a significant
NASA Astrophysics Data System (ADS)
Jiang, Shixiao W.; Lu, Haihao; Zhou, Douglas; Cai, David
2016-08-01
Characterizing dispersive wave turbulence in the long time dynamics is central to understanding of many natural phenomena, e.g., in atmosphere ocean dynamics, nonlinear optics, and plasma physics. Using the β-Fermi–Pasta–Ulam nonlinear system as a prototypical example, we show that in thermal equilibrium and non-equilibrium steady state the turbulent state even in the strongly nonlinear regime possesses an effective linear stochastic structure in renormalized normal variables. In this framework, we can well characterize the spatiotemporal dynamics, which are dominated by long-wavelength renormalized waves. We further demonstrate that the energy flux is nearly saturated by the long-wavelength renormalized waves in non-equilibrium steady state. The scenario of such effective linear stochastic dynamics can be extended to study turbulent states in other nonlinear wave systems.
Two-state approach to stochastic hair bundle dynamics
NASA Astrophysics Data System (ADS)
Clausznitzer, Diana; Lindner, Benjamin; Jülicher, Frank; Martin, Pascal
2008-04-01
Hair cells perform the mechanoelectrical transduction of sound signals in the auditory and vestibular systems of vertebrates. The part of the hair cell essential for this transduction is the so-called hair bundle. In vitro experiments on hair cells from the sacculus of the American bullfrog have shown that the hair bundle comprises active elements capable of producing periodic deflections like a relaxation oscillator. Recently, a continuous nonlinear stochastic model of the hair bundle motion [Nadrowski , Proc. Natl. Acad. Sci. U.S.A. 101, 12195 (2004)] has been shown to reproduce the experimental data in stochastic simulations faithfully. Here, we demonstrate that a binary filtering of the hair bundle's deflection (experimental data and continuous hair bundle model) does not change significantly the spectral statistics of the spontaneous as well as the periodically driven hair bundle motion. We map the continuous hair bundle model to the FitzHugh-Nagumo model of neural excitability and discuss the bifurcations between different regimes of the system in terms of the latter model. Linearizing the nullclines and assuming perfect time-scale separation between the variables we can map the FitzHugh-Nagumo system to a simple two-state model in which each of the states corresponds to the two possible values of the binary-filtered hair bundle trajectory. For the two-state model, analytical expressions for the power spectrum and the susceptibility can be calculated [Lindner and Schimansky-Geier, Phys. Rev. E 61, 6103 (2000)] and show the same features as seen in the experimental data as well as in simulations of the continuous hair bundle model.
Dynamical inference for transitions in stochastic systems with α-stable Lévy noise
NASA Astrophysics Data System (ADS)
Gao, Ting; Duan, Jinqiao; Kan, Xingye; Cheng, Zhuan
2016-07-01
A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) α -stable Lévy noise. With either discrete time or continuous time observations, we infer such transitions between metastable states by computing the corresponding non-local Zakai equation (and its discrete time counterpart) and examining the most probable orbits for the state system. Examples are presented to demonstrate this approach. This work was partly supported by the NSF Grant 1025422.
Simulation of quantum dynamics based on the quantum stochastic differential equation.
Li, Ming
2013-01-01
The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm. PMID:23781156
de Uña-Álvarez, Jacobo; Meira-Machado, Luís
2015-06-01
Multi-state models are often used for modeling complex event history data. In these models the estimation of the transition probabilities is of particular interest, since they allow for long-term predictions of the process. These quantities have been traditionally estimated by the Aalen-Johansen estimator, which is consistent if the process is Markov. Several non-Markov estimators have been proposed in the recent literature, and their superiority with respect to the Aalen-Johansen estimator has been proved in situations in which the Markov condition is strongly violated. However, the existing estimators have the drawback of requiring that the support of the censoring distribution contains the support of the lifetime distribution, which is not often the case. In this article, we propose two new methods for estimating the transition probabilities in the progressive illness-death model. Some asymptotic results are derived. The proposed estimators are consistent regardless the Markov condition and the referred assumption about the censoring support. We explore the finite sample behavior of the estimators through simulations. The main conclusion of this piece of research is that the proposed estimators are much more efficient than the existing non-Markov estimators in most cases. An application to a clinical trial on colon cancer is included. Extensions to progressive processes beyond the three-state illness-death model are discussed. PMID:25735883
The Stochastic Multi-strain Dengue Model: Analysis of the Dynamics
NASA Astrophysics Data System (ADS)
Aguiar, Maíra; Stollenwerk, Nico; Kooi, Bob W.
2011-09-01
Dengue dynamics is well known to be particularly complex with large fluctuations of disease incidences. An epidemic multi-strain model motivated by dengue fever epidemiology shows deterministic chaos in wide parameter regions. The addition of seasonal forcing, mimicking the vectorial dynamics, and a low import of infected individuals, which is realistic in the dynamics of infectious diseases epidemics show complex dynamics and qualitatively a good agreement between empirical DHF monitoring data and the obtained model simulation. The addition of noise can explain the fluctuations observed in the empirical data and for large enough population size, the stochastic system can be well described by the deterministic skeleton.
Stochastic formation of magnetic vortex structures in asymmetric disks triggered by chaotic dynamics
Im, Mi-Young; Lee, Ki-Suk; Vogel, Andreas; Hong, Jung-Il; Meier, Guido; Fischer, Peter
2014-12-17
The non-trivial spin configuration in a magnetic vortex is a prototype for fundamental studies of nanoscale spin behaviour with potential applications in magnetic information technologies. Arrays of magnetic vortices interfacing with perpendicular thin films have recently been proposed as enabler for skyrmionic structures at room temperature, which has opened exciting perspectives on practical applications of skyrmions. An important milestone for achieving not only such skyrmion materials but also general applications of magnetic vortices is a reliable control of vortex structures. However, controlling magnetic processes is hampered by stochastic behaviour, which is associated with thermal fluctuations in general. Here we showmore » that the dynamics in the initial stages of vortex formation on an ultrafast timescale plays a dominating role for the stochastic behaviour observed at steady state. Our results show that the intrinsic stochastic nature of vortex creation can be controlled by adjusting the interdisk distance in asymmetric disk arrays.« less
Monzel, C.; Schmidt, D.; Kleusch, C.; Kirchenbüchler, D.; Seifert, U.; Smith, A-S; Sengupta, K.; Merkel, R.
2015-01-01
Stochastic displacements or fluctuations of biological membranes are increasingly recognized as an important aspect of many physiological processes, but hitherto their precise quantification in living cells was limited due to a lack of tools to accurately record them. Here we introduce a novel technique—dynamic optical displacement spectroscopy (DODS), to measure stochastic displacements of membranes with unprecedented combined spatiotemporal resolution of 20 nm and 10 μs. The technique was validated by measuring bending fluctuations of model membranes. DODS was then used to explore the fluctuations in human red blood cells, which showed an ATP-induced enhancement of non-Gaussian behaviour. Plasma membrane fluctuations of human macrophages were quantified to this accuracy for the first time. Stimulation with a cytokine enhanced non-Gaussian contributions to these fluctuations. Simplicity of implementation, and high accuracy make DODS a promising tool for comprehensive understanding of stochastic membrane processes. PMID:26437911
Stochastic formation of magnetic vortex structures in asymmetric disks triggered by chaotic dynamics
Im, Mi-Young; Lee, Ki-Suk; Vogel, Andreas; Hong, Jung-Il; Meier, Guido; Fischer, Peter
2014-12-17
The non-trivial spin configuration in a magnetic vortex is a prototype for fundamental studies of nanoscale spin behaviour with potential applications in magnetic information technologies. Arrays of magnetic vortices interfacing with perpendicular thin films have recently been proposed as enabler for skyrmionic structures at room temperature, which has opened exciting perspectives on practical applications of skyrmions. An important milestone for achieving not only such skyrmion materials but also general applications of magnetic vortices is a reliable control of vortex structures. However, controlling magnetic processes is hampered by stochastic behaviour, which is associated with thermal fluctuations in general. Here we show that the dynamics in the initial stages of vortex formation on an ultrafast timescale plays a dominating role for the stochastic behaviour observed at steady state. Our results show that the intrinsic stochastic nature of vortex creation can be controlled by adjusting the interdisk distance in asymmetric disk arrays.
Monzel, C; Schmidt, D; Kleusch, C; Kirchenbüchler, D; Seifert, U; Smith, A-S; Sengupta, K; Merkel, R
2015-01-01
Stochastic displacements or fluctuations of biological membranes are increasingly recognized as an important aspect of many physiological processes, but hitherto their precise quantification in living cells was limited due to a lack of tools to accurately record them. Here we introduce a novel technique--dynamic optical displacement spectroscopy (DODS), to measure stochastic displacements of membranes with unprecedented combined spatiotemporal resolution of 20 nm and 10 μs. The technique was validated by measuring bending fluctuations of model membranes. DODS was then used to explore the fluctuations in human red blood cells, which showed an ATP-induced enhancement of non-Gaussian behaviour. Plasma membrane fluctuations of human macrophages were quantified to this accuracy for the first time. Stimulation with a cytokine enhanced non-Gaussian contributions to these fluctuations. Simplicity of implementation, and high accuracy make DODS a promising tool for comprehensive understanding of stochastic membrane processes. PMID:26437911
NASA Astrophysics Data System (ADS)
Monzel, C.; Schmidt, D.; Kleusch, C.; Kirchenbüchler, D.; Seifert, U.; Smith, A.-S.; Sengupta, K.; Merkel, R.
2015-10-01
Stochastic displacements or fluctuations of biological membranes are increasingly recognized as an important aspect of many physiological processes, but hitherto their precise quantification in living cells was limited due to a lack of tools to accurately record them. Here we introduce a novel technique--dynamic optical displacement spectroscopy (DODS), to measure stochastic displacements of membranes with unprecedented combined spatiotemporal resolution of 20 nm and 10 μs. The technique was validated by measuring bending fluctuations of model membranes. DODS was then used to explore the fluctuations in human red blood cells, which showed an ATP-induced enhancement of non-Gaussian behaviour. Plasma membrane fluctuations of human macrophages were quantified to this accuracy for the first time. Stimulation with a cytokine enhanced non-Gaussian contributions to these fluctuations. Simplicity of implementation, and high accuracy make DODS a promising tool for comprehensive understanding of stochastic membrane processes.
Pools versus Queues: The Variable Dynamics of Stochastic “Steady States”
Lofgren, Eric T.
2015-01-01
Mathematical models in ecology and epidemiology often consider populations “at equilibrium”, where in-flows, such as births, equal out-flows, such as death. For stochastic models, what is meant by equilibrium is less clear – should the population size be fixed or growing and shrinking with equal probability? Two different mechanisms to implement a stochastic steady state are considered. Under these mechanisms, both a predator-prey model and an epidemic model have vastly different outcomes, including the median population values for both predators and prey and the median levels of infection within a hospital (P < 0.001 for all comparisons). These results suggest that the question of how a stochastic steady state is modeled, and what it implies for the dynamics of the system, should be carefully considered. PMID:26090860
Pinning distributed synchronization of stochastic dynamical networks: a mixed optimization approach.
Tang, Yang; Gao, Huijun; Lu, Jianquan; Kurths, Jürgen Kurthsrgen
2014-10-01
This paper is concerned with the problem of pinning synchronization of nonlinear dynamical networks with multiple stochastic disturbances. Two kinds of pinning schemes are considered: 1) pinned nodes are fixed along the time evolution and 2) pinned nodes are switched from time to time according to a set of Bernoulli stochastic variables. Using Lyapunov function methods and stochastic analysis techniques, several easily verifiable criteria are derived for the problem of pinning distributed synchronization. For the case of fixed pinned nodes, a novel mixed optimization method is developed to select the pinned nodes and find feasible solutions, which is composed of a traditional convex optimization method and a constraint optimization evolutionary algorithm. For the case of switching pinning scheme, upper bounds of the convergence rate and the mean control gain are obtained theoretically. Simulation examples are provided to show the advantages of our proposed optimization method over previous ones and verify the effectiveness of the obtained results. PMID:25291734
Cycles, randomness, and transport from chaotic dynamics to stochastic processes
NASA Astrophysics Data System (ADS)
Gaspard, Pierre
2015-09-01
An overview of advances at the frontier between dynamical systems theory and nonequilibrium statistical mechanics is given. Sensitivity to initial conditions is a mechanism at the origin of dynamical randomness—alias temporal disorder—in deterministic dynamical systems. In spatially extended systems, sustaining transport processes, such as diffusion, relationships can be established between the characteristic quantities of dynamical chaos and the transport coefficients, bringing new insight into the second law of thermodynamics. With methods from dynamical systems theory, the microscopic time-reversal symmetry can be shown to be broken at the statistical level of description in nonequilibrium systems. In this way, the thermodynamic entropy production turns out to be related to temporal disorder and its time asymmetry away from equilibrium.
Cycles, randomness, and transport from chaotic dynamics to stochastic processes.
Gaspard, Pierre
2015-09-01
An overview of advances at the frontier between dynamical systems theory and nonequilibrium statistical mechanics is given. Sensitivity to initial conditions is a mechanism at the origin of dynamical randomness-alias temporal disorder-in deterministic dynamical systems. In spatially extended systems, sustaining transport processes, such as diffusion, relationships can be established between the characteristic quantities of dynamical chaos and the transport coefficients, bringing new insight into the second law of thermodynamics. With methods from dynamical systems theory, the microscopic time-reversal symmetry can be shown to be broken at the statistical level of description in nonequilibrium systems. In this way, the thermodynamic entropy production turns out to be related to temporal disorder and its time asymmetry away from equilibrium. PMID:26428559
Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports.
Schilde, M; Doerner, K F; Hartl, R F
2011-12-01
The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15%. Moreover, improvements of up to 41% can be achieved for some test instances. PMID:23543641
Stochasticity in staged models of epidemics: quantifying the dynamics of whooping cough.
Black, Andrew J; McKane, Alan J
2010-08-01
Although many stochastic models can accurately capture the qualitative epidemic patterns of many childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns; much of this stems from the use of deterministic models to try to understand stochastic simulations. We argue that a systematic method of analysing models of the spread of childhood diseases is required in order to consistently separate out the effects of demographic stochasticity, external forcing and modelling choices. Such a technique is provided by formulating the models as master equations and using the van Kampen system-size expansion to provide analytical expressions for quantities of interest. We apply this method to the susceptible-exposed-infected-recovered (SEIR) model with distributed exposed and infectious periods and calculate the form that stochastic oscillations take on in terms of the model parameters. With the use of a suitable approximation, we apply the formalism to analyse a model of whooping cough which includes seasonal forcing. This allows us to more accurately interpret the results of simulations and to make a more quantitative assessment of the predictions of the model. We show that the observed dynamics are a result of a macroscopic limit cycle induced by the external forcing and resonant stochastic oscillations about this cycle. PMID:20164086
Stochasticity in staged models of epidemics: quantifying the dynamics of whooping cough
Black, Andrew J.; McKane, Alan J.
2010-01-01
Although many stochastic models can accurately capture the qualitative epidemic patterns of many childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns; much of this stems from the use of deterministic models to try to understand stochastic simulations. We argue that a systematic method of analysing models of the spread of childhood diseases is required in order to consistently separate out the effects of demographic stochasticity, external forcing and modelling choices. Such a technique is provided by formulating the models as master equations and using the van Kampen system-size expansion to provide analytical expressions for quantities of interest. We apply this method to the susceptible–exposed–infected–recovered (SEIR) model with distributed exposed and infectious periods and calculate the form that stochastic oscillations take on in terms of the model parameters. With the use of a suitable approximation, we apply the formalism to analyse a model of whooping cough which includes seasonal forcing. This allows us to more accurately interpret the results of simulations and to make a more quantitative assessment of the predictions of the model. We show that the observed dynamics are a result of a macroscopic limit cycle induced by the external forcing and resonant stochastic oscillations about this cycle. PMID:20164086
Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems
Venturi, D.; Karniadakis, G. E.
2014-01-01
Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519
Energy-optimal path planning by stochastic dynamically orthogonal level-set optimization
NASA Astrophysics Data System (ADS)
Subramani, Deepak N.; Lermusiaux, Pierre F. J.
2016-04-01
A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. Based on partial differential equations, the methodology rigorously leverages the level-set equation that governs time-optimal reachability fronts for a given relative vehicle-speed function. To set up the energy optimization, the relative vehicle-speed and headings are considered to be stochastic and new stochastic Dynamically Orthogonal (DO) level-set equations are derived. Their solution provides the distribution of time-optimal reachability fronts and corresponding distribution of time-optimal paths. An optimization is then performed on the vehicle's energy-time joint distribution to select the energy-optimal paths for each arrival time, among all stochastic time-optimal paths for that arrival time. Numerical schemes to solve the reduced stochastic DO level-set equations are obtained, and accuracy and efficiency considerations are discussed. These reduced equations are first shown to be efficient at solving the governing stochastic level-sets, in part by comparisons with direct Monte Carlo simulations. To validate the methodology and illustrate its accuracy, comparisons with semi-analytical energy-optimal path solutions are then completed. In particular, we consider the energy-optimal crossing of a canonical steady front and set up its semi-analytical solution using a energy-time nested nonlinear double-optimization scheme. We then showcase the inner workings and nuances of the energy-optimal path planning, considering different mission scenarios. Finally, we study and discuss results of energy-optimal missions in a wind-driven barotropic quasi-geostrophic double-gyre ocean circulation.
Long scale evolution of a nonlinear stochastic dynamic system for modeling market price bubbles
NASA Astrophysics Data System (ADS)
Kiselev, S. A.; Phillips, Andy; Gabitov, I.
2000-07-01
This Letter investigates the stochastic dynamics of a simplified agent-based microscopic model describing stock market evolution. Our mathematical model includes a stochastic market and a sealed-bid double auction. The dynamics of the model are determined by the game of two types of traders: (i) `intelligent' traders whose strategy is based on nonlinear technical data analysis 1 and (ii) `random' traders that act without a consistent strategy. We demonstrate the effect of time-scale separations on the market dynamics. We study the characteristics of the market relaxation in response to perturbations caused by large cash flows generated between these two groups of traders. We also demonstrate that our model exhibits the formation of a price bubble 2 and the subsequent transition to a bear market 3. Bear market - a macroscopically long stage of a market evolution when the stock price declines significantly, 15% or more.
Point group identification algorithm in dynamic response analysis of nonlinear stochastic systems
NASA Astrophysics Data System (ADS)
Li, Tao; Chen, Jian-bing; Li, Jie
2016-03-01
The point group identification (PGI) algorithm is proposed to determine the representative point sets in response analysis of nonlinear stochastic dynamic systems. The PGI algorithm is employed to identify point groups and their feature points in an initial point set by combining subspace clustering analysis and the graph theory. Further, the representative point set of the random-variate space is determined according to the minimum generalized F-discrepancy. The dynamic responses obtained by incorporating the algorithm PGI into the probability density evolution method (PDEM) are compared with those by the Monte Carlo simulation method. The investigations indicate that the proposed method can reduce the number of the representative points, lower the generalized F-discrepancy of the representative point set, and also ensure the accuracy of stochastic structural dynamic analysis.
Stochastic collective dynamics of charged-particle beams in the stability regime.
Petroni, N C; De Martino, S; De Siena, S; Illuminati, F
2001-01-01
We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time-reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by lambda(c)sqrt[N], where N is the number of particles in the beam and lambda(c) the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schrödinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so-called "quantum-like approaches" to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam-field interaction, both the focusing and the transverse oscillations of the beam, either together or independently. PMID:11304370
Stochastic Wilson-Cowan models of neuronal network dynamics with memory and delay
NASA Astrophysics Data System (ADS)
Goychuk, Igor; Goychuk, Andriy
2015-04-01
We consider a simple Markovian class of the stochastic Wilson-Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory, which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory and inhibitory neurons. Such avalanches emerge due to the network size dependent noise (mesoscopic noise). Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around -1.16. We show that this power law is robust upon a variation of the refractory time over several orders of magnitude. However, the avalanche time distribution is biexponential. It does not reflect any genuine power law dependence.
Computing the optimal path in stochastic dynamical systems.
Bauver, Martha; Forgoston, Eric; Billings, Lora
2016-08-01
In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces. PMID:27586597
Computing the optimal path in stochastic dynamical systems
NASA Astrophysics Data System (ADS)
Bauver, Martha; Forgoston, Eric; Billings, Lora
2016-08-01
In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.
Scaling dynamics of deep orbits in a periodic stochastic web
NASA Astrophysics Data System (ADS)
Lowenstein, J. H.
1991-04-01
In a fourfold-symmetric stochastic web generated by a two-dimensional area-preserving map, those phase-space orbits that remain forever in the central part of the chaotic channels are selected by a suitable cutoff condition. By means of a horseshoe construction, these deep orbits are classified according to (i) their paths on the square lattice of hyperbolic fixed points, (ii) their transit times between successive lattice sites, and (iii) their horseshoe branch (left or ) at each lattice site. The set of initial conditions for the deep orbits can be placed on a tree that branches with infinite multiplicity at each level: level N of the tree corresponds to paths of N+1 steps on the lattice. Empirically, one finds two scaling relations, one for the level number and the other for the number of map iterations between successive saddle points. Using a transfer-matrix technique, the scaling relations are exploited to calculate the multifractal properties [Hausdorff dimension, Hausdorff measure, the f(α) curve] of the set of deep orbits, to obtain an invariant probability measure and to derive a Green function for the diffusion process on the lattice. Numerical calculations of many of these quantities are carried out for the value 0.5 of the control parameter.
Stochastic lattice gas model describing the dynamics of the SIRS epidemic process
NASA Astrophysics Data System (ADS)
de Souza, David R.; Tomé, Tânia
2010-03-01
We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S → I → R → S (SIRS). The open process S → I → R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations.
Stochastic dynamic causal modelling of fMRI data: Should we care about neural noise?
Daunizeau, J.; Stephan, K.E.; Friston, K.J.
2012-01-01
Dynamic causal modelling (DCM) was introduced to study the effective connectivity among brain regions using neuroimaging data. Until recently, DCM relied on deterministic models of distributed neuronal responses to external perturbation (e.g., sensory stimulation or task demands). However, accounting for stochastic fluctuations in neuronal activity and their interaction with task-specific processes may be of particular importance for studying state-dependent interactions. Furthermore, allowing for random neuronal fluctuations may render DCM more robust to model misspecification and finesse problems with network identification. In this article, we examine stochastic dynamic causal models (sDCM) in relation to their deterministic counterparts (dDCM) and highlight questions that can only be addressed with sDCM. We also compare the network identification performance of deterministic and stochastic DCM, using Monte Carlo simulations and an empirical case study of absence epilepsy. For example, our results demonstrate that stochastic DCM can exploit the modelling of neural noise to discriminate between direct and mediated connections. We conclude with a discussion of the added value and limitations of sDCM, in relation to its deterministic homologue. PMID:22579726
Jenny, Patrick Torrilhon, Manuel; Heinz, Stefan
2010-02-20
In this paper, a stochastic model is presented to simulate the flow of gases, which are not in thermodynamic equilibrium, like in rarefied or micro situations. For the interaction of a particle with others, statistical moments of the local ensemble have to be evaluated, but unlike in molecular dynamics simulations or DSMC, no collisions between computational particles are considered. In addition, a novel integration technique allows for time steps independent of the stochastic time scale. The stochastic model represents a Fokker-Planck equation in the kinetic description, which can be viewed as an approximation to the Boltzmann equation. This allows for a rigorous investigation of the relation between the new model and classical fluid and kinetic equations. The fluid dynamic equations of Navier-Stokes and Fourier are fully recovered for small relaxation times, while for larger values the new model extents into the kinetic regime. Numerical studies demonstrate that the stochastic model is consistent with Navier-Stokes in that limit, but also that the results become significantly different, if the conditions for equilibrium are invalid. The application to the Knudsen paradox demonstrates the correctness and relevance of this development, and comparisons with existing kinetic equations and standard solution algorithms reveal its advantages. Moreover, results of a test case with geometrically complex boundaries are presented.
Buesing, Lars; Bill, Johannes; Nessler, Bernhard; Maass, Wolfgang
2011-01-01
The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons. PMID:22096452
NASA Technical Reports Server (NTRS)
Lau, K.-M.
1985-01-01
The rudiments of a stochastic-dynamical model for climatic systems with multiple equilibrium states are presented as a means for analyzing the long-term variability of the El Nino/Southern Oscillation (ENSO) events. It is shown that a combination of the unstable air-sea interaction, the seasonal cycle, and stochastic intraseasonal forcings must be considered in any model for ENSO. In particular, the instability in the air-sea interaction may be triggered by stochastic forcing. The possibility that stochastic events initiate the conditions leading to ENSO exacerbates the already difficult task of predicting ENSO patterns.
Fixation, transient landscape, and diffusion dilemma in stochastic evolutionary game dynamics
NASA Astrophysics Data System (ADS)
Zhou, Da; Qian, Hong
2011-09-01
Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical “device” that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.
Torque correlation length and stochastic twist dynamics of DNA.
Banigan, Edward J; Marko, John F
2014-06-01
We introduce a short correlation length for torque in twisting-stiff biomolecules, which is necessary for the physical property that torque fluctuations be finite in amplitude. We develop a nonequilibrium theory of dynamics of DNA twisting which predicts two crossover time scales for temporal torque correlations in single-molecule experiments. Bending fluctuations can be included, and at linear order we find that they do not affect the twist dynamics. However, twist fluctuations affect bending, and we predict the spatial inhomogeneity of twist, torque, and buckling arising in nonequilibrium "rotor-bead" experiments. PMID:25019813
Hermitian non-Markovian stochastic master equations for quantum dissipative dynamics
NASA Astrophysics Data System (ADS)
Yan, Yun-An; Zhou, Yun
2015-08-01
It remains a challenge for theory to simulate nonperturbative and non-Markovian quantum dissipative dynamics at low temperatures. In this study we suggest a Hermitian non-Markovian stochastic master equation suitable for dissipative dynamics at arbitrary temperatures. The memory effect of the bath is embedded within two real correlated Gaussian noises. This scheme is numerically verified by the hierarchical equation of motion and symmetry preserving for a symmetric two-level system. An exemplary application is carried out for the dynamics over a broad range of temperatures to investigate the temperature dependence of the Rabi frequency shift and the non-Markovianity.
Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes.
Kumar, Ashutosh; Chatterjee, Sambarta; Nandi, Mintu; Dua, Arti
2016-08-28
Dynamic co-operativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic co-operativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative co-operativity. For fewer enzymes, dynamic co-operativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic co-operativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the single-pathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour. PMID:27586952
Stochastic dynamics of coupled active particles in an overdamped limit
NASA Astrophysics Data System (ADS)
Ann, Minjung; Lee, Kong-Ju-Bock; Park, Pyeong Jun
2015-10-01
We introduce a model for Brownian dynamics of coupled active particles in an overdamped limit. Our system consists of several identical active particles and one passive particle. Each active particle is elastically coupled to the passive particle and there is no direct coupling among the active particles. We investigate the dynamics of the system with respect to the number of active particles, viscous friction, and coupling between the active and passive particles. For this purpose, we consider an intracellular transport process as an application of our model and perform a Brownian dynamics simulation using realistic parameters for processive molecular motors such as kinesin-1. We determine an adequate energy conversion function for molecular motors and study the dynamics of intracellular transport by multiple motors. The results show that the average velocity of the coupled system is not affected by the number of active motors and that the stall force increases linearly as the number of motors increases. Our results are consistent with well-known experimental observations. We also examine the effects of coupling between the motors and the cargo, as well as of the spatial distribution of the motors around the cargo. Our model might provide a physical explanation of the cooperation among active motors in the cellular transport processes.
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
Ueckermann, M.P.; Lermusiaux, P.F.J.; Sapsis, T.P.
2013-01-15
The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.
Kalyuzhny, Michael; Kadmon, Ronen; Shnerb, Nadav M
2015-06-01
Understanding the forces shaping ecological communities is crucial to basic science and conservation. Neutral theory has made considerable progress in explaining static properties of communities, like species abundance distributions (SADs), with a simple and generic model, but was criticised for making unrealistic predictions of fundamental dynamic patterns and for being sensitive to interspecific differences in fitness. Here, we show that a generalised neutral theory incorporating environmental stochasticity may resolve these limitations. We apply the theory to real data (the tropical forest of Barro Colorado Island) and demonstrate that it much better explains the properties of short-term population fluctuations and the decay of compositional similarity with time, while retaining the ability to explain SADs. Furthermore, the predictions are considerably more robust to interspecific fitness differences. Our results suggest that this integration of niches and stochasticity may serve as a minimalistic framework explaining fundamental static and dynamic characteristics of ecological communities. PMID:25903067
Analysis of some large-scale nonlinear stochastic dynamic systems with subspace-EPC method
NASA Astrophysics Data System (ADS)
Er, GuoKang; Iu, VaiPan
2011-09-01
The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-EPC) method. The space of the state variables of the large-scale nonlinear stochastic dynamic system excited by Gaussian white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system are then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in the other subspace is formulated. Therefore, the FPK equations in low dimensions are obtained from the original FPK equation in high dimensions and the FPK equations in low dimensions are solvable with the exponential polynomial closure method. Examples about multi-degree-offreedom NSD systems with various polynomial types of nonlinearities in displacements are given to show the effectiveness of the subspace-EPC method in these cases.
On the Role of Stochastic Channel Behavior in Intracellular Ca2+ Dynamics
Falcke, Martin
2003-01-01
I present a stochastic model for intracellular Ca2+ oscillations. The model starts from stochastic binding and dissociation of Ca2+ to binding sites on a single subunit of the IP3-receptor channel but is capable of simulating large numbers of clusters for many oscillation periods too. I find oscillations with variable periods ranging from 17 s to 120 s and a standard deviation well in the experimentally observed range. Long period oscillations can be perceived as nucleation phenomenon and can be observed for a large variety of single channel dynamics. Their period depends on the geometric characteristics of the cluster array. Short periods are in the range of the time scale of channel dynamics. Both long and short period oscillations occur for parameters with a nonoscillatory deterministic regime. PMID:12524264
Ultrafast dynamics of finite Hubbard clusters: A stochastic mean-field approach
NASA Astrophysics Data System (ADS)
Lacroix, Denis; Hermanns, S.; Hinz, C. M.; Bonitz, M.
2014-09-01
Finite lattice models are a prototype for interacting quantum systems and capture essential properties of condensed matter systems. With the dramatic progress in ultracold atoms in optical lattices, finite fermionic Hubbard systems have become directly accessible in experiments, including their ultrafast dynamics far from equilibrium. Here, we present a theoretical approach that is able to treat these dynamics in any dimension and fully includes inhomogeneity effects. The method consists in stochastic sampling of mean-field trajectories and is—for not too large two-body interaction strength—found to be much more accurate than time-dependent mean-field at the same order of numerical costs. Furthermore, it can well compete with recent nonequilibrium Green function approaches using second-order Born approximation, which are of substantially larger complexity. The performance of the stochastic mean-field approach is demonstrated for Hubbard clusters with up to 512 particles in one, two, and three dimensions.
Non-equilibrium dynamics of stochastic gene regulation.
Ghosh, Anandamohan
2015-01-01
The process of gene regulation is comprised of intrinsically random events resulting in large cell-to-cell variability in mRNA and protein numbers. With gene expression being the central dogma of molecular biology, it is essential to understand the origin and role of these fluctuations. An intriguing observation is that the number of mRNA present in a cell are not only random and small but also that they are produced in bursts. The gene switches between an active and an inactive state, and the active gene transcribes mRNA in bursts. Transcriptional noise being bursty, so are the number of proteins and the subsequent gene expression levels. It is natural to ask the question: what is the reason for the bursty mRNA dynamics? And can the bursty dynamics be shown to be entropically favorable by studying the reaction kinetics underlying the gene regulation mechanism? The dynamics being an out-of-equilibrium process, the fluctuation theorem for entropy production in the reversible reaction channel is discussed. We compute the entropy production rate for varying degrees of burstiness. We find that the reaction parameters that maximize the burstiness simultaneously maximize the entropy production rate. PMID:25288134
APPLICATION OF DYNAMIC STOCHASTIC MACROECONOMIC MODEL FOR LONG-TERM DISASTER PREVENTION PLANNING
NASA Astrophysics Data System (ADS)
Segi, Shunsuke; Ishikura, Tomoki; Yokomatsu, Muneta
This paper builds a dynamic stochastic macroeconomic model which deals with investment to disaster prevention infrastructure stock. The nature of disaster such as uncertainty, magnitude of damage and long run effects of damage are explicitly modeled. The model can derive optimal policy with regard to investment to productive capital stock and disaster prevention infrastructure stock. Furthermore, the numerical simulations give some interesting implications about the relationship between optimal investment policy, magnitude of disaster, level of economic development and disaster prevention technology.
NASA Astrophysics Data System (ADS)
Zhang, Ning; Zhang, Hui-Min; Liu, Zhi-Qiang; Ding, Xue-Li; Yang, Ming-Hao; Gu, Hua-Guang; Ren, Wei
2009-11-01
Dissolved cardiac myocytes can couple together and generate synchronous beatings in culture. We observed a synchronized early after-depolarization(EAD)-like rhythm in cultured cardiac myocytes and reproduced the experimental observation in a network mathematical model whose dynamics are close to a Hopf bifurcation. The mechanism for this EAD-like rhythm is attributed to noised-induced stochastic alternatings between the focus and the limit cycle. These results provide novel understandings for pathological heart rhythms like the early immature beatings.
NASA Astrophysics Data System (ADS)
Shi, Jingtao
2014-04-01
This paper is concerned with the relationship between maximum principle and dynamic programming for zero-sum stochastic differential games of jump diffusions. Under the assumption that the value function is smooth enough, relations among the adjoint processes, the generalised Hamiltonian function and the value function are given. A portfolio optimisation problem under model uncertainty in an incomplete financial market is discussed to show the applications of our result.
Ecohydrology of groundwater-dependent ecosystems: 2. Stochastic soil moisture dynamics
NASA Astrophysics Data System (ADS)
Tamea, Stefania; Laio, Francesco; Ridolfi, Luca; D'Odorico, Paolo; Rodriguez-Iturbe, Ignacio
2009-05-01
In groundwater-dependent ecosystems, interactions between rainfall, water table fluctuations, and vegetation are exerted through the soil water content. The dynamics of soil moisture, in fact, are strongly coupled to fluctuations of the water table and, together, they control the overall ecosystem dynamics. We propose here a simple process-based stochastic model for the study of soil moisture dynamics at a generic depth, to complement the stochastic model of water table depth presented in the companion paper. The model presented here is based on a local and depth-dependent water balance driven by stochastic rainfall (marked Poisson noise) and accounting for processes such as rainfall infiltration, root water uptake, and capillary rise. We obtain a semianalytical formulation of the stationary probability distribution of soil water content at different depths, which is studied for different values of soil, climate, and vegetation parameters. The probability distributions are used to investigate the ecohydrology of groundwater-dependent ecosystems, including the quantitative description of the vegetation-water table-soil moisture interplay and the probabilistic analysis of root water uptake.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models
Daunizeau, J.; Friston, K.J.; Kiebel, S.J.
2009-01-01
In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power. PMID:19862351
NASA Astrophysics Data System (ADS)
Sutrisno; Widowati; Solikhin
2016-06-01
In this paper, we propose a mathematical model in stochastic dynamic optimization form to determine the optimal strategy for an integrated single product inventory control problem and supplier selection problem where the demand and purchasing cost parameters are random. For each time period, by using the proposed model, we decide the optimal supplier and calculate the optimal product volume purchased from the optimal supplier so that the inventory level will be located at some point as close as possible to the reference point with minimal cost. We use stochastic dynamic programming to solve this problem and give several numerical experiments to evaluate the model. From the results, for each time period, the proposed model was generated the optimal supplier and the inventory level was tracked the reference point well.
Host–parasitoid spatial models: the interplay of demographic stochasticity and dynamics
Wilson, H. B.; Hassell, M. P.
1997-01-01
Host–parasitoid metapopulation models have typically been deterministic models formulated with population numbers as a continuous variable. Spatial heterogeneity in local population abundance is a typical (and often essential) feature of these models and means that, even when average population density is high, some patches have small population sizes. In addition, large temporal population fluctuations are characteristic of many of these models, and this also results in periodically small local population sizes. Whenever population abundances are small, demographic stochasticity can become important in several ways. To investigate this problem, we have reformulated a deterministic, host–parasitoid metapopulation as an integer-based model in which encounters between hosts and parasitoids, and the fecundity of individuals are modelled as stochastic processes. This has a number of important consequences: (1) stochastic fluctuations at small population sizes tend to be amplified by the dynamics to cause massive population variability, i.e. the demographic stochasticity has a destabilizing effect; (2) the spatial patterns of local abundance observed in the deterministic counterpart are largely maintained (although the area of 'spatial chaos' is extended); (3) at small population sizes, dispersal by discrete individuals leads to a smaller fraction of new patches being colonized, so that parasitoids with small dispersal rates have a greater tendency for extinction and higher dispersal rates have a larger competitive advantage; and (4) competing parasitoids that could coexist in the deterministic model due to spatial segregation cannot now coexist for any combination of parameters.
Perthame, Benoît; Gauduchon, Mathias
2010-09-01
Deterministic population models for adaptive dynamics are derived mathematically from individual-centred stochastic models in the limit of large populations. However, it is common that numerical simulations of both models fit poorly and give rather different behaviours in terms of evolution speeds and branching patterns. Stochastic simulations involve extinction phenomenon operating through demographic stochasticity, when the number of individual 'units' is small. Focusing on the class of integro-differential adaptive models, we include a similar notion in the deterministic formulations, a survival threshold, which allows phenotypical traits in the population to vanish when represented by few 'individuals'. Based on numerical simulations, we show that the survival threshold changes drastically the solution; (i) the evolution speed is much slower, (ii) the branching patterns are reduced continuously and (iii) these patterns are comparable to those obtained with stochastic simulations. The rescaled models can also be analysed theoretically. One can recover the concentration phenomena on well-separated Dirac masses through the constrained Hamilton-Jacobi equation in the limit of small mutations and large observation times. PMID:19734200
Modeling dynamics of HIV infected cells using stochastic cellular automaton
NASA Astrophysics Data System (ADS)
Precharattana, Monamorn; Triampo, Wannapong
2014-08-01
Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. Several cellular automata (CA) models have been introduced to gain insights into the dynamics of the disease progression but none of them has taken into account effects of certain immune cells such as the dendritic cells (DCs) and the CD8+ T lymphocytes (CD8+ T cells). In this work, we present a CA model, which incorporates effects of the HIV specific immune response focusing on the cell-mediated immunities, and investigate the interaction between the host immune response and the HIV infected cells in the lymph nodes. The aim of our work is to propose a model more realistic than the one in Precharattana et al. (2010) [10], by incorporating roles of the DCs, the CD4+ T cells, and the CD8+ T cells into the model so that it would reproduce the HIV infection dynamics during the primary phase of HIV infection.
Stochastic dynamics of a warmer Great Barrier Reef.
Cooper, Jennifer K; Spencer, Matthew; Bruno, John F
2015-07-01
Pressure on natural communities from human activities continues to increase. Even unique ecosystems like the Great Barrier Reef (GBR), that until recently were considered near-pristine and well-protected, are showing signs of rapid degradation. We collated recent (1996-2006) spatiotemporal relationships between benthic community composition on the GBR and environmental variables (ocean temperature and local threats resulting from human activity). We built multivariate models of the effects of these variables on short-term dynamics, and developed an analytical approach to study their long-term consequences. We used this approach to study the effects of ocean warming under different levels of local threat. Observed short-term changes in benthic community structure (e.g., declining coral cover) were associated with ocean temperature (warming) and local threats. Our model projected that, in the long-term, coral cover of less than 10% was not implausible. With increasing temperature and/or local threats, corals were initially replaced by sponges, gorgonians, and other taxa, with an eventual moderately high probability of domination (> 50%) by macroalgae when temperature increase was greatest (e.g., 3.5 degrees C of warming). Our approach to modeling community dynamics, based on multivariate statistical models, enabled us to project how environmental change (and thus local and international policy decisions) will influence the future state of coral reefs. The same approach could be applied to other systems for which time series of ecological and environmental variables are available. PMID:26378303
Phase space theory of quantum–classical systems with nonlinear and stochastic dynamics
Burić, Nikola Popović, Duška B.; Radonjić, Milan; Prvanović, Slobodan
2014-04-15
A novel theory of hybrid quantum–classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum–classical phase space. Both, the quantum and classical descriptions of the respective parts of the hybrid system are treated as fundamental. Therefore, the description of the quantum–classical interaction has to be postulated, and includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement. -- Highlights: •A novel theory of quantum–classical systems is developed. •Framework of quantum constrained dynamical systems is used. •A dynamical description of the measurement induced collapse is obtained.
GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: Dynamics and stochastic simulations
NASA Astrophysics Data System (ADS)
Antoine, Xavier; Duboscq, Romain
2015-08-01
GPELab is a free Matlab toolbox for modeling and numerically solving large classes of systems of Gross-Pitaevskii equations that arise in the physics of Bose-Einstein condensates. The aim of this second paper, which follows (Antoine and Duboscq, 2014), is to first present the various pseudospectral schemes available in GPELab for computing the deterministic and stochastic nonlinear dynamics of Gross-Pitaevskii equations (Antoine, et al., 2013). Next, the corresponding GPELab functions are explained in detail. Finally, some numerical examples are provided to show how the code works for the complex dynamics of BEC problems.
An Approach for Dynamic Optimization of Prevention Program Implementation in Stochastic Environments
NASA Astrophysics Data System (ADS)
Kang, Yuncheol; Prabhu, Vittal
The science of preventing youth problems has significantly advanced in developing evidence-based prevention program (EBP) by using randomized clinical trials. Effective EBP can reduce delinquency, aggression, violence, bullying and substance abuse among youth. Unfortunately the outcomes of EBP implemented in natural settings usually tend to be lower than in clinical trials, which has motivated the need to study EBP implementations. In this paper we propose to model EBP implementations in natural settings as stochastic dynamic processes. Specifically, we propose Markov Decision Process (MDP) for modeling and dynamic optimization of such EBP implementations. We illustrate these concepts using simple numerical examples and discuss potential challenges in using such approaches in practice.
Solan, Eilon; Vieille, Nicolas
2015-01-01
In 1953, Lloyd Shapley contributed his paper “Stochastic games” to PNAS. In this paper, he defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that it admits a stationary equilibrium. In this Perspective, we summarize the historical context and the impact of Shapley’s contribution. PMID:26556883
Dynamic modeling of tourism by stochastic method: a case of the Beijing-Tianjin-Hebei region
NASA Astrophysics Data System (ADS)
Dai, Juan; Zhang, Shihui; Xue, Chongsheng
2009-10-01
As an efficient way to stimulate the growth of economy, tourism is promoted by most counties allover the world, and has become one of the world's largest and fastest-growing industries. Essentially, tourism is a spatiotemporal system, with tourist attractions located in different geographic areas and tourist flows exchanging between different geographic regions. In this paper, we present a dynamic model for the simulation of tourism and tourist's activities in the context of GIS and stochastic method, using a case of the Beijing-Tianjin-Hebei region. The model is developed on stochastic method and multiple geospatial data sources. In the model, the spatiotemporal behavior of tourist on the Earth's Surface is governed by the evolution rules, which are extracted from the researches on tourist's activities and executed via stochastic method and multiple geospatial data. By means of the model, we simulate the tourism in the Beijing-Tianjin- Hebei region, and find that there is good correspondence between the tourist arrivals calculated with the model and those obtained from the tourism statistics. This shows that the animated dynamic modeling of tourism based on geospatial data can be used as an indicator of the tourism in the realistic world, and is also can be embedded in the GIS applications.
Integrated Stochastic Evaluation of Flood and Vegetation Dynamics in Riverine Landscapes
NASA Astrophysics Data System (ADS)
Miyamoto, H.; Kimura, R.
2014-12-01
Areal expansion of trees on gravel beds and sand bars has been a serious problem for river management in Japan. From the viewpoints of ecological restoration and flood control, it would be necessary to accurately predict the vegetation dynamics for a long period of time. This presentation tries to evaluate both vegetation overgrowth tendency and flood protection safety in an integrated manner for several vegetated channels in Kako River, Japan. The predominant tree species in Kako River are willows and bamboos. The evaluation employs a stochastic process model, which has been developed for statistically evaluating flow and vegetation status in a river course through the Monte Carlo simulation. The model for vegetation dynamics includes the effects of tree growth, mortality by flood impacts, and infant tree invasion. Through the Monte Carlo simulation for several cross sections in Kako River, responses of the vegetated channels are stochastically evaluated in terms of the changes of discharge magnitude and channel geomorphology. The result shows that the river channels with high flood protection priority are extracted from the several channel sections with the corresponding vegetation status. The present investigation suggests that the stochastic analysis could be one of the powerful diagnostic methods for river management.
NASA Astrophysics Data System (ADS)
McKetterick, Thomas John; Giuggioli, Luca
2014-10-01
Delayed dynamics result from finite transmission speeds of a signal in the form of energy, mass, or information. In stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic, oscillatory, and unstable evolution. Despite the vast literature, quantifying this rich behavior is limited by a lack of explicit analytic studies of high-dimensional stochastic delay systems. Here we fill this gap for systems governed by a linear Langevin equation of any number of delays and spatial dimensions with additive Gaussian noise. By exploiting Laplace transforms we are able to derive an exact time-dependent analytic solution of the Langevin equation. By using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables. As an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment. We propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay. We highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and/or in their spatial separation. We also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay.
Zhu, Z. W.; Zhang, W. D. Xu, J.
2014-03-15
The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.
NASA Astrophysics Data System (ADS)
Teodorescu, Razvan
2009-10-01
Systems of oscillators coupled non-linearly (stochastically or not) are ubiquitous in nature and can explain many complex phenomena: coupled Josephson junction arrays, cardiac pacemaker cells, swarms or flocks of insects and birds, etc. They are know to have a non-trivial phase diagram, which includes chaotic, partially synchronized, and fully synchronized phases. A traditional model for this class of problems is the Kuramoto system of oscillators, which has been studied extensively for the last three decades. The model is a canonical example for non-equilibrium, dynamical phase transitions, so little understood in physics. From a stochastic analysis point of view, the transition is described by the large deviations principle, which offers little information on the scaling behavior near the critical point. I will discuss a special case of the model, which allows a rigorous analysis of the critical properties of the model, and reveals a new, anomalous scaling behavior in the vicinity of the critical point.
Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost
Bokanowski, Olivier; Picarelli, Athena; Zidani, Hasnaa
2015-02-15
This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.
Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?
NASA Astrophysics Data System (ADS)
Choustova, Olga
2007-02-01
We apply the mathematical formalism of Bohmian mechanics to describe dynamics of shares. The main distinguishing feature of the financial Bohmian model is the possibility to take into account market psychology by describing expectations of traders by the pilot wave. We also discuss some objections (coming from conventional financial mathematics of stochastic processes) against the deterministic Bohmian model. In particular, the objection that such a model contradicts to the efficient market hypothesis which is the cornerstone of the modern market ideology. Another objection is of pure mathematical nature: it is related to the quadratic variation of price trajectories. One possibility to reply to this critique is to consider the stochastic Bohm-Vigier model, instead of the deterministic one. We do this in the present note.
Dynamics of stochastic predator-prey models with Holling II functional response
NASA Astrophysics Data System (ADS)
Liu, Qun; Zu, Li; Jiang, Daqing
2016-08-01
In this paper, we consider the dynamics of stochastic predator-prey models with Holling II functional response. For the stochastic systems, we firstly establish sufficient conditions for the existence of the globally positive solutions. Then we investigate the asymptotic moment estimations of the positive solutions and study the ultimately bounded in the mean of them. Thirdly, by constructing some suitable Lyapunov functions, we verify that there are unique stationary distributions and they are ergodic. The obtained results show that the systems still retain some stability in the sense of weak stability provided that the intensity of the white noise is relatively small. Finally, some numerical simulations are introduced to illustrate our main results.
Stochastic growth dynamics and composite defects in quenched immiscible binary condensates
NASA Astrophysics Data System (ADS)
Liu, I.-K.; Pattinson, R. W.; Billam, T. P.; Gardiner, S. A.; Cornish, S. L.; Huang, T.-M.; Lin, W.-W.; Gou, S.-C.; Parker, N. G.; Proukakis, N. P.
2016-02-01
We study the sensitivity of coupled condensate formation dynamics on the history of initial stochastic domain formation in the context of instantaneously quenched elongated harmonically trapped immiscible two-component atomic Bose gases. The spontaneous generation of defects in the fastest condensing component, and subsequent coarse-graining dynamics, can lead to a deep oscillating microtrap into which the other component condenses, thereby establishing a long-lived composite defect in the form of a dark-bright solitary wave. We numerically map out diverse key aspects of these competing growth dynamics, focusing on the role of shot-to-shot fluctuations and global parameter changes (initial state choices, quench parameters, and condensate growth rates), with our findings also qualitatively confirmed by realistic finite-duration quenches. We conclude that phase-separated structures observable on experimental time scales are likely to be metastable states whose form is influenced by the stability and dynamics of the spontaneously emerging dark-bright solitary wave.
Miller, David A.; Clark, W.R.; Arnold, S.J.; Bronikowski, A.M.
2011-01-01
Comparative evaluations of population dynamics in species with temporal and spatial variation in life-history traits are rare because they require long-term demographic time series from multiple populations. We present such an analysis using demographic data collected during the interval 1978-1996 for six populations of western terrestrial garter snakes (Thamnophis elegans) from two evolutionarily divergent ecotypes. Three replicate populations from a slow-living ecotype, found in mountain meadows of northeastern California, were characterized by individuals that develop slowly, mature late, reproduce infrequently with small reproductive effort, and live longer than individuals of three populations of a fast-living ecotype found at lakeshore locales. We constructed matrix population models for each of the populations based on 8-13 years of data per population and analyzed both deterministic dynamics based on mean annual vital rates and stochastic dynamics incorporating annual variation in vital rates. (1) Contributions of highly variable vital rates to fitness (??s) were buffered against the negative effects of stochastic variation, and this relationship was consistent with differences between the meadow (M-slow) and lakeshore (L-fast) ecotypes. (2) Annual variation in the proportion of gravid females had the greatest negative effect among all vital rates on ?? s. The magnitude of variation in the proportion of gravid females and its effect on ??s was greater in M-slow than L-fast populations. (3) Variation in the proportion of gravid females, in turn, depended on annual variation in prey availability, and its effect on ??s was 4- 23 times greater in M-slow than L-fast populations. In addition to differences in stochastic dynamics between ecotypes, we also found higher mean mortality rates across all age classes in the L-fast populations. Our results suggest that both deterministic and stochastic selective forces have affected the evolution of divergent life
Stochastic reversal dynamics of two interacting magnetic dipoles: A simple model experiment.
Plihon, Nicolas; Miralles, Sophie; Bourgoin, Mickael; Pinton, Jean-François
2016-07-01
We report an experimental study of the dynamics of two coupled magnetic dipoles. The experiment consists in two coplanar permanent disk magnets separated by a distance d, each allowed to rotate on a fixed parallel axis-each magnet's axis being perpendicular to its dipolar moment vector. A torque of adjustable strength can be externally applied to one of the magnets, the other magnet being free. The driving torque may be time-independent or temporally fluctuating. We study the influence of the parameters of the driving torque on the dynamics of the coupled system, in particular the emergence of dynamical regimes such as stochastic reversals. We report transitions between stationary and stochastic reversal regimes. All the observed features can be understood by a simple mechanical dynamical model. The transition between statistically stationary regimes and reversals is explained introducing an effective potential energy incorporating both the coupling between magnets and the external driving. Relations between this simple experimental model with macroscopic models of magnetic spin coupling, as well as with chaotic reversals of turbulent dynamos, are discussed. PMID:27575140
Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical Networks
Rosenfeld, Simon
2009-01-01
The question of dynamical stability and stochastic behavior of large biochemical networks is discussed. It is argued that stringent conditions of asymptotic stability have very little chance to materialize in a multidimensional system described by the differential equations of chemical kinetics. The reason is that the criteria of asymptotic stability (Routh-Hurwitz, Lyapunov criteria, Feinberg’s Deficiency Zero theorem) would impose the limitations of very high algebraic order on the kinetic rates and stoichiometric coefficients, and there are no natural laws that would guarantee their unconditional validity. Highly nonlinear, dynamically unstable systems, however, are not necessarily doomed to collapse, as a simple Jacobian analysis would suggest. It is possible that their dynamics may assume the form of pseudo-random fluctuations quite similar to a shot noise, and, therefore, their behavior may be described in terms of Langevin and Fokker-Plank equations. We have shown by simulation that the resulting pseudo-stochastic processes obey the heavy-tailed Generalized Pareto Distribution with temporal sequence of pulses forming the set of constituent-specific Poisson processes. Being applied to intracellular dynamics, these properties are naturally associated with burstiness, a well documented phenomenon in the biology of gene expression. PMID:19838330
Stochastic reversal dynamics of two interacting magnetic dipoles: A simple model experiment
NASA Astrophysics Data System (ADS)
Plihon, Nicolas; Miralles, Sophie; Bourgoin, Mickael; Pinton, Jean-François
2016-07-01
We report an experimental study of the dynamics of two coupled magnetic dipoles. The experiment consists in two coplanar permanent disk magnets separated by a distance d , each allowed to rotate on a fixed parallel axis—each magnet's axis being perpendicular to its dipolar moment vector. A torque of adjustable strength can be externally applied to one of the magnets, the other magnet being free. The driving torque may be time-independent or temporally fluctuating. We study the influence of the parameters of the driving torque on the dynamics of the coupled system, in particular the emergence of dynamical regimes such as stochastic reversals. We report transitions between stationary and stochastic reversal regimes. All the observed features can be understood by a simple mechanical dynamical model. The transition between statistically stationary regimes and reversals is explained introducing an effective potential energy incorporating both the coupling between magnets and the external driving. Relations between this simple experimental model with macroscopic models of magnetic spin coupling, as well as with chaotic reversals of turbulent dynamos, are discussed.
Stenseth, N. C.; rnstad, O. N. Bj; Falck, W.; Fromentin, J.-M.; ter, J. Gj s; Gray, J. S.
1999-01-01
Skagerrak populations of Atlantic cod (Gadus morhua L.) have been surveyed at several fixed stations since 1919. These coastal populations consist of local stocks with a low age of maturity and a short life span. We investigated 60 time-series of 0-group juveniles (i.e. young of the year) sampled annually from 1945 to 1994. An age-structured model was developed which incorporates asymmetrical interactions between the juvenile cohorts (0-group and 1-group; i.e. one-year-old juveniles) and stochastic reproduction. The model was expressed in delay coordinates in order to estimate model parameters directly from the time-series and thereby test the model predictions. The autocovariance structure of the time-series was consistent with the delay coordinates model superimposed upon a long-term trend. The model illustrates how both regulatory (density-dependent) and disruptive (stochastic) forces are crucial in shaping the dynamics of the coastal cod populations. The age-structured life cycle acts to resonance the stochasticity inherent in the recruitment process.
Stochastic modeling of aphid population growth with nonlinear, power-law dynamics.
Matis, James H; Kiffe, Thomas R; Matis, Timothy I; Stevenson, Douglass E
2007-08-01
This paper develops a deterministic and a stochastic population size model based on power-law kinetics for the black-margined pecan aphid. The deterministic model in current use incorporates cumulative-size dependency, but its solution is symmetric. The analogous stochastic model incorporates the prolific reproductive capacity of the aphid. These models are generalized in this paper to include a delayed feedback mechanism for aphid death. Whereas the per capita aphid death rate in the current model is proportional to cumulative size, delayed feedback is implemented by assuming that the per capita rate is proportional to some power of cumulative size, leading to so-called power-law dynamics. The solution to the resulting differential equations model is a left-skewed abundance curve. Such skewness is characteristic of observed aphid data, and the generalized model fits data well. The assumed stochastic model is solved using Kolmogrov equations, and differential equations are given for low order cumulants. Moment closure approximations, which are simple to apply, are shown to give accurate predictions of the two endpoints of practical interest, namely (1) a point estimate of peak aphid count and (2) an interval estimate of final cumulative aphid count. The new models should be widely applicable to other aphid species, as they are based on three fundamental properties of aphid population biology. PMID:17306309
a Stochastic CAGE Model for the Orientational Dynamics of Single Molecules in Nematic Phases
NASA Astrophysics Data System (ADS)
Frezzato, Diego; Saielli, Giacomo; Polimeno, Antonino; Nordio, Pier Luigi
A stochastic cage model for the orientational dynamics of a molecule in isotropic and nematic phases of a liquid crystal has been developed, following the methodology introduced in Refs. 1, 2. The model has been parameterized on the basis of statistical data obtained from the analysis of Molecular Dynamics (MD) simulations of a Gay-Berne mesogen and is based on the general assumption of a timescale separation between the fast inertial librational motion inside the instantaneous cage potential and the slow diffusive motion of the cage itself. The model is able to reproduce single molecule time correlation functions both for the angular momentum and the reorientation of the long molecular axis of the molecule. A complete description of the dynamics of a Gay-Berne particle is given with a single set of physical parameters, from a very fast (hundreds of femtoseconds) timescale up to a timescale of nanoseconds.
A stochastic agent-based model of pathogen propagation in dynamic multi-relational social networks
Khan, Bilal; Dombrowski, Kirk; Saad, Mohamed
2015-01-01
We describe a general framework for modeling and stochastic simulation of epidemics in realistic dynamic social networks, which incorporates heterogeneity in the types of individuals, types of interconnecting risk-bearing relationships, and types of pathogens transmitted across them. Dynamism is supported through arrival and departure processes, continuous restructuring of risk relationships, and changes to pathogen infectiousness, as mandated by natural history; dynamism is regulated through constraints on the local agency of individual nodes and their risk behaviors, while simulation trajectories are validated using system-wide metrics. To illustrate its utility, we present a case study that applies the proposed framework towards a simulation of HIV in artificial networks of intravenous drug users (IDUs) modeled using data collected in the Social Factors for HIV Risk survey. PMID:25859056
ANOSPEX: a stochastic, spatially explicit model for studying Anopheles metapopulation dynamics.
Oluwagbemi, Olugbenga O; Fornadel, Christen M; Adebiyi, Ezekiel F; Norris, Douglas E; Rasgon, Jason L
2013-01-01
Anopheles mosquitoes transmit malaria, a major public health problem among many African countries. One of the most effective methods to control malaria is by controlling the Anopheles mosquito vectors that transmit the parasites. Mathematical models have both predictive and explorative utility to investigate the pros and cons of different malaria control strategies. We have developed a C++ based, stochastic spatially explicit model (ANOSPEX; Ano pheles Spatially-Explicit) to simulate Anopheles metapopulation dynamics. The model is biologically rich, parameterized by field data, and driven by field-collected weather data from Macha, Zambia. To preliminarily validate ANOSPEX, simulation results were compared to field mosquito collection data from Macha; simulated and observed dynamics were similar. The ANOSPEX model will be useful in a predictive and exploratory manner to develop, evaluate and implement traditional and novel strategies to control malaria, and for understanding the environmental forces driving Anopheles population dynamics. PMID:23861847
Coron, Camille
2016-01-01
We are interested in the long-time behavior of a diploid population with sexual reproduction and randomly varying population size, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with competition, weak cooperation and Mendelian reproduction. This stochastic process is indexed by a scaling parameter K that goes to infinity, following a large population assumption. When the individual birth and natural death rates are of order K, the sequence of stochastic processes indexed by K converges toward a new slow-fast dynamics with variable population size. We indeed prove the convergence toward 0 of a fast variable giving the deviation of the population from quasi Hardy-Weinberg equilibrium, while the sequence of slow variables giving the respective numbers of occurrences of each allele converges toward a 2-dimensional diffusion process that reaches (0,0) almost surely in finite time. The population size and the proportion of a given allele converge toward a Wright-Fisher diffusion with stochastically varying population size and diploid selection. We insist on differences between haploid and diploid populations due to population size stochastic variability. Using a non trivial change of variables, we study the absorption of this diffusion and its long time behavior conditioned on non-extinction. In particular we prove that this diffusion starting from any non-trivial state and conditioned on not hitting (0,0) admits a unique quasi-stationary distribution. We give numerical approximations of this quasi-stationary behavior in three biologically relevant cases: neutrality, overdominance, and separate niches. PMID:25840519
NASA Astrophysics Data System (ADS)
Dybiec, Bartłomiej; Gudowska-Nowak, Ewa
2009-05-01
A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the existence of timescale separation between the dynamics of the measured observable and the typical timescale of the noise allows external fluctuations to be modeled as temporally uncorrelated and therefore white. However, in many natural phenomena the assumptions concerning the above mentioned properties of 'Gaussianity' and 'whiteness' of the noise can be violated. In this context, in contrast to the spatiotemporal coupling characterizing general forms of non-Markovian or semi-Markovian Lévy walks, so called Lévy flights correspond to the class of Markov processes which can still be interpreted as white, but distributed according to a more general, infinitely divisible, stable and non-Gaussian law. Lévy noise-driven non-equilibrium systems are known to manifest interesting physical properties and have been addressed in various scenarios of physical transport exhibiting a superdiffusive behavior. Here we present a brief overview of our recent investigations aimed at understanding features of stochastic dynamics under the influence of Lévy white noise perturbations. We find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by memoryless, non-Gaussian, heavy-tailed fluctuations with infinite variance.
Popinga, Alex; Vaughan, Tim; Stadler, Tanja; Drummond, Alexei J
2015-02-01
Estimation of epidemiological and population parameters from molecular sequence data has become central to the understanding of infectious disease dynamics. Various models have been proposed to infer details of the dynamics that describe epidemic progression. These include inference approaches derived from Kingman's coalescent theory. Here, we use recently described coalescent theory for epidemic dynamics to develop stochastic and deterministic coalescent susceptible-infected-removed (SIR) tree priors. We implement these in a Bayesian phylogenetic inference framework to permit joint estimation of SIR epidemic parameters and the sample genealogy. We assess the performance of the two coalescent models and also juxtapose results obtained with a recently published birth-death-sampling model for epidemic inference. Comparisons are made by analyzing sets of genealogies simulated under precisely known epidemiological parameters. Additionally, we analyze influenza A (H1N1) sequence data sampled in the Canterbury region of New Zealand and HIV-1 sequence data obtained from known United Kingdom infection clusters. We show that both coalescent SIR models are effective at estimating epidemiological parameters from data with large fundamental reproductive number [Formula: see text] and large population size [Formula: see text]. Furthermore, we find that the stochastic variant generally outperforms its deterministic counterpart in terms of error, bias, and highest posterior density coverage, particularly for smaller [Formula: see text] and [Formula: see text]. However, each of these inference models is shown to have undesirable properties in certain circumstances, especially for epidemic outbreaks with [Formula: see text] close to one or with small effective susceptible populations. PMID:25527289
The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process
NASA Astrophysics Data System (ADS)
Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko
2012-06-01
A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.
Davidchack, Ruslan L.
2010-12-10
We investigate the influence of numerical discretization errors on computed averages in a molecular dynamics simulation of TIP4P liquid water at 300 K coupled to different deterministic (Nose-Hoover and Nose-Poincare) and stochastic (Langevin) thermostats. We propose a couple of simple practical approaches to estimating such errors and taking them into account when computing the averages. We show that it is possible to obtain accurate measurements of various system quantities using step sizes of up to 70% of the stability threshold of the integrator, which for the system of TIP4P liquid water at 300 K corresponds to the step size of about 7 fs.
NASA Astrophysics Data System (ADS)
Warren, Patrick B.
2009-09-01
A recently proposed model for skin cell proliferation [E. Clayton , Nature (London) 446, 185 (2007)] is extended to incorporate mitotic autoregulation, and hence homeostasis as a fixed point of the dynamics. Unlimited cell proliferation in such a model can be viewed as a model for carcinogenesis. One way in which this can arise is homeostatic metastability, in which the cell populations escape from the homeostatic basin of attraction by a large but rare stochastic fluctuation. Such an event can be viewed as the final step in a multistage model of carcinogenesis. Homeostatic metastability offers a possible explanation for the peculiar epidemiology of lung cancer in ex-smokers.
Evolutionary dynamics on stochastic evolving networks for multiple-strategy games
NASA Astrophysics Data System (ADS)
Wu, Bin; Zhou, Da; Wang, Long
2011-10-01
Evolutionary game theory on dynamical networks has received much attention. Most of the work has been focused on 2×2 games such as prisoner's dilemma and snowdrift, with general n×n games seldom addressed. In particular, analytical methods are still lacking. Here we generalize the stochastic linking dynamics proposed by Wu, Zhou, Fu, Luo, Wang, and Traulsen [PLoS ONEBSYMBO1932-620310.1371/journal.pone.0011187 5, e11187 (2010)] to n×n games. We analytically obtain that the fast linking dynamics results in the replicator dynamics with a rescaled payoff matrix. In the rescaled matrix, intuitively, each entry is the product of the original entry and the average duration time of the corresponding link. This result is shown to be robust to a wide class of imitation processes. As applications, we show both analytically and numerically that the biodiversity, modeled as the stability of a zero-sum rock-paper-scissors game, cannot be altered by the fast linking dynamics. In addition, we show that the fast linking dynamics can stabilize tit-for-tat as an evolutionary stable strategy in the repeated prisoner's dilemma game provided the interaction between the identical strategies happens sufficiently often. Our method paves the way for an analytical study of the multiple-strategy coevolutionary dynamics.
NASA Astrophysics Data System (ADS)
Wang, Tingting; Dai, Weidi; Jiao, Pengfei; Wang, Wenjun
2016-05-01
Many real-world data can be represented as dynamic networks which are the evolutionary networks with timestamps. Analyzing dynamic attributes is important to understanding the structures and functions of these complex networks. Especially, studying the influential nodes is significant to exploring and analyzing networks. In this paper, we propose a method to identify influential nodes in dynamic social networks based on identifying such nodes in the temporal communities which make up the dynamic networks. Firstly, we detect the community structures of all the snapshot networks based on the degree-corrected stochastic block model (DCBM). After getting the community structures, we capture the evolution of every community in the dynamic network by the extended Jaccard’s coefficient which is defined to map communities among all the snapshot networks. Then we obtain the initial influential nodes of the dynamic network and aggregate them based on three widely used centrality metrics. Experiments on real-world and synthetic datasets demonstrate that our method can identify influential nodes in dynamic networks accurately, at the same time, we also find some interesting phenomena and conclusions for those that have been validated in complex network or social science.
Contributions to the computational analysis of multi-dimensional stochastic dynamical systems
NASA Astrophysics Data System (ADS)
Wojtkiewicz, Steven F., Jr.
2000-12-01
Several contributions in the area of computational stochastic dynamics are discussed; specifically, the response of stochastic dynamical systems by high order closure, the response of Poisson and Gaussian white noise driven systems by solution of a transformed generalized Kolmogorov equation, and control of nonlinear systems by response moment specification. Statistical moments of response are widely used in the analysis of stochastic dynamical systems of engineering interest. It is known that, if the inputs to the system are Gaussian or filtered Gaussian white noise, Ito's rule can be used to generate a system of first order linear differential equations governing the evolution of the moments. For nonlinear systems, the moment equations form an infinite hierarchy, necessitating the application of a closure procedure to truncate the system at some finite dimension at the expense of making the moment equations nonlinear. Various methods to close these moment equations have been developed. The efficacy of cumulant-neglect closure methods for complex dynamical systems is examined. Various methods have been developed to determine the response of dynamical systems subjected to additive and/or multiplicative Gaussian white noise excitations. While Gaussian white noise and filtered Gaussian white noise provide efficient and useful models of various environmental loadings, a broader class of random processes, filtered Poisson processes, are often more realistic in modeling disturbances that originate from impact-type loadings. The response of dynamical systems to combinations of Poisson and Gaussian white noise forms a Markov process whose transition density satisfies a pair of initial-boundary value problem termed the generalized Kolmogorov equations. A numerical solution algorithm for these IBVP's is developed and applied to several representative systems. Classical covariance control theory is extended to the case of nonlinear systems using the method of statistical
NASA Astrophysics Data System (ADS)
Irving, J. D.; Singha, K.
2010-12-01
Traditionally, hydrological measurements have been used to estimate subsurface properties controlling groundwater flow and contaminant transport. However, such measurements are limited by their support volume and expense. A considerable benefit of geophysical measurements is that they provide a degree of spatial coverage and resolution that are unattainable with other methods, and the data can be acquired in a cost-effective manner. In particular, dynamic geophysical data allow us to indirectly observe changes in hydrological state variables as flow and transport processes occur, and can thus provide a link to hydrological properties when coupled with a process-based model. Stochastic fusion of these two data types offers the potential to provide not only estimates of subsurface hydrological properties, but also a quantification of their uncertainty. This information is critical when considering the end use of the data, which may be for groundwater remediation and management decision making. Here, we examine a number of key issues in the stochastic fusion of dynamic hydrogeophysical data. We focus our attention on the specific problem of integrating time-lapse crosshole electrical resistivity measurements and saline tracer-test concentration data in order to estimate the spatial distribution of hydraulic conductivity (K). To assimilate the geophysical and hydrological measurements in a stochastic manner, we use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology. This provides multiple realizations of the subsurface K field that are consistent with the measured data and assumptions regarding model structure and data errors. To account for incomplete petrophysical knowledge, the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration following the general form of Archie’s law. To make the spatially distributed, fully stochastic inverse problem computationally tractable, we take
Stochastic mean-field formulation of the dynamics of diluted neural networks
NASA Astrophysics Data System (ADS)
Angulo-Garcia, D.; Torcini, A.
2015-02-01
We consider pulse-coupled leaky integrate-and-fire neural networks with randomly distributed synaptic couplings. This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the microscopic level. Our main aim is to mimic the effect of the dilution as a noise source acting on the dynamics of a globally coupled nonchaotic system. Indeed, the evolution of a diluted neural network can be well approximated as a fully pulse-coupled network, where each neuron is driven by a mean synaptic current plus additive noise. These terms represent the average and the fluctuations of the synaptic currents acting on the single neurons in the diluted system. The main microscopic and macroscopic dynamical features can be retrieved with this stochastic approximation. Furthermore, the microscopic stability of the diluted network can be also reproduced, as demonstrated from the almost coincidence of the measured Lyapunov exponents in the deterministic and stochastic cases for an ample range of system sizes. Our results strongly suggest that the fluctuations in the synaptic currents are responsible for the emergence of chaos in this class of pulse-coupled networks.
The role of phase dynamics in a stochastic model of a passively advected scalar
NASA Astrophysics Data System (ADS)
Moradi, Sara; Anderson, Johan
2016-05-01
Collective synchronous motion of the phases is introduced in a model for the stochastic passive advection-diffusion of a scalar with external forcing. The model for the phase coupling dynamics follows the well known Kuramoto model paradigm of limit-cycle oscillators. The natural frequencies in the Kuramoto model are assumed to obey a given scale dependence through a dispersion relation of the drift-wave form -βk/1 +k2 , where β is a constant representing the typical strength of the gradient. The present aim is to study the importance of collective phase dynamics on the characteristic time evolution of the fluctuation energy and the formation of coherent structures. Our results show that the assumption of a fully stochastic phase state of turbulence is more relevant for high values of β, where we find that the energy spectrum follows a k-7 /2 scaling. Whereas for lower β there is a significant difference between a-synchronised and synchronised phase states, one could expect the formation of coherent modulations in the latter case.
NASA Astrophysics Data System (ADS)
Polyakov, Evgeny A.
2016-02-01
The time-dependent fermionic Hartree-Fock equations can be stochastically extended in such a way as to become the exact representation of quantum dynamics. This fact was first observed in the work of Juillet and Chomaz [Phys. Rev. Lett. 88, 142503 (2002), 10.1103/PhysRevLett.88.142503]. During the past decade, this observation has led to the emergence of a whole family of stochastic wave-function methods for fermions. The common feature of all these methods is that they are based on the expansion of the density operator over the dyadic product of the two fermionic Slater determinant states. In this work, we develop a unified and rigorous foundation for this family of methods. We find a general form of stochastic equations and describe the sufficient conditions under which these methods converge towards exact quantum dynamics. To achieve these goals, we employ the representation of quantum dynamics in generalized phase space. In particular, we consider the quasiprobability distributions which emerge in these stochastic methods and their master equations. It is shown that the convergence towards exact quantum dynamics is controlled by the problem of boundary terms. We provide an example of stochastic Hartree-Fock method which is well-defined and free from this problem.
Schilde, M.; Doerner, K.F.; Hartl, R.F.
2014-01-01
In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches. PMID:25844013
Kamimoto, Kenji; Kaneko, Kota; Kok, Cindy Yuet-Yin; Okada, Hajime; Miyajima, Atsushi; Itoh, Tohru
2016-01-01
Dynamic remodeling of the intrahepatic biliary epithelial tissue plays key roles in liver regeneration, yet the cellular basis for this process remains unclear. We took an unbiased approach based on in vivo clonal labeling and tracking of biliary epithelial cells in the three-dimensional landscape, in combination with mathematical simulation, to understand their mode of proliferation in a mouse liver injury model where the nascent biliary structure formed in a tissue-intrinsic manner. An apparent heterogeneity among biliary epithelial cells was observed: whereas most of the responders that entered the cell cycle upon injury exhibited a limited and tapering growth potential, a select population continued to proliferate, making a major contribution in sustaining the biliary expansion. Our study has highlighted a unique mode of epithelial tissue dynamics, which depends not on a hierarchical system driven by fixated stem cells, but rather, on a stochastically maintained progenitor population with persistent proliferative activity. PMID:27431614
A stochastic, local mode study of neon-liquid surface collision dynamics.
Packwood, Daniel M; Phillips, Leon F
2011-01-14
Equations of motion for a fast, light rare gas atom passing over a liquid surface are derived and used to infer the dynamics of neon collisions with squalane and perfluorinated polyether surfaces from experimental data. The equations incorporate the local mode model of a liquid surface via a stochastic process and explicitly account for impulsive collisional energy loss to the surface. The equations predict angular distributions for scattering of neon that are in good quantitative agreement with experimental data. Our key dynamical conclusions are that experimental angular distributions derive mainly from local mode surface topography rather than from structural features of individual surface molecules, and that the available data for these systems can be accounted for almost exclusively by single collisions between neon atoms and the liquid surface. PMID:21042647
Self-organization of traffic jams in cities: Effects of stochastic dynamics and signal periods
NASA Astrophysics Data System (ADS)
Chowdhury, Debashish; Schadschneider, Andreas
1999-02-01
We propose a cellular automata model for vehicular traffic in cities by combining (and appropriately modifying) ideas borrowed from the Biham-Middleton-Levine (BML) model of city traffic and the Nagel-Schreckenberg (NS) model of highway traffic. We demonstrate a phase transition from the ``free-flowing'' dynamical phase to the completely ``jammed'' phase at a vehicle density which depends on the time periods of the synchronized signals and the separation between them. The intrinsic stochasticity of the dynamics, which triggers the onset of jamming, is similar to that in the NS model, while the phenomenon of complete jamming through self-organization as well as the final jammed configurations are similar to those in the BML model. Using our model, we have made an investigation of the time dependence of the average speeds of the cars in the ``free-flowing'' phase as well as the dependence of flux and jamming on the time period of the signals.
Sensitivity of train stochastic dynamics to long-term evolution of track irregularities
NASA Astrophysics Data System (ADS)
Lestoille, N.; Soize, C.; Funfschilling, C.
2016-05-01
The influence of the track geometry on the dynamic response of the train is of great concern for the railway companies, because they have to guarantee the safety of the train passengers in ensuring the stability of the train. In this paper, the long-term evolution of the dynamic response of the train on a stretch of the railway track is studied with respect to the long-term evolution of the track geometry. The characterisation of the long-term evolution of the train response allows the railway companies to start off maintenance operations of the track at the best moment. The study is performed using measurements of the track geometry, which are carried out very regularly by a measuring train. A stochastic model of the studied stretch of track is created in order to take into account the measurement uncertainties in the track geometry. The dynamic response of the train is simulated with a multibody software. A noise is added in output of the simulation to consider the uncertainties in the computational model of the train dynamics. Indicators on the dynamic response of the train are defined, allowing to visualize the long-term evolution of the stability and the comfort of the train, when the track geometry deteriorates.
NASA Astrophysics Data System (ADS)
Er, Guo-Kang
2014-04-01
In this paper, the state-space-split method is extended for the dimension reduction of some high-dimensional Fokker-Planck-Kolmogorov equations or the nonlinear stochastic dynamical systems in high dimensions subject to external excitation which is the filtered Gaussian white noise governed by the second order stochastic differential equation. The selection of sub state variables and then the dimension-reduction procedure for a class of nonlinear stochastic dynamical systems is given when the external excitation is the filtered Gaussian white noise. The stretched Euler-Bernoulli beam with hinge support at two ends, point-spring supports, and excited by uniformly distributed load being filtered Gaussian white noise governed by the second-order stochastic differential equation is analyzed and numerical results are presented. The results obtained with the presented procedure are compared with those obtained with the Monte Carlo simulation and equivalent linearization method to show the effectiveness and advantage of the state-space-split method and exponential polynomial closure method in analyzing the stationary probabilistic solutions of the multi-degree-of-freedom nonlinear stochastic dynamical systems excited by filtered Gaussian white noise.
Water resources planning and management : A stochastic dual dynamic programming approach
NASA Astrophysics Data System (ADS)
Goor, Q.; Pinte, D.; Tilmant, A.
2008-12-01
Allocating water between different users and uses, including the environment, is one of the most challenging task facing water resources managers and has always been at the heart of Integrated Water Resources Management (IWRM). As water scarcity is expected to increase over time, allocation decisions among the different uses will have to be found taking into account the complex interactions between water and the economy. Hydro-economic optimization models can capture those interactions while prescribing efficient allocation policies. Many hydro-economic models found in the literature are formulated as large-scale non linear optimization problems (NLP), seeking to maximize net benefits from the system operation while meeting operational and/or institutional constraints, and describing the main hydrological processes. However, those models rarely incorporate the uncertainty inherent to the availability of water, essentially because of the computational difficulties associated stochastic formulations. The purpose of this presentation is to present a stochastic programming model that can identify economically efficient allocation policies in large-scale multipurpose multireservoir systems. The model is based on stochastic dual dynamic programming (SDDP), an extension of traditional SDP that is not affected by the curse of dimensionality. SDDP identify efficient allocation policies while considering the hydrologic uncertainty. The objective function includes the net benefits from the hydropower and irrigation sectors, as well as penalties for not meeting operational and/or institutional constraints. To be able to implement the efficient decomposition scheme that remove the computational burden, the one-stage SDDP problem has to be a linear program. Recent developments improve the representation of the non-linear and mildly non- convex hydropower function through a convex hull approximation of the true hydropower function. This model is illustrated on a cascade of 14
NASA Astrophysics Data System (ADS)
Karamintziou, Sofia D.; Tsirogiannis, George L.; Stathis, Pantelis G.; Tagaris, George A.; Boviatsis, Efstathios J.; Sakas, Damianos E.; Nikita, Konstantina S.
2014-10-01
Objective. During deep brain stimulation (DBS) surgery for the treatment of advanced Parkinson's disease (PD), microelectrode recording (MER) in conjunction with functional stimulation techniques are commonly applied for accurate electrode implantation. However, the development of automatic methods for clinical decision making has to date been characterized by the absence of a robust single-biomarker approach. Moreover, it has only been restricted to the framework of MER without encompassing intraoperative macrostimulation. Here, we propose an integrated series of novel single-biomarker approaches applicable to the entire electrophysiological procedure by means of a stochastic dynamical model. Approach. The methods are applied to MER data pertinent to ten DBS procedures. Considering the presence of measurement noise, we initially employ a multivariate phase synchronization index for automatic delineation of the functional boundaries of the subthalamic nucleus (STN) and determination of the acceptable MER trajectories. By introducing the index into a nonlinear stochastic model, appropriately fitted to pre-selected MERs, we simulate the neuronal response to periodic stimuli (130 Hz), and examine the Lyapunov exponent as an indirect indicator of the clinical effectiveness yielded by stimulation at the corresponding sites. Main results. Compared with the gold-standard dataset of annotations made intraoperatively by clinical experts, the STN detection methodology demonstrates a false negative rate of 4.8% and a false positive rate of 0%, across all trajectories. Site eligibility for implantation of the DBS electrode, as implicitly determined through the Lyapunov exponent of the proposed stochastic model, displays a sensitivity of 71.43%. Significance. The suggested comprehensive method exhibits remarkable performance in automatically determining both the acceptable MER trajectories and the optimal stimulation sites, thereby having the potential to accelerate precise
Stochastic Calculus and Differential Equations for Physics and Finance
NASA Astrophysics Data System (ADS)
McCauley, Joseph L.
2013-02-01
1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.
Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere
Tang Wenbo; Mahalov, Alex
2013-03-15
We develop a three-dimensional numerical model for the E-F region ionosphere and study the Lagrangian dynamics for plasma flows in this region. Our interest rests on the charge-neutral interactions and the statistics associated with stochastic Lagrangian motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology-the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using Lagrangian measures such as the finite-time Lyapunov exponents, we locate the Lagrangian skeletons for mixing in plasma, hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic Lagrangian motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of non-Gaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.
Stochastic dynamic programming illuminates the link between environment, physiology, and evolution.
Mangel, Marc
2015-05-01
I describe how stochastic dynamic programming (SDP), a method for stochastic optimization that evolved from the work of Hamilton and Jacobi on variational problems, allows us to connect the physiological state of organisms, the environment in which they live, and how evolution by natural selection acts on trade-offs that all organisms face. I first derive the two canonical equations of SDP. These are valuable because although they apply to no system in particular, they share commonalities with many systems (as do frictionless springs). After that, I show how we used SDP in insect behavioral ecology. I describe the puzzles that needed to be solved, the SDP equations we used to solve the puzzles, and the experiments that we used to test the predictions of the models. I then briefly describe two other applications of SDP in biology: first, understanding the developmental pathways followed by steelhead trout in California and second skipped spawning by Norwegian cod. In both cases, modeling and empirical work were closely connected. I close with lessons learned and advice for the young mathematical biologists. PMID:25033778
A Stochastic Fractional Dynamics Model of Space-time Variability of Rain
NASA Technical Reports Server (NTRS)
Kundu, Prasun K.; Travis, James E.
2013-01-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment.
A stochastic fractional dynamics model of space-time variability of rain
NASA Astrophysics Data System (ADS)
Kundu, Prasun K.; Travis, James E.
2013-09-01
varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, which allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.
Effective field theory during inflation. II. Stochastic dynamics and power spectrum suppression
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2016-02-01
We obtain the nonequilibrium effective action of an inflatonlike scalar field—the system—by tracing over sub-Hubble degrees of freedom of "environmental" light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflatonlike field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super-Hubble fluctuations of the inflaton field, P (k ;η )=P0(k )e-γ (k ;η ) where P0(k ) is the nearly scale invariant power spectrum in absence of coupling. γ (k ;η )>0 describes the suppression of the power spectrum; it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action for the case of a heavy scalar field of mass M ≫H ; this case yields a local "Fermi" limit with a very weak self-interaction of the inflatonlike field and dissipative terms that are suppressed by powers of H /M . We conjecture on the possibility that the large scale anomalies in the cosmic microwave background may originate in dissipative processes from inflaton coupling to sub-Hubble degrees of freedom.
Wu, Wei; Wang, Jin
2014-09-14
We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.
Li, Cheng-Wei; Chen, Bor-Sen
2009-01-01
In order to investigate the possible mechanisms for eve stripe formation of Drosophila embryo, a spatio-temporal gene/protein interaction network model is proposed to mimic dynamic behaviors of protein synthesis, protein decay, mRNA decay, protein diffusion, transcription regulations and autoregulation to analyze the interplay of genes and proteins at different compartments in early embryogenesis. In this study, we use the maximum likelihood (ML) method to identify the stochastic 3-D Embryo Space-Time (3-DEST) dynamic model for gene/protein interaction network via 3-D mRNA and protein expression data and then use the Akaike Information Criterion (AIC) to prune the gene/protein interaction network. The identified gene/protein interaction network allows us not only to analyze the dynamic interplay of genes and proteins on the border of eve stripes but also to infer that eve stripes are established and maintained by network motifs built by the cooperation between transcription regulations and diffusion mechanisms in early embryogenesis. Literature reference with the wet experiments of gene mutations provides a clue for validating the identified network. The proposed spatio-temporal dynamic model can be extended to gene/protein network construction of different biological phenotypes, which depend on compartments, e.g. postnatal stem/progenitor cell differentiation. PMID:20054403
NASA Astrophysics Data System (ADS)
Druce, Donald J.
1990-01-01
A monthly stochastic dynamic programing model was recently developed and implemented at British Columbia (B.C.) Hydro to provide decision support for short-term energy exports and, if necessary, for flood control on the Peace River in northern British Columbia. The model establishes the marginal cost of supplying energy from the B.C. Hydro system, as well as a monthly operating policy for the G.M. Shrum and Peace Canyon hydroelectric plants and the Williston Lake storage reservoir. A simulation model capable of following the operating policy then determines the probability of refilling Williston Lake and possible spill rates and volumes. Reservoir inflows are input to both models in daily and monthly formats. The results indicate that flood control can be accommodated without sacrificing significant export revenue.
Salazar-Cavazos, Emanuel; Santillán, Moisés
2014-02-01
In this work, we develop a detailed, stochastic, dynamical model for the tryptophan operon of E. coli, and estimate all of the model parameters from reported experimental data. We further employ the model to study the system performance, considering the amount of biochemical noise in the trp level, the system rise time after a nutritional shift, and the amount of repressor molecules necessary to maintain an adequate level of repression, as indicators of the system performance regime. We demonstrate that the level of cooperativity between repressor molecules bound to the first two operators in the trp promoter affects all of the above enlisted performance characteristics. Moreover, the cooperativity level found in the wild-type bacterial strain optimizes a cost-benefit function involving low biochemical noise in the tryptophan level, short rise time after a nutritional shift, and low number of regulatory molecules. PMID:24307084
Stochastic Dynamical Model of a Growing Citation Network Based on a Self-Exciting Point Process
NASA Astrophysics Data System (ADS)
Golosovsky, Michael; Solomon, Sorin
2012-08-01
We put under experimental scrutiny the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose a citation network of physics papers and traced the citation history of 40 195 papers published in one year. Contrary to common belief, we find that the citation dynamics of the individual papers follows the superlinear preferential attachment, with the exponent α=1.25-1.3. Moreover, we show that the citation process cannot be described as a memoryless Markov chain since there is a substantial correlation between the present and recent citation rates of a paper. Based on our findings we construct a stochastic growth model of the citation network, perform numerical simulations based on this model and achieve an excellent agreement with the measured citation distributions.
NASA Astrophysics Data System (ADS)
Seybold, P. G.; Kier, L. B.; Cheng, C.-K.
1999-12-01
Emissions from the 1S and 1D excited states of atomic oxygen play a prominent role in creating the dramatic light displays (aurora borealis) seen in the skies over polar regions of the Northern Hemisphere. A probabilistic asynchronous cellular automaton model described previously has been applied to the excited-state dynamics of atomic oxygen. The model simulates the time-dependent variations in ground (3P) and excited-state populations that occur under user-defined probabilistic transition rules for both pulse and steady-state conditions. Although each trial simulation is itself an independent "experiment", deterministic values for the excited-state emission lifetimes and quantum yields emerge as limiting cases for large numbers of cells or large numbers of trials. Stochastic variations in the lifetimes and emission yields can be estimated from repeated trials.
NASA Astrophysics Data System (ADS)
Yang, Gang; Tang, Zheng; Dai, Hongwei
Through analyzing the dynamics characteristic of maximum neural network with an added vertex, we find that the solution quality is mainly determined by the added vertex weights. In order to increase maximum neural network ability, a stochastic nonlinear self-feedback and flexible annealing strategy are embedded in maximum neural network, which makes the network more powerful to escape local minima and be independent of the initial values. Simultaneously, we present that solving ability of maximum neural network is dependence on problem. We introduce a new parameter into our network to improve the solving ability. The simulation in k random graph and some DIMACS clique instances in the second DIMACS challenge shows that our improved network is superior to other algorithms in light of the solution quality and CPU time.
Stochastic dynamics of charge fluctuations in dusty plasma: A non-Markovian approach
Asgari, H.; Muniandy, S. V.; Wong, C. S.
2011-08-15
Dust particles in typical laboratory plasma become charged largely by collecting electrons and/or ions. Most of the theoretical studies in dusty plasma assume that the grain charge remains constant even though it fluctuates due to the discrete nature of the charge. The rates of ions and electrons absorption depend on the grain charge, hence its temporal evolution. Stochastic charging model based on the standard Langevin equation assumes that the underlying process is Markovian. In this work, the memory effect in dust charging dynamics is incorporated using fractional calculus formalism. The resulting fractional Langevin equation is solved to obtain the amplitude and correlation function for the dust charge fluctuation. It is shown that the effects of ion-neutral collisions can be interpreted in phenomenological sense through the nonlocal fractional order derivative.
Kaburagi, Takashi; Muramatsu, Daigo; Matsumoto, Takashi
2007-06-01
A novel algorithm is proposed for predicting transmembrane protein secondary structure from two-dimensional vector trajectories consisting of a hydropathy index and formal charge of a test amino acid sequence using stochastic dynamical system models. Two prediction problems are discussed. One is the prediction of transmembrane region counts; another is that of transmembrane regions, i.e. predicting whether or not each amino acid belongs to a transmembrane region. The prediction accuracies, using a collection of well-characterized transmembrane protein sequences and benchmarking sequences, suggest that the proposed algorithm performs reasonably well. An experiment was performed with a glutamate transporter homologue from Pyrococcus horikoshii. The predicted transmembrane regions of the five human glutamate transporter sequences and observations based on the computed likelihood are reported. PMID:17688311
NASA Astrophysics Data System (ADS)
Lin, Yen Ting; Doering, Charles R.
2016-02-01
We present a theoretical framework to analyze the dynamics of gene expression with stochastic bursts. Beginning with an individual-based model which fully accounts for the messenger RNA (mRNA) and protein populations, we propose an expansion of the master equation for the joint process. The resulting coarse-grained model reduces the dimensionality of the system, describing only the protein population while fully accounting for the effects of discrete and fluctuating mRNA population. Closed form expressions for the stationary distribution of the protein population and mean first-passage times of the coarse-grained model are derived and large-scale Monte Carlo simulations show that the analysis accurately describes the individual-based process accounting for mRNA population, in contrast to the failure of commonly proposed diffusion-type models.
Johnston, Iain G.; Jones, Nick S.
2015-01-01
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for treating several important examples of these stochastic processes, most notably gene expression and random partitioning at single-cell divisions or after a steady state has been reached. Comparatively little work exists exploring different and specific ways that repeated cell divisions can lead to stochastic inheritance of unequilibrated cellular populations. Here we introduce a mathematical formalism to describe cellular agents that are subject to random creation, replication and/or degradation, and are inherited according to a range of random dynamics at cell divisions. We obtain closed-form generating functions describing systems at any time after any number of cell divisions for binomial partitioning and divisions provoking a deterministic or random, subtractive or additive change in copy number, and show that these solutions agree exactly with stochastic simulation. We apply this general formalism to several example problems involving the dynamics of mitochondrial DNA during development and organismal lifetimes. PMID:26339194
Well posedness and asymptotic analysis for the stochastic equations of geophysical fluid dynamics
NASA Astrophysics Data System (ADS)
Glatt-Holtz, Nathan Edward
2008-10-01
This work collects three interrelated projects that develop rigorous mathematical tools for the study of the stochastically forced equations of geophysical fluid dynamics and turbulence. Since the presence of persistent random fluctuations are ubiquitous in fluid flow problems, the development of new analytical techniques in this setting are ultimately of paramount practical interest in the pursuit of more accurate models. The first two projects address the question of well posedness. One work considers the Primitive equations of the ocean. These systems are widely used in numerical studies of geophysical scale fluid flow. We consider a two dimensional model forced by multiplicative noise terms. For the case when the initial data and its vertical gradient take values in L2, we prove the global existence and uniqueness of solutions in a fixed probability space. The proof is based on finite dimensional approximations, anisotropic Sobolev estimates, and weak convergence techniques. The work concludes with a sketch of the physical derivation of the governing equations. The second project introduces new results for the stochastic Navier-Stokes system on bounded domains in space dimensions two and three. We establish the local existence and uniqueness of pathwise solutions evolving in H1. For the two dimensional case global existence is established without employing moment estimates at fixed times. The proof relies on a pairwise comparison technique facilitated by decompositions into high and low modes to surmount the critical issue of compactness. In the final chapter we introduce a class of singular perturbation systems in the presence of a small white noise. Modifying the renormalization group procedure developed by Chen, Goldenfeld and Oono, we derive an associated reduced system which we use to construct an approximate solution that separates scales. Rigorous results demonstrating that these approximate solutions remain valid with high probability on large time
Hu, Yan; Wen, Jing-Ya; Li, Xiao-Li; Wang, Da-Zhou; Li, Yu
2013-10-15
A dynamic multimedia fuzzy-stochastic integrated environmental risk assessment approach was developed for contaminated sites management. The contaminant concentrations were simulated by a validated interval dynamic multimedia fugacity model, and different guideline values for the same contaminant were represented as a fuzzy environmental guideline. Then, the probability of violating environmental guideline (Pv) can be determined by comparison between the modeled concentrations and the fuzzy environmental guideline, and the constructed relationship between the Pvs and environmental risk levels was used to assess the environmental risk level. The developed approach was applied to assess the integrated environmental risk at a case study site in China, simulated from 1985 to 2020. Four scenarios were analyzed, including "residential land" and "industrial land" environmental guidelines under "strict" and "loose" strictness. It was found that PAH concentrations will increase steadily over time, with soil found to be the dominant sink. Source emission in soil was the leading input and atmospheric sedimentation was the dominant transfer process. The integrated environmental risks primarily resulted from petroleum spills and coke ovens, while the soil environmental risks came from coal combustion. The developed approach offers an effective tool for quantifying variability and uncertainty in the dynamic multimedia integrated environmental risk assessment and the contaminated site management. PMID:23995555
Evolutionary dynamics of imatinib-treated leukemic cells by stochastic approach
NASA Astrophysics Data System (ADS)
Pizzolato, Nicola; Valenti, Davide; Adorno, Dominique; Spagnolo, Bernardo
2009-09-01
The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a statistical approach. Cancer progression is explored by applying a Monte Carlo method to simulate the stochastic behavior of cell reproduction and death in a population of blood cells which can experience genetic mutations. In CML front line therapy is represented by the tyrosine kinase inhibitor imatinib which strongly affects the reproduction of leukemic cells only. In this work, we analyze the effects of a targeted therapy on the evolutionary dynamics of normal, first-mutant and cancerous cell populations. Several scenarios of the evolutionary dynamics of imatinib-treated leukemic cells are described as a consequence of the efficacy of the different modelled therapies. We show how the patient response to the therapy changes when a high value of the mutation rate from healthy to cancerous cells is present. Our results are in agreement with clinical observations. Unfortunately, development of resistance to imatinib is observed in a fraction of patients, whose blood cells are characterized by an increasing number of genetic alterations. We find that the occurrence of resistance to the therapy can be related to a progressive increase of deleterious mutations.
Dynamic phase transition in the prisoner's dilemma on a lattice with stochastic modifications
NASA Astrophysics Data System (ADS)
Saif, M. Ali; Gade, Prashant M.
2010-03-01
We present a detailed study of the prisoner's dilemma game with stochastic modifications on a two-dimensional lattice, in the presence of evolutionary dynamics. By very nature of the rules, the cooperators have incentives to cheat and fear being cheated. They may cheat even when this is not dictated by the evolutionary dynamics. We consider two variants here. In each case, the agents mimic the action (cooperation or defection) in the previous time step of the most successful agent in the neighborhood. But over and above this, the fraction p of cooperators spontaneously change their strategy to pure defector at every time step in the first variant. In the second variant, there are no pure cooperators. All cooperators keep defecting with probability p at every time step. In both cases, the system switches from a coexistence state to an all-defector state for higher values of p. We show that the transition between these states unambiguously belongs to the directed percolation universality class in 2 + 1 dimensions. We also study the local persistence. The persistence exponents obtained are higher than the ones obtained in previous studies, underlining their dependence on details of the dynamics.
2013-01-01
Background A number of studies have established that stochasticity in gene expression may play an important role in many biological phenomena. This therefore calls for further investigations to identify the molecular mechanisms at stake, in order to understand and manipulate cell-to-cell variability. In this work, we explored the role played by chromatin dynamics in the regulation of stochastic gene expression in higher eukaryotic cells. Results For this purpose, we generated isogenic chicken-cell populations expressing a fluorescent reporter integrated in one copy per clone. Although the clones differed only in the genetic locus at which the reporter was inserted, they showed markedly different fluorescence distributions, revealing different levels of stochastic gene expression. Use of chromatin-modifying agents showed that direct manipulation of chromatin dynamics had a marked effect on the extent of stochastic gene expression. To better understand the molecular mechanism involved in these phenomena, we fitted these data to a two-state model describing the opening/closing process of the chromatin. We found that the differences between clones seemed to be due mainly to the duration of the closed state, and that the agents we used mainly seem to act on the opening probability. Conclusions In this study, we report biological experiments combined with computational modeling, highlighting the importance of chromatin dynamics in stochastic gene expression. This work sheds a new light on the mechanisms of gene expression in higher eukaryotic cells, and argues in favor of relatively slow dynamics with long (hours to days) periods of quiet state. PMID:23442824
Stochastic dynamics of superparamagnetic moments in polidisperse ferrofluids
NASA Astrophysics Data System (ADS)
Scherer, C.
2007-12-01
In previous works, we studied the dynamics of the magnetic moments in ferrofluids te{schererBJP,scherer-matuttis, scherer-ricci}, and other authors have also dealt with this problem te{shliomis}. In our previous works also computational simulations have been performed. The present work differs from those in two important aspects: (i) the magnetic particles are not of uniform size, but have a lognormal distribution of diameters; (ii) the parameters used in the simulations, like magnetization, anisotropy constant, liquid viscosity, applied field, temperature, etc., correspond to the values for realistic ferrofluids (in the previous works we used values, which were convenient for the simulations). For this reason, we will briefly re-derive the equations of motion, keeping all the relevant constants in them. To avoid big powers of 10 in the simulations, we introduce an appropriate system of units. The equations of motion for the particles' rotation and for the rotation of their magnetic moments are stochastic differential equations with multiplicative noise. Therefore, they have to be interpreted as Stratonovich-Langevin equations and the roles of stochastic calculus have to be used in the simulations. In our simulations, the response functions are "measured" and from them the complex susceptibilities are calculated. We performed several simulations, varying each parameter around a standard value, in order to see how the susceptibilities are correlated with the physical constants of the material. In the conclusions of special mention is the verification that the line broadening is very big. To be explicit, the ratio of the line-width of the polydisperse to that of the monodisperse with a diameter equal to the median diameter of the polydisperse, is much bigger than the ratio of the diameter's distribution width to the median diameter. It is interesting to note that for small dispersion width of diameters the resonance frequency does not change significantly with
Stochastic mean-field dynamics for fermions in the weak-coupling limit
Lacroix, Denis
2006-04-15
Assuming that the effect of the residual interaction beyond the mean field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of the Markovian quantum jump are presented. A simplified scenario for the introduction of fluctuations beyond the mean field is presented first. In this theory, part of the quantum correlations between the residual interaction and the one-body density matrix are neglected and jumps occur between many-body densities formed of pairs of states D={phi}{sub a}><{phi}{sub b}/<{phi}{sub b}{phi}{sub a}>, where {phi}{sub a}> and {phi}{sub b}> are antisymmetrized products of single-particle states. The underlying stochastic mean-field theory is discussed and is applied to the monopole vibration of a spherical {sup 40}Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. This framework is however too simplistic to account for both fluctuation and dissipation. In the second part of this work, an alternative quantum jump method is obtained without making the approximation on quantum correlations. By restricting to two-particle-two-hole residual interactions, the evolution of the one-body density matrix of a correlated system is transformed into a Lindblad equation. The associated dissipative dynamics can be simulated by quantum jumps between densities written as D=|{phi}><{phi}|, where |{phi}> is a normalized Slater determinant. The associated stochastic Schroedinger equation for single-particle wave functions is given.
Hui, Tsz Hin; Zheng, Fan; Lin, Yuan; Fu, Chuanhai
2016-05-01
Dynamic nuclei are involved in a wide variety of fundamental biological processes including cell migration, cell division and fertilization. Here, we develop a mathematical model, in combination with live-cell imaging at high temporal resolution, to quantitatively elucidate how the linear and rotational motions of the nucleus are governed by the stochastic dynamics of the microtubule cytoskeleton. Our simulation and experimental results demonstrate that microtubule rescue and catastrophe frequencies are the decisive factors in regulating the nuclear movement. Lower rescue and catastrophe frequencies can lead to significantly larger angular and translational oscillations of the nucleus. In addition, our model also suggests that the stochastic dynamics of individual spatially distributed microtubules works collectively as a restoring force to maintain nuclear centering and hence ensures symmetric cell division, in excellent agreement with direct experimental observations. PMID:26921917
NASA Astrophysics Data System (ADS)
Erdmann, Thorsten; Albert, Philipp J.; Schwarz, Ulrich S.
2013-11-01
Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.
Erdmann, Thorsten; Albert, Philipp J.; Schwarz, Ulrich S.
2013-11-07
Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.
Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model
NASA Astrophysics Data System (ADS)
Suzuki, Akio; Konno, Hidetoshi
2011-09-01
The dynamics of ventricular fibrillation (VF) has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR) model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS) such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf) for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.
NASA Astrophysics Data System (ADS)
Arnoux, A.; Batou, A.; Soize, C.; Gagliardini, L.
2013-08-01
This paper is devoted to the construction of a stochastic reduced order computational model of structures having numerous local elastic modes in low frequency dynamics. We are particularly interested in automotive vehicles which are made up of stiff parts and flexible components. This type of structure is characterized by the fact that it exhibits, in the low frequency range, not only the classical global elastic modes but also numerous local elastic modes which cannot easily be separated from the global elastic modes. To solve this difficult problem, an innovative method has recently been proposed for constructing a reduced order computational dynamical model adapted to this particular situation for the low frequency range. Then a new adapted generalized eigenvalue problem is introduced and allows a global vector basis to be constructed for the global displacements space. This method requires to decompose the domain of the structure into sub-domains. Such a decomposition is carried out using the Fast Marching Method. This global vector basis is then used to construct the reduced order computational model. Since there are model uncertainties induced by modeling errors in the computational model, the nonparametric probabilistic approach of uncertainties is used and implemented in the reduced order computational model. The methodology is applied to a complex computational model of an automotive vehicle.
A matrix product algorithm for stochastic dynamics on locally tree-like graphs
NASA Astrophysics Data System (ADS)
Barthel, Thomas; de Bacco, Caterina; Franz, Silvio
In this talk, I describe a novel algorithm for the efficient simulation of generic stochastic dynamics of classical degrees of freedom defined on the vertices of locally tree-like graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon the cavity method and ideas from quantum many-body theory, the algorithm is based on a matrix product approximation of the so-called edge messages - conditional probabilities of vertex variable trajectories. The matrix product edge messages (MPEM) are constructed recursively. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the MPEM in truncations. In contrast to Monte Carlo simulations, the approach has a better error scaling and works for both, single instances as well as the thermodynamic limit. Due to the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations with unprecedented accuracy. The method is demonstrated for the prototypical non-equilibrium Glauber dynamics of an Ising spin system. Reference: arXiv:1508.03295.
NASA Astrophysics Data System (ADS)
Hoang, Tuan L.; Marian, Jaime; Bulatov, Vasily V.; Hosemann, Peter
2015-11-01
An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) [6] is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a procedure for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the τ-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe3+, He+ and H+) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.
Low-dimensional stochastic dynamics underly the emergence of spontaneous movement in electric fish
NASA Astrophysics Data System (ADS)
Melanson, Alexandre; Jun, James J.; Mejias, Jorge F.; Maler, Leonard; Longtin, Andre
2015-03-01
Observing unconstrained animals can lead to simple descriptions of complex behaviours. We apply this principle here to infer the neural basis of spontaneous movements in electric fish. Long-term monitoring of fish in freely swimming, stimuli-free conditions has revealed a sequence of behavioural states that alternate randomly between periods of activity (movement, high active sensing rate) and inactivity (no movement, low active sensing rate). We show that key features of this sequence are well captured by a 1-D diffusion process in a double well energy landscape, where we assume the existence of a slow variable that modulates the relative depth of the wells. Model validation is two-fold: i) state duration distributions are well fitted by exponential mixtures, indicating non-stationary transition rates in the switching process. ii) Monte Carlo simulations with progressive tilting of the double well is consistent with the observed transition-triggered average. We interpret the stochastic variable of this dynamical model as a decision-like variable that, upon reaching a threshold, triggers the transition between states. We thus identify threshold crossing as a possible mechanism for spontaneous movement initiation and offer a dynamical explanation for slower behavioural changes. Funded by NSERC
A stochastic-dynamical approach to the study of the natural variability of the climate
NASA Technical Reports Server (NTRS)
Straus, D. M.; Halem, M.
1981-01-01
A method, suggested by Leith (1975), which employed stochastic-dynamic forecasts obtained from a general circulation model in such a way as to satisfy the definition of climatic noise, was used to validate assumptions accounting for the effects of external influences in estimating the climatic noise. Two assumptions were investigated: (1) that the weather fluctuations can be represented as a Markov process, and (2) that changing external conditions do not influence the atmosphere's statistical properties on short time scales. The general circulation model's simulation of the daily weather fluctuations was generated by performing integrations with prescribed climatological boundary conditions for random initial atmospheric states, with resulting dynamical forecasts providing an ensemble of simulated data for the autoregressive modeling of weather fluctuations. To estimate the climatic noise from the observational data (consisting of hourly values of sea level pressure and surface temperature at 54 U.S. stations for the month of January for the years 1949-1975) use of the short time-scale assumption is made. The simulated and observed data were found not to be consistent with either white noise or a Markov process of weather fluctuations. Good agreement was found between the results of the hypothetical testing of the simulated and the observed surface temperatures; and only partial support was found for the short time-scale assumption, i.e., for sea level pressure.
Kamimoto, Kenji; Kaneko, Kota; Kok, Cindy Yuet-Yin; Okada, Hajime; Miyajima, Atsushi; Itoh, Tohru
2016-01-01
Dynamic remodeling of the intrahepatic biliary epithelial tissue plays key roles in liver regeneration, yet the cellular basis for this process remains unclear. We took an unbiased approach based on in vivo clonal labeling and tracking of biliary epithelial cells in the three-dimensional landscape, in combination with mathematical simulation, to understand their mode of proliferation in a mouse liver injury model where the nascent biliary structure formed in a tissue-intrinsic manner. An apparent heterogeneity among biliary epithelial cells was observed: whereas most of the responders that entered the cell cycle upon injury exhibited a limited and tapering growth potential, a select population continued to proliferate, making a major contribution in sustaining the biliary expansion. Our study has highlighted a unique mode of epithelial tissue dynamics, which depends not on a hierarchical system driven by fixated stem cells, but rather, on a stochastically maintained progenitor population with persistent proliferative activity. DOI: http://dx.doi.org/10.7554/eLife.15034.001 PMID:27431614
Stochastic dynamics of electrical membrane with voltage-dependent ion channel fluctuations
NASA Astrophysics Data System (ADS)
Qian, Hong; Zhang, Xue-Juan; Qian, Min
2014-04-01
A Brownian-ratchet-like stochastic theory for the electrochemical membrane system of Hodgkin-Huxley (HH) is developed. The system is characterized by a continuous variable Q_m(t) , representing mobile membrane charge density, and a discrete variable Kt representing ion channel conformational dynamics. A Nernst-Planck-Nyquist-Johnson-type equilibrium is obtained when multiple conducting ions have a common reversal potential. Detailed balance yields a previously unknown relation between the channel switching rates and membrane capacitance, bypassing an Eyring-type explicit treatment of gating charge kinetics. From a molecular structural standpoint, the membrane charge Qm is a more natural dynamic variable than the potential Vm; our formalism treats Qm-dependent conformational transition rates \\lambda_{ij} as intrinsic parameters. Therefore, in principle, \\lambda_{ij} vs. Vm is experimental-protocol-dependent, e.g., different from voltage or charge clamping measurements. For constant membrane capacitance per unit area Cm and neglecting the membrane potential induced by gating charges, V_m=Q_m/C_m , and HH's formalism is recovered. The presence of two types of ions, with different channels and reversal potentials, gives rise to a nonequilibrium steady state with positive entropy production ep. For rapidly fluctuating channels, an expression for ep is obtained.
Stochastic flocking dynamics of the Cucker-Smale model with multiplicative white noises
NASA Astrophysics Data System (ADS)
Ahn, Shin Mi; Ha, Seung-Yeal
2010-10-01
We present a strong asymptotic stochastic flocking estimate for the stochastically perturbed Cucker-Smale model. We characterize a form of multiplicative white noises and present sufficient conditions on the control parameters to guarantee the almost sure exponential convergence toward constant equilibrium states. When the strength of multiplicative noises is sufficiently large, we show that the strong stochastic flocking occurs even for negative communication weights.
Inertial stochastic dynamics. I. Long-time-step methods for Langevin dynamics
NASA Astrophysics Data System (ADS)
Beard, Daniel A.; Schlick, Tamar
2000-05-01
Two algorithms are presented for integrating the Langevin dynamics equation with long numerical time steps while treating the mass terms as finite. The development of these methods is motivated by the need for accurate methods for simulating slow processes in polymer systems such as two-site intermolecular distances in supercoiled DNA, which evolve over the time scale of milliseconds. Our new approaches refine the common Brownian dynamics (BD) scheme, which approximates the Langevin equation in the highly damped diffusive limit. Our LTID ("long-time-step inertial dynamics") method is based on an eigenmode decomposition of the friction tensor. The less costly integrator IBD ("inertial Brownian dynamics") modifies the usual BD algorithm by the addition of a mass-dependent correction term. To validate the methods, we evaluate the accuracy of LTID and IBD and compare their behavior to that of BD for the simple example of a harmonic oscillator. We find that the LTID method produces the expected correlation structure for Langevin dynamics regardless of the level of damping. In fact, LTID is the only consistent method among the three, with error vanishing as the time step approaches zero. In contrast, BD is accurate only for highly overdamped systems. For cases of moderate overdamping, and for the appropriate choice of time step, IBD is significantly more accurate than BD. IBD is also less computationally expensive than LTID (though both are the same order of complexity as BD), and thus can be applied to simulate systems of size and time scale ranges previously accessible to only the usual BD approach. Such simulations are discussed in our companion paper, for long DNA molecules modeled as wormlike chains.
Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture
NASA Astrophysics Data System (ADS)
Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong
The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.
Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu
2016-01-01
Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor. PMID:27346701
Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu
2016-01-01
Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor. PMID:27346701
Councill, Elizabeth L
2016-03-01
Previous work has shown that an effective method of maintaining spawning stock biomass (SSB), the biomass of fish that are reproductively mature, within an exploited stock is to regulate harvest so that maximum fishing mortality rates occur after peak spawning during the year. This is known as post-recruitment harvest. The goal of this work is to examine if the advantages of post-recruitment harvest hold when reported stochasticity in the age and time distribution of harvest rates, known as selectivity, is considered. A hybrid dynamical systems model, one in which both continuous-time and discrete-time processes operate simultaneously, was derived, and recursive solutions were found. Results from other studies indicating the benefit of post-recruitment harvest were verified using this hybrid model when selectivity was considered fixed. Simulations were repeated including variance in selectivity using a Markov Chain Monte Carlo (MCMC) procedure. Results show that the benefits of post-recruitment harvest to the preservation of SSB were considerably less advantageous when each age class was assumed to be subject to annual stochastic selectivity. Furthermore, the stochastic scenarios gave estimates of SSB that were lower than their fixed selectivity analogs, indicating that the benefits of theoretical post-recruitment harvest may be diminished to some extent when stochasticity plays a large role in the dynamics. PMID:26721378
NASA Astrophysics Data System (ADS)
Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu
2016-06-01
Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.
Holistic irrigation water management approach based on stochastic soil water dynamics
NASA Astrophysics Data System (ADS)
Alizadeh, H.; Mousavi, S. J.
2012-04-01
Appreciating the essential gap between fundamental unsaturated zone transport processes and soil and water management due to low effectiveness of some of monitoring and modeling approaches, this study presents a mathematical programming model for irrigation management optimization based on stochastic soil water dynamics. The model is a nonlinear non-convex program with an economic objective function to address water productivity and profitability aspects in irrigation management through optimizing irrigation policy. Utilizing an optimization-simulation method, the model includes an eco-hydrological integrated simulation model consisting of an explicit stochastic module of soil moisture dynamics in the crop-root zone with shallow water table effects, a conceptual root-zone salt balance module, and the FAO crop yield module. Interdependent hydrology of soil unsaturated and saturated zones is treated in a semi-analytical approach in two steps. At first step analytical expressions are derived for the expected values of crop yield, total water requirement and soil water balance components assuming fixed level for shallow water table, while numerical Newton-Raphson procedure is employed at the second step to modify value of shallow water table level. Particle Swarm Optimization (PSO) algorithm, combined with the eco-hydrological simulation model, has been used to solve the non-convex program. Benefiting from semi-analytical framework of the simulation model, the optimization-simulation method with significantly better computational performance compared to a numerical Mote-Carlo simulation-based technique has led to an effective irrigation management tool that can contribute to bridging the gap between vadose zone theory and water management practice. In addition to precisely assessing the most influential processes at a growing season time scale, one can use the developed model in large scale systems such as irrigation districts and agricultural catchments. Accordingly
Sakaris, P.C.; Irwin, E.R.
2010-01-01
We developed stochastic matrix models to evaluate the effects of hydrologic alteration and variable mortality on the population dynamics of a lotie fish in a regulated river system. Models were applied to a representative lotic fish species, the flathead catfish (Pylodictis olivaris), for which two populations were examined: a native population from a regulated reach of the Coosa River (Alabama, USA) and an introduced population from an unregulated section of the Ocmulgee River (Georgia, USA). Size-classified matrix models were constructed for both populations, and residuals from catch-curve regressions were used as indices of year class strength (i.e., recruitment). A multiple regression model indicated that recruitment of flathead catfish in the Coosa River was positively related to the frequency of spring pulses between 283 and 566 m3/s. For the Ocmulgee River population, multiple regression models indicated that year class strength was negatively related to mean March discharge and positively related to June low flow. When the Coosa population was modeled to experience five consecutive years of favorable hydrologic conditions during a 50-year projection period, it exhibited a substantial spike in size and increased at an overall 0.2% annual rate. When modeled to experience five years of unfavorable hydrologic conditions, the Coosa population initially exhibited a decrease in size but later stabilized and increased at a 0.4% annual rate following the decline. When the Ocmulgee River population was modeled to experience five years of favorable conditions, it exhibited a substantial spike in size and increased at an overall 0.4% annual rate. After the Ocmulgee population experienced five years of unfavorable conditions, a sharp decline in population size was predicted. However, the population quickly recovered, with population size increasing at a 0.3% annual rate following the decline. In general, stochastic population growth in the Ocmulgee River was more
Localized dynamic kinetic-energy-based models for stochastic coherent adaptive large eddy simulation
NASA Astrophysics Data System (ADS)
De Stefano, Giuliano; Vasilyev, Oleg V.; Goldstein, Daniel E.
2008-04-01
Stochastic coherent adaptive large eddy simulation (SCALES) is an extension of the large eddy simulation approach in which a wavelet filter-based dynamic grid adaptation strategy is employed to solve for the most "energetic" coherent structures in a turbulent field while modeling the effect of the less energetic background flow. In order to take full advantage of the ability of the method in simulating complex flows, the use of localized subgrid-scale models is required. In this paper, new local dynamic one-equation subgrid-scale models based on both eddy-viscosity and non-eddy-viscosity assumptions are proposed for SCALES. The models involve the definition of an additional field variable that represents the kinetic energy associated with the unresolved motions. This way, the energy transfer between resolved and residual flow structures is explicitly taken into account by the modeling procedure without an equilibrium assumption, as in the classical Smagorinsky approach. The wavelet-filtered incompressible Navier-Stokes equations for the velocity field, along with the additional evolution equation for the subgrid-scale kinetic energy variable, are numerically solved by means of the dynamically adaptive wavelet collocation solver. The proposed models are tested for freely decaying homogeneous turbulence at Reλ=72. It is shown that the SCALES results, obtained with less than 0.5% of the total nonadaptive computational nodes, closely match reference data from direct numerical simulation. In contrast to classical large eddy simulation, where the energetic small scales are poorly simulated, the agreement holds not only in terms of global statistical quantities but also in terms of spectral distribution of energy and, more importantly, enstrophy all the way down to the dissipative scales.
Two-strain competition in quasi-neutral stochastic disease dynamics
Technology Transfer Automated Retrieval System (TEKTRAN)
We develop a new perturbation method for studying quasi-neutral competition in a broad class of stochastic competition models, and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic Susceptible-Infected-S...
Collaborative Research: Robust Climate Projections and Stochastic Stability of Dynamical Systems
Ghil, Michael; McWilliams, James; Neelin, J. David; Zaliapin, Ilya; Chekroun, Mickael; Kondrashov, Dmitri; Simonnet, Eric
2011-10-13
The project was completed along the lines of the original proposal, with additional elements arising as new results were obtained. The originally proposed three thrusts were expanded to include an additional, fourth one. (i) The e ffects of stochastic perturbations on climate models have been examined at the fundamental level by using the theory of deterministic and random dynamical systems, in both nite and in nite dimensions. (ii) The theoretical results have been implemented first on a delay-diff erential equation (DDE) model of the El-Nino/Southern-Oscillation (ENSO) phenomenon. (iii) More detailed, physical aspects of model robustness have been considered, as proposed, within the stripped-down ICTP-AGCM (formerly SPEEDY) climate model. This aspect of the research has been complemented by both observational and intermediate-model aspects of mid-latitude and tropical climate. (iv) An additional thrust of the research relied on new and unexpected results of (i) and involved reduced-modeling strategies and associated prediction aspects have been tested within the team's empirical model reduction (EMR) framework. Finally, more detailed, physical aspects have been considered within the stripped-down SPEEDY climate model. The results of each of these four complementary e fforts are presented in the next four sections, organized by topic and by the team members concentrating on the topic under discussion.
Banerjee, Kinshuk
2015-05-14
In this work, we have studied the stochastic response of a single voltage-gated potassium ion channel to a periodic external voltage that keeps the system out-of-equilibrium. The system exhibits memory, resulting from time-dependent driving, that is reflected in terms of dynamic hysteresis in the current-voltage characteristics. The hysteresis loop area has a maximum at some intermediate voltage frequency and disappears in the limits of low and high frequencies. However, the (average) dissipation at long-time limit increases and finally goes to saturation with rising frequency. This raises the question: how diminishing hysteresis can be associated with growing dissipation? To answer this, we have studied the nonequilibrium thermodynamics of the system and analyzed different thermodynamic functions which also exhibit hysteresis. Interestingly, by applying a temporal symmetry analysis in the high-frequency limit, we have analytically shown that hysteresis in some of the periodic responses of the system does not vanish. On the contrary, the rates of free energy and internal energy change of the system as well as the rate of dissipative work done on the system show growing hysteresis with frequency. Hence, although the current-voltage hysteresis disappears in the high-frequency limit, the memory of the ion channel is manifested through its specific nonequilibrium thermodynamic responses. PMID:25978913
Construction of dynamic stochastic simulation models using knowledge-based techniques
NASA Technical Reports Server (NTRS)
Williams, M. Douglas; Shiva, Sajjan G.
1990-01-01
Over the past three decades, computer-based simulation models have proven themselves to be cost-effective alternatives to the more structured deterministic methods of systems analysis. During this time, many techniques, tools and languages for constructing computer-based simulation models have been developed. More recently, advances in knowledge-based system technology have led many researchers to note the similarities between knowledge-based programming and simulation technologies and to investigate the potential application of knowledge-based programming techniques to simulation modeling. The integration of conventional simulation techniques with knowledge-based programming techniques is discussed to provide a development environment for constructing knowledge-based simulation models. A comparison of the techniques used in the construction of dynamic stochastic simulation models and those used in the construction of knowledge-based systems provides the requirements for the environment. This leads to the design and implementation of a knowledge-based simulation development environment. These techniques were used in the construction of several knowledge-based simulation models including the Advanced Launch System Model (ALSYM).
Using stochastic dual dynamic programming in problems with multiple near-optimal solutions
NASA Astrophysics Data System (ADS)
Rougé, Charles; Tilmant, Amaury
2016-05-01
Stochastic dual dynamic programming (SDDP) is one of the few algorithmic solutions available to optimize large-scale water resources systems while explicitly considering uncertainty. This paper explores the consequences of, and proposes a solution to, the existence of multiple near-optimal solutions (MNOS) when using SDDP for mid or long-term river basin management. These issues arise when the optimization problem cannot be properly parametrized due to poorly defined and/or unavailable data sets. This work shows that when MNOS exists, (1) SDDP explores more than one solution trajectory in the same run, suggesting different decisions in distinct simulation years even for the same point in the state-space, and (2) SDDP is shown to be very sensitive to even minimal variations of the problem setting, e.g., initial conditions—we call this "algorithmic chaos." Results that exhibit such sensitivity are difficult to interpret. This work proposes a reoptimization method, which simulates system decisions by periodically applying cuts from one given year from the SDDP run. Simulation results obtained through this reoptimization approach are steady state solutions, meaning that their probability distributions are stable from year to year.
Coordinating two-period ordering and advertising policies in a dynamic market with stochastic demand
NASA Astrophysics Data System (ADS)
Wang, Junping; Wang, Shengdong; Min, Jie
2015-03-01
In this paper, we study the optimal two-stage advertising and ordering policies and the channel coordination issues in a supply chain composed of one manufacturer and one retailer. The manufacturer sells a short-life-cycle product through the retailer facing stochastic demand in dynamic markets characterised by price declines and product obsolescence. Following a two-period newsvendor framework, we develop two members' optimal ordering and advertising models under both the centralised and decentralised settings, and present the closed-form solutions to the developed models as well. Moreover, we design a two-period revenue-sharing contract, and develop sufficient conditions such that the channel coordination can be achieved and a win-win outcome can be guaranteed. Our analysis suggests that the centralised decision creates an incentive for the retailer to increase the advertising investments in two periods and put the purchase forward, but the decentralised decision mechanism forces the retailer to decrease the advertising investments in two periods and postpone/reduce its purchase in the first period. This phenomenon becomes more evident when demand variability is high.
Banerjee, Kinshuk
2015-05-14
In this work, we have studied the stochastic response of a single voltage-gated potassium ion channel to a periodic external voltage that keeps the system out-of-equilibrium. The system exhibits memory, resulting from time-dependent driving, that is reflected in terms of dynamic hysteresis in the current-voltage characteristics. The hysteresis loop area has a maximum at some intermediate voltage frequency and disappears in the limits of low and high frequencies. However, the (average) dissipation at long-time limit increases and finally goes to saturation with rising frequency. This raises the question: how diminishing hysteresis can be associated with growing dissipation? To answer this, we have studied the nonequilibrium thermodynamics of the system and analyzed different thermodynamic functions which also exhibit hysteresis. Interestingly, by applying a temporal symmetry analysis in the high-frequency limit, we have analytically shown that hysteresis in some of the periodic responses of the system does not vanish. On the contrary, the rates of free energy and internal energy change of the system as well as the rate of dissipative work done on the system show growing hysteresis with frequency. Hence, although the current-voltage hysteresis disappears in the high-frequency limit, the memory of the ion channel is manifested through its specific nonequilibrium thermodynamic responses.
Effect of reaction-step-size noise on the switching dynamics of stochastic populations.
Be'er, Shay; Heller-Algazi, Metar; Assaf, Michael
2016-05-01
In genetic circuits, when the messenger RNA lifetime is short compared to the cell cycle, proteins are produced in geometrically distributed bursts, which greatly affects the cellular switching dynamics between different metastable phenotypic states. Motivated by this scenario, we study a general problem of switching or escape in stochastic populations, where influx of particles occurs in groups or bursts, sampled from an arbitrary distribution. The fact that the step size of the influx reaction is a priori unknown and, in general, may fluctuate in time with a given correlation time and statistics, introduces an additional nondemographic reaction-step-size noise into the system. Employing the probability-generating function technique in conjunction with Hamiltonian formulation, we are able to map the problem in the leading order onto solving a stationary Hamilton-Jacobi equation. We show that compared to the "usual case" of single-step influx, bursty influx exponentially decreases the population's mean escape time from its long-lived metastable state. In particular, close to bifurcation we find a simple analytical expression for the mean escape time which solely depends on the mean and variance of the burst-size distribution. Our results are demonstrated on several realistic distributions and compare well with numerical Monte Carlo simulations. PMID:27300840
Effect of reaction-step-size noise on the switching dynamics of stochastic populations
NASA Astrophysics Data System (ADS)
Be'er, Shay; Heller-Algazi, Metar; Assaf, Michael
2016-05-01
In genetic circuits, when the messenger RNA lifetime is short compared to the cell cycle, proteins are produced in geometrically distributed bursts, which greatly affects the cellular switching dynamics between different metastable phenotypic states. Motivated by this scenario, we study a general problem of switching or escape in stochastic populations, where influx of particles occurs in groups or bursts, sampled from an arbitrary distribution. The fact that the step size of the influx reaction is a priori unknown and, in general, may fluctuate in time with a given correlation time and statistics, introduces an additional nondemographic reaction-step-size noise into the system. Employing the probability-generating function technique in conjunction with Hamiltonian formulation, we are able to map the problem in the leading order onto solving a stationary Hamilton-Jacobi equation. We show that compared to the "usual case" of single-step influx, bursty influx exponentially decreases the population's mean escape time from its long-lived metastable state. In particular, close to bifurcation we find a simple analytical expression for the mean escape time which solely depends on the mean and variance of the burst-size distribution. Our results are demonstrated on several realistic distributions and compare well with numerical Monte Carlo simulations.
Linear processes in stochastic population dynamics: theory and application to insect development.
Solari, Hernán G; Natiello, Mario A
2014-01-01
We consider stochastic population processes (Markov jump processes) that develop as a consequence of the occurrence of random events at random time intervals. The population is divided into subpopulations or compartments. The events occur at rates that depend linearly on the number of individuals in the different described compartments. The dynamics is presented in terms of Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously proposed, higher-order approximations are completely new. Further, we analyse a model for insect development as a sequence of E developmental stages regulated by rates that are linear in the implied subpopulations. Transition to the next stage competes with death at all times. The process ends at a predetermined stage, for example, pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time. PMID:24696664
Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks.
Billiard, Sylvain; Ferrière, Régis; Méléard, Sylvie; Tran, Viet Chi
2015-11-01
How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and maintenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of a favorable mutation, a genetical bottleneck occurs and the marker associated with this favorable mutant is hitchhiked. By rigorously analysing the hitchhiking effect and how the neutral diversity is restored afterwards, we obtain the condition for a time-scale separation; under this condition, we show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions. We discuss the implications of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint importance of mutations, ecological parameters, and trait values in the restoration of neutral diversity after a selective sweep. PMID:25544270
Stochastic Mesocortical Dynamics and Robustness of Working Memory during Delay-Period.
Reneaux, Melissa; Gupta, Rahul; Karmeshu
2015-01-01
The role of prefronto-mesoprefrontal system in the dopaminergic modulation of working memory during delayed response tasks is well-known. Recently, a dynamical model of the closed-loop mesocortical circuit has been proposed which employs a deterministic framework to elucidate the system's behavior in a qualitative manner. Under natural conditions, noise emanating from various sources affects the circuit's functioning to a great extent. Accordingly in the present study, we reformulate the model into a stochastic framework and investigate its steady state properties in the presence of constant background noise during delay-period. From the steady state distribution, global potential landscape and signal-to-noise ratio are obtained which help in defining robustness of the circuit dynamics. This provides insight into the robustness of working memory during delay-period against its disruption due to background noise. The findings reveal that the global profile of circuit's robustness is predominantly governed by the level of D1 receptor activity and high D1 receptor stimulation favors the working memory-associated sustained-firing state over the spontaneous-activity state of the system. Moreover, the circuit's robustness is further fine-tuned by the levels of excitatory and inhibitory activities in a way such that the robustness of sustained-firing state exhibits an inverted-U shaped profile with respect to D1 receptor stimulation. It is predicted that the most robust working memory is formed possibly at a subtle ratio of the excitatory and inhibitory activities achieved at a critical level of D1 receptor stimulation. The study also paves a way to understand various cognitive deficits observed in old-age, acute stress and schizophrenia and suggests possible mechanistic routes to the working memory impairments based on the circuit's robustness profile. PMID:26636712
Stochastic Mesocortical Dynamics and Robustness of Working Memory during Delay-Period
Karmeshu
2015-01-01
The role of prefronto-mesoprefrontal system in the dopaminergic modulation of working memory during delayed response tasks is well-known. Recently, a dynamical model of the closed-loop mesocortical circuit has been proposed which employs a deterministic framework to elucidate the system’s behavior in a qualitative manner. Under natural conditions, noise emanating from various sources affects the circuit’s functioning to a great extent. Accordingly in the present study, we reformulate the model into a stochastic framework and investigate its steady state properties in the presence of constant background noise during delay-period. From the steady state distribution, global potential landscape and signal-to-noise ratio are obtained which help in defining robustness of the circuit dynamics. This provides insight into the robustness of working memory during delay-period against its disruption due to background noise. The findings reveal that the global profile of circuit’s robustness is predominantly governed by the level of D1 receptor activity and high D1 receptor stimulation favors the working memory-associated sustained-firing state over the spontaneous-activity state of the system. Moreover, the circuit’s robustness is further fine-tuned by the levels of excitatory and inhibitory activities in a way such that the robustness of sustained-firing state exhibits an inverted-U shaped profile with respect to D1 receptor stimulation. It is predicted that the most robust working memory is formed possibly at a subtle ratio of the excitatory and inhibitory activities achieved at a critical level of D1 receptor stimulation. The study also paves a way to understand various cognitive deficits observed in old-age, acute stress and schizophrenia and suggests possible mechanistic routes to the working memory impairments based on the circuit’s robustness profile. PMID:26636712
Stochastic resonance in soft matter systems: combined effects of static and dynamic disorder
NASA Astrophysics Data System (ADS)
Perc, Matjaž; Gosak, Marko; Kralj, Samo
We study the impact of static and dynamic disorder on the phenomenon of stochastic resonance (SR) in a representative soft matter system. Due to their extreme susceptibility to weak perturbations soft matter systems appear to be excellent candidates for the observation of SR. Indeed, we derive generic SR equations from a polymer stabilized ferroelectric liquid crystal (LC) cell, which is a typical soft matter representative constituting one of the basic components in several electro-optic applications. We generalize these equations further in order to study an even broader class of qualitatively different systems, especially disclosing the influence of different types of static disorder and interaction ranges amongst LC molecules on the SR response. We determine the required conditions for the observation of SR in the examined system, and moreover, reveal that a random field type static disorder yields qualitatively different responses with respect to random dilution, random bond and spin glass universality classes. In particular, while the latter three decrease the level of dynamic disorder (Gaussian noise) warranting the optimal response, the former evokes exactly the opposite effect, hence increasing the optimal noise level that is needed to resonantly fine-tune the system's response in accordance with the weak deterministic electric field. These observations are shown to be independent of the system size and range of interactions, thus implying their general validity and potentially wide applicability also within other similar settings. We argue that soft matter systems might be particularly adequate as a base for different SR-based sensitive detectors and thus potent candidates for additional theoretical as well as experimental research in the presently outlined direction.
NASA Astrophysics Data System (ADS)
Kaczmarczyk, S.; Iwankiewicz, R.; Terumichi, Y.
2009-08-01
Moving slender elastic elements such as ropes, cables and belts are pivotal components of vertical transportation systems such as traction elevators. Their lengths vary within the host building structure during the elevator operation which results in the change of the mass and stiffness characteristics of the system. The structure of modern high-rise buildings is flexible and when subjected to loads due to strong winds and earthquakes it vibrates at low frequencies. The inertial load induced by the building motion excites the flexible components of the elevator system. The compensating ropes due to their lower tension are particularly affected and undergo large dynamic deformations. The paper focuses on the presentation of the non-stationary model of a building-compensating rope system and on the analysis to predict its dynamic response. The excitation mechanism is represented by a harmonic process and the results of computer simulations to predict transient resonance response are presented. The analysis of the simulation results leads to recommendations concerning the selection of the weight of the compensation assembly to minimize the effects of an adverse dynamic response of the system. The scenario when the excitation is represented as a narrow-band stochastic process with the state vector governed by stochastic equations is then discussed and the stochastic differential equations governing the second-order statistical moments of the state vector are developed.
NASA Astrophysics Data System (ADS)
Davidsen, Claus; Liu, Suxia; Mo, Xingguo; Rosbjerg, Dan; Bauer-Gottwein, Peter
2014-05-01
Optimal management of conjunctive use of surface water and groundwater has been attempted with different algorithms in the literature. In this study, a hydro-economic modelling approach to optimize conjunctive use of scarce surface water and groundwater resources under uncertainty is presented. A stochastic dynamic programming (SDP) approach is used to minimize the basin-wide total costs arising from water allocations and water curtailments. Dynamic allocation problems with inclusion of groundwater resources proved to be more complex to solve with SDP than pure surface water allocation problems due to head-dependent pumping costs. These dynamic pumping costs strongly affect the total costs and can lead to non-convexity of the future cost function. The water user groups (agriculture, industry, domestic) are characterized by inelastic demands and fixed water allocation and water supply curtailment costs. As in traditional SDP approaches, one step-ahead sub-problems are solved to find the optimal management at any time knowing the inflow scenario and reservoir/aquifer storage levels. These non-linear sub-problems are solved using a genetic algorithm (GA) that minimizes the sum of the immediate and future costs for given surface water reservoir and groundwater aquifer end storages. The immediate cost is found by solving a simple linear allocation sub-problem, and the future costs are assessed by interpolation in the total cost matrix from the following time step. Total costs for all stages, reservoir states, and inflow scenarios are used as future costs to drive a forward moving simulation under uncertain water availability. The use of a GA to solve the sub-problems is computationally more costly than a traditional SDP approach with linearly interpolated future costs. However, in a two-reservoir system the future cost function would have to be represented by a set of planes, and strict convexity in both the surface water and groundwater dimension cannot be maintained
Collaborative tracking and control in time-dependent stochastic dynamical systems
NASA Astrophysics Data System (ADS)
Forgoston, Eric; Hsieh, Ani; Schwartz, Ira; Yecko, Philip
2013-11-01
We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. Lagrangian Coherent Structures (LCS) are found using collaborative tracking, and a control policy is formulated that utilizes knowledge of the LCS. The control strategy enables mobile sensors to autonomously maintain a desired distribution in the environment, and is evaluated with experimental data. Research supported by the Office of Naval Research.
Voter, A F; Sindhikara, Daniel J; Kim, Seonah; Roitberg, Adrian E
2009-01-01
Molecular dynamics simulations starting from different initial conditions are commonly used to mimic the behavior of an experimental ensemble. We show in this article that when a Langevin thermostat is used to maintain constant temperature during such simulations, extreme care must be taken when choosing the random number seeds used in order to prevent statistical correlation among the MD trajectories. While recent studies have shown that stochastically thermostatted trajectories evolving within a single potential basin with identical random number seeds tend to synchronize, we show that there is a synchronization effect even for complex, biologically relevant systems. We demonstrate this effect in simulations of Alanine trimer and pentamer and in a simulation of a temperature-jump experiment for peptide folding of a 14-residue peptide. Even in replica-exchange simulations, in which the trajectories are at different temperatures, we find partial synchronization occurring when the same random number seed is employed. We explain this by extending the recent derivation of the synchronization effect for two trajectories in a harmonic well to the case in which the trajectories are at two different temperatures. Our results suggest several ways in which mishandling selection of a pseudo random number generator initial seed can lead to corruption of simulation data. Simulators can fall into this trap in simple situations such as neglecting to specifically indicate different random seeds in either parallel or sequential restart simulations, utilizing a simulation package with a weak pseudorandom number generator, or using an advanced simulation algorithm that hasn't been programmed to distribute initial seeds.
NASA Astrophysics Data System (ADS)
Chowdhury, A. F. M. K.; Lockart, N.; Willgoose, G. R.; Kuczera, G. A.; Nadeeka, P. M.
2014-12-01
This study used high resolution spatially distributed rainfall data produced by NSW/ACT Regional Climate Modelling (NARCliM) project. NARCliM dynamically downscaled four Global Climate Models using three Regional Climate Models within the Weather Research and Forecasting model to generate gridded climate data at 10 km spatial resolution for south eastern Australia. These dataset are being used in this project to evaluate the urban water security of reservoirs on the east coast of Australia. A stochastic model to simulate rainfall series was developed for runoff generation using parameters calibrated to NARCliM. This study has developed a Markov Chain model, which simulates the occurrence of daily rainfall using the transition probability of dry and wet days, while the precipitation for the wet days are generated using a two parameter gamma distribution. We have identified significant seasonal and intra- to inter-decadal variations of the model parameters at our field site. Incorporating the temporal variability (for instance, calibrating the model parameters to each decade independently), we have found that the model satisfactorily preserves the daily, monthly and annual characteristics of the NARCliM rainfall. In addition to the temporal variability, we have observed that the model parameters vary spatially at our site with potential orographic effects that vary both seasonally and decadally. However, the parameters of the model fitted to the NARCliM rainfall are significantly different from the parameters fitted to the ground-based climate station rainfall. Suitability of the model for the generation of long time series (e.g. 1000 years) required for reservoir simulation will be discussed.
Synthetic Chloride-Selective Carbon Nanotubes Examined by Using Molecular and Stochastic Dynamics
Hilder, Tamsyn A.; Gordon, Dan; Chung, Shin-Ho
2010-01-01
Synthetic channels, such as nanotubes, offer the possibility of ion-selective nanoscale pores which can broadly mimic the functions of various biological ion channels, and may one day be used as antimicrobial agents, or for treatment of cystic fibrosis. We have designed a carbon nanotube that is selectively permeable to anions. The virtual nanotubes are constructed from a hexagonal array of carbon atoms (graphene) rolled up to form a tubular structure, with an effective radius of 4.53 Å and length of 34 Å. The pore ends are terminated with polar carbonyl groups. The nanotube thus formed is embedded in a lipid bilayer and a reservoir containing ionic solutions is added at each end of the pore. The conductance properties of these synthetic channels are then examined with molecular and stochastic dynamics simulations. Profiles of the potential of mean force at 0 mM reveal that a cation moving across the pore encounters an insurmountable free energy barrier of ∼25 kT in height. In contrast, for anions, there are two energy wells of ∼12 kT near each end of the tube, separated by a central free energy barrier of 4 kT. The conductance of the pore, with symmetrical 500 mM solutions in the reservoirs, is 72 pS at 100 mV. The current saturates with an increasing ionic concentration, obeying a Michaelis-Menten relationship. The pore is normally occupied by two ions, and the rate-limiting step in conduction is the time taken for the resident ion near the exit gate to move out of the energy well. PMID:20858417
Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.
Szabó-Solticzky, András; Berthouze, Luc; Kiss, Istvan Z; Simon, Péter L
2016-04-01
An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models. PMID:26063525
Saltz, David; Rubenstein, Daniel I; White, Gary C
2006-10-01
Theory proposes that increased environmental stochasticity negatively impacts population viability. Thus, in addition to the directional changes predicted for weather parameters under global climate change (GCC), the increase in variance of these parameters may also have a negative effect on biodiversity. As a case study, we assessed the impact of interannual variance in precipitation on the viability of an Asiatic wild ass (Equus hemionus) population reintroduced in Makhtesh Ramon Nature Reserve, Israel. We monitored the population from 1985 to 1999 to determine what environmental factors affect reproductive success. Annual precipitation during the year before conception, drought conditions during gestation, and population size determined reproductive success. We used the parameters derived from this model to assess population performance under various scenarios in a Leslie matrix type model with demographic and environmental stochasticity. Specifically, we used a change in the precipitation regime in our study area to formulate a GCC scenario and compared the simulated dynamics of the population with a no-change scenario. The coefficient of variation in population size under the global change scenario was 30% higher than under the no-change scenario. Minor die-offs (> or = 15%) following droughts increased extinction probability nearly 10-fold. Our results support the idea that an increase in environmental stochasticity due to GCC may, in itself, pose a significant threat to biodiversity. PMID:17002758
Deng, Chenhui; Plan, Elodie L; Karlsson, Mats O
2016-06-01
Parameter variation in pharmacometric analysis studies can be characterized as within subject parameter variability (WSV) in pharmacometric models. WSV has previously been successfully modeled using inter-occasion variability (IOV), but also stochastic differential equations (SDEs). In this study, two approaches, dynamic inter-occasion variability (dIOV) and adapted stochastic differential equations, were proposed to investigate WSV in pharmacometric count data analysis. These approaches were applied to published count models for seizure counts and Likert pain scores. Both approaches improved the model fits significantly. In addition, stochastic simulation and estimation were used to explore further the capability of the two approaches to diagnose and improve models where existing WSV is not recognized. The results of simulations confirmed the gain in introducing WSV as dIOV and SDEs when parameters vary randomly over time. Further, the approaches were also informative as diagnostics of model misspecification, when parameters changed systematically over time but this was not recognized in the structural model. The proposed approaches in this study offer strategies to characterize WSV and are not restricted to count data. PMID:27165151
NASA Astrophysics Data System (ADS)
Lin, Hai; Shuai, J. W.
2010-04-01
A stochastic spatial model based on the Monte Carlo approach is developed to study the dynamics of human immunodeficiency virus (HIV) infection. We aim to propose a more detailed and realistic simulation frame by incorporating many important features of HIV dynamics, which include infections, replications and mutations of viruses, antigen recognitions, activations and proliferations of lymphocytes, and diffusions, encounters and interactions of virions and lymphocytes. Our model successfully reproduces the three-phase pattern observed in HIV infection, and the simulation results for the time distribution from infection to AIDS onset are also in good agreement with the clinical data. The interactions of viruses and the immune system in all the three phases are investigated. We assess the relative importance of various immune system components in the acute phase. The dynamics of how the two important factors, namely the viral diversity and the asymmetric battle between HIV and the immune system, result in AIDS are investigated in detail with the model.
NASA Astrophysics Data System (ADS)
Turner, Sean; Galelli, Stefano; Wilcox, Karen
2015-04-01
Water reservoir systems are often affected by recurring large-scale ocean-atmospheric anomalies, known as teleconnections, that cause prolonged periods of climatological drought. Accurate forecasts of these events -- at lead times in the order of weeks and months -- may enable reservoir operators to take more effective release decisions to improve the performance of their systems. In practice this might mean a more reliable water supply system, a more profitable hydropower plant or a more sustainable environmental release policy. To this end, climate indices, which represent the oscillation of the ocean-atmospheric system, might be gainfully employed within reservoir operating models that adapt the reservoir operation as a function of the climate condition. This study develops a Stochastic Dynamic Programming (SDP) approach that can incorporate climate indices using a Hidden Markov Model. The model simulates the climatic regime as a hidden state following a Markov chain, with the state transitions driven by variation in climatic indices, such as the Southern Oscillation Index. Time series analysis of recorded streamflow data reveals the parameters of separate autoregressive models that describe the inflow to the reservoir under three representative climate states ("normal", "wet", "dry"). These models then define inflow transition probabilities for use in a classic SDP approach. The key advantage of the Hidden Markov Model is that it allows conditioning the operating policy not only on the reservoir storage and the antecedent inflow, but also on the climate condition, thus potentially allowing adaptability to a broader range of climate conditions. In practice, the reservoir operator would effect a water release tailored to a specific climate state based on available teleconnection data and forecasts. The approach is demonstrated on the operation of a realistic, stylised water reservoir with carry-over capacity in South-East Australia. Here teleconnections relating
A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
Atzberger, Paul J. . E-mail: atzberg@math.ucsb.edu; Kramer, Peter R.; Peskin, Charles S.
2007-06-10
In modeling many biological systems, it is important to take into account flexible structures which interact with a fluid. At the length scale of cells and cell organelles, thermal fluctuations of the aqueous environment become significant. In this work, it is shown how the immersed boundary method of [C.S. Peskin, The immersed boundary method, Acta Num. 11 (2002) 1-39.] for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps. An important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved, partially resolved, or fully resolved while retaining a good level of accuracy. Error estimates in each of these regimes are given for the method. A number of theoretical and numerical checks are furthermore performed to assess its physical fidelity. For a conservative force, the method is found to simulate particles with the correct Boltzmann equilibrium statistics. It is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters. The method is also shown to reproduce a well-known hydrodynamic effect of a Brownian particle in which the velocity autocorrelation function exhibits an algebraic ({tau} {sup -3/2}) decay for long times [B.J. Alder, T.E. Wainwright, Decay of the Velocity Autocorrelation Function, Phys. Rev. A 1(1) (1970) 18-21]. A few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method. Specifically, we present simulations of osmotic effects of molecular dimers, worm-like chain polymer knots, and a basic model of a molecular motor immersed in fluid
Louis, H; Tlidi, M; Louvergneaux, E
2016-07-11
We perform a statistical analysis of the optical solitary wave propagation in an ultra-slow stochastic non-local focusing Kerr medium such as liquid crystals. Our experimental results show that the localized beam trajectory presents a dynamical random walk whose beam position versus the propagation distance z depicts two different kind of evolutions A power law is found for the beam position standard deviation during the first stage of propagation. It obeys approximately z^{3}/^{2} up to ten times the power threshold for solitary wave generation. PMID:27410886
Louis, H; Tlidi, M; Louvergneaux, E
2016-07-11
We perform a statistical analysis of the optical solitary wave propagation in an ultra-slow stochastic non-local focusing Kerr medium such as liquid crystals. Our experimental results show that the localized beam trajectory presents a dynamical random walk whose beam position versus the propagation distance z depicts two different kind of evolutions A power law is found for the beam position standard deviation during the first stage of propagation. It obeys approximately z^{3}/^{2} up to ten times the power threshold for solitary wave generation. PMID:27410887
Sullivan, P.J.; Swartzman, G.L.
1984-03-01
The dynamics of the Hudson river striped bass (Morone saxatilis) stock were analyzed using a stochastic age structured model. The effect of river flow on recruitment was combined with the mortality due to fishing and power plant water uptake to obtain an overall effect of these variables on the fishery. Model equations and parameters were documented and their underlying assumptions presented. Preliminary model runs resulted in yields well below those actually observed. Calibration of model parameters brought these values closer to the observed yields, but stock values proved inexact. The influence of power plant mortality on fishery yield was evident, but the simulation results remain inconclusive. 11 references, 4 figures, 6 tables.
Deterministic and stochastic dynamics of bed load tracer particles in a coarse grained river
NASA Astrophysics Data System (ADS)
Phillips, C. B.; Martin, R. L.; Jerolmack, D. J.
2012-12-01
Understanding the mechanics of a single coarse sediment particle, and the mechanics of sediment transport at the flood scale, is critical to linking event scale bed load transport rates to annual bed load fluxes. We present research on the dynamics of coarse sediment tracer particles tagged with passive radio transponder tags, observing motion resulting from individual floods and the cumulative transport over many floods spanning two years, in the Mameyes River in the Luquillo Mountains of Puerto Rico. This region presents an ideal study area due to the high frequency of coarse sediment mobilizing events, which allows us to field test the applicability of recently-proposed deterministic and stochastic theories for particle motion. Data for each flood are composed of (1) measured 'flight' lengths for each transported particle, (2) the fraction of tagged particles mobilized, and (3) high-resolution river stage measurements. At the single flood scale, measured tracer particle flight lengths are exponentially distributed, and modal flight lengths scale linearly with excess shear velocity. This is in quantitative agreement with recent theory and laboratory experiments, suggesting that moving particles' velocity is determined by momentum balance with the fluid. The fraction of mobile particles per event increases rapidly with flood stage, creating a logistic-like curve whose inflection point is used to empirically define the threshold of motion. This finding is in contrast to the linear relation observed in small-scale experiments and predicted from momentum balance between sediment and fluid; we use a particle Stokes number argument to suggest that a collision cascade from grain-grain interactions is responsible for the nonlinear relation between mobile fraction and fluid stress, in dynamical equivalence with aeolian sand transport. To examine particle dispersion and relate it to transport mechanics, it is necessary to remove the time over which the fluid stress is
NASA Astrophysics Data System (ADS)
Sharma, Pankaj; Jain, Ajai
2014-12-01
Stochastic dynamic job shop scheduling problem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatching rules in such shop from makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures viewpoint. A discrete event simulation model of a stochastic dynamic job shop manufacturing system is developed for investigation purpose. Nine dispatching rules identified from literature are incorporated in the simulation model. The simulation experiments are conducted under due date tightness factor of 3, shop utilization percentage of 90% and setup times less than processing times. Results indicate that shortest setup time (SIMSET) rule provides the best performance for mean flow time and number of tardy jobs measures. The job with similar setup and modified earliest due date (JMEDD) rule provides the best performance for makespan, maximum flow time, mean tardiness, maximum tardiness, total setups and mean setup time measures.
Stochastic Convection Parameterizations
NASA Technical Reports Server (NTRS)
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
NASA Astrophysics Data System (ADS)
Hacıefendioğlu, K.
2012-04-01
The deconvolution effect of the near-fault earthquake ground motions on the stochastic dynamic response of tunnel-soil deposit interaction systems are investigated by using the finite element method. Two different earthquake input mechanisms are used to consider the deconvolution effects in the analyses: the standard rigid-base input and the deconvolved-base-rock input model. The Bolu tunnel in Turkey is chosen as a numerical example. As near-fault ground motions, 1999 Kocaeli earthquake ground motion is selected. The interface finite elements are used between tunnel and soil deposit. The mean of maximum values of quasi-static, dynamic and total responses obtained from the two input models are compared with each other.
NASA Astrophysics Data System (ADS)
Johnson, Todd; Bartol, Tom; Sejnowski, Terrence; Mjolsness, Eric
2015-07-01
A stochastic reaction network model of Ca2+ dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, ‘graph-constrained correlation dynamics’, requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice.
NASA Astrophysics Data System (ADS)
Guo, Kongming; Jiang, Jun; Xu, Yalan
2016-09-01
In this paper, a simple but accurate semi-analytical method to approximate probability density function of stochastic closed curve attractors is proposed. The expression of distribution applies to systems with strong nonlinearities, while only weak noise condition is needed. With the understanding that additive noise does not change the longitudinal distribution of the attractors, the high-dimensional probability density distribution is decomposed into two low-dimensional distributions: the longitudinal and the transverse probability density distributions. The longitudinal distribution can be calculated from the deterministic systems, while the probability density in the transverse direction of the curve can be approximated by the stochastic sensitivity function method. The effectiveness of this approach is verified by comparing the expression of distribution with the results of Monte Carlo numerical simulations in several planar systems.
Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics
Strehl, Robert; Ilie, Silvana
2015-12-21
In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.
Forgoston, Eric; Billings, Lora; Yecko, Philip; Schwartz, Ira B.
2011-01-01
We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets by computing regions of uncertainty, almost invariant sets, and Lagrangian coherent structures. The combination of geometric and probabilistic methods allows us to design regions of control, which provide an increase in loitering time while minimizing the amount of control actuation. We show how the loitering time in almost invariant sets scales exponentially with respect to the control actuation, causing an exponential increase in loitering times with only small changes in actuation force. The result is that the control actuation makes almost invariant sets more invariant. PMID:21456830
The stochastic evolution of a protocell: the Gillespie algorithm in a dynamically varying volume.
Carletti, T; Filisetti, A
2012-01-01
We propose an improvement of the Gillespie algorithm allowing us to study the time evolution of an ensemble of chemical reactions occurring in a varying volume, whose growth is directly related to the amount of some specific molecules, belonging to the reactions set. This allows us to study the stochastic evolution of a protocell, whose volume increases because of the production of container molecules. Several protocell models are considered and compared with the deterministic models. PMID:22536297
NASA Astrophysics Data System (ADS)
Kim, Hee Y.; Jureller, Justin E.; Kuznetsov, Andrey; Philipson, Louis H.; Scherer, Norbert F.
2008-02-01
Elucidating the mechanisms of insulin granule trafficking in pancreatic β-cells is a critical step in understanding Type II Diabetes and abnormal insulin secretion. In this paper, rapid-sampling stochastic scanning multiphoton multifocal microscopy (SS-MMM) was developed to capture fast insulin granule dynamics in vivo. Stochastic scanning of (a diffractive optic generated) 10×10 hexagonal array of foci with a galvanometer yields a uniformly sampled image with fewer spatio-temporal artifacts than obtained by conventional or multibeam raster scanning. In addition, segmented spatio-temporal image correlation spectroscopy (Segmented STICS) was developed to extract dynamics of insulin granules from the image sequences. Measurements we conducted on MIN6 cells, which exhibit an order of magnitude lower granule number density, allow comparison of particle tracking with Segmented-STICS. Segmentation of the images into 8×8 pixel segments (similar to a size of one granule) allows some amount of spatial averaging, which can reduce the computation time required to calculate the correlation function, yet retains information about the local spatial heterogeneity of transport. This allows the correlation analysis to quantify the dynamics within each of the segments producing a "map" of the localized properties of the cell. The results obtained from Segmented STICS are compared with dynamics determined from particle tracking analysis of the same images. The resulting range of diffusion coefficients of insulin granules are comparable to previously published values indicating that SS-MMM and segmented- STICS will be useful to address the imaging challenges presented by β-cells, particularly the extremely large number density of granules.
Developing stochastic model of thrust and flight dynamics for small UAVs
NASA Astrophysics Data System (ADS)
Tjhai, Chandra
This thesis presents a stochastic thrust model and aerodynamic model for small propeller driven UAVs whose power plant is a small electric motor. First a model which relates thrust generated by a small propeller driven electric motor as a function of throttle setting and commanded engine RPM is developed. A perturbation of this model is then used to relate the uncertainty in throttle and engine RPM commanded to the error in the predicted thrust. Such a stochastic model is indispensable in the design of state estimation and control systems for UAVs where the performance requirements of the systems are specied in stochastic terms. It is shown that thrust prediction models for small UAVs are not a simple, explicit functions relating throttle input and RPM command to thrust generated. Rather they are non-linear, iterative procedures which depend on a geometric description of the propeller and mathematical model of the motor. A detailed derivation of the iterative procedure is presented and the impact of errors which arise from inaccurate propeller and motor descriptions are discussed. Validation results from a series of wind tunnel tests are presented. The results show a favorable statistical agreement between the thrust uncertainty predicted by the model and the errors measured in the wind tunnel. The uncertainty model of aircraft aerodynamic coefficients developed based on wind tunnel experiment will be discussed at the end of this thesis.
Asymptotically exact analysis of stochastic metapopulation dynamics with explicit spatial structure.
Ovaskainen, Otso; Cornell, Stephen J
2006-02-01
We describe a mathematically exact method for the analysis of spatially structured Markov processes. The method is based on a systematic perturbation expansion around the deterministic, non-spatial mean-field theory, using the theory of distributions to account for space and the underlying stochastic differential equations to account for stochasticity. As an example, we consider a spatial version of the Levins metapopulation model, in which the habitat patches are distributed in the d-dimensional landscape Rd in a random (but possibly correlated) manner. Assuming that the dispersal kernel is characterized by a length scale L, we examine how the behavior of the metapopulation deviates from the mean-field model for a finite but large L. For example, we show that the equilibrium fraction of occupied patches is given by p(0)+c/L(d)+O(L(-3d/2)), where p(0) is the equilibrium state of the Levins model and the constant c depends on p(0), the dispersal kernel, and the structure of the landscape. We show that patch occupancy can be increased or decreased by spatial structure, but is always decreased by stochasticity. Comparison with simulations show that the analytical results are not only asymptotically exact (as L-->infinity), but a good approximation also when L is relatively small. PMID:16246386
A stochastic model for magnetic dynamics in single-molecule magnets
NASA Astrophysics Data System (ADS)
López-Ruiz, R.; Almeida, P. T.; Vaz, M. G. F.; Novak, M. A.; Béron, F.; Pirota, K. R.
2016-04-01
Hysteresis and magnetic relaxation curves were performed on double well potential systems with quantum tunneling possibility via stochastic simulations. Simulation results are compared with experimental ones using the Mn12 single-molecule magnet, allowing us to introduce time dependence in the model. Despite being a simple simulation model, it adequately reproduces the phenomenology of a thermally activated quantum tunneling and can be extended to other systems with different parameters. Assuming competition between the reversal modes, thermal (over) and tunneling (across) the anisotropy barrier, a separation of classical and quantum contributions to relaxation time can be obtained.
NASA Astrophysics Data System (ADS)
Yu, Zhaoxu; Li, Shugang; Li, Fangfei
2016-01-01
The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.
NASA Astrophysics Data System (ADS)
Milovanov, Alexander V.
2001-04-01
The formulation of the fractional Fokker-Planck-Kolmogorov (FPK) equation [Physica D 76, 110 (1994)] has led to important advances in the description of the stochastic dynamics of Hamiltonian systems. Here, the long-time behavior of the basic transport processes obeying the fractional FPK equation is analyzed. A derivation of the large-scale turbulent transport coefficient for a Hamiltonian system with 112 degrees of freedom is proposed in connection with the fractal structure of the particle chaotic trajectories. The principal transport regimes (i.e., a diffusion-type process, ballistic motion, subdiffusion in the limit of the frozen Hamiltonian, and behavior associated with self-organized criticality) are obtained as partial cases of the generalized transport law. A comparison with recent numerical and experimental studies is given.
Milovanov, A V
2001-04-01
The formulation of the fractional Fokker-Planck-Kolmogorov (FPK) equation [Physica D 76, 110 (1994)] has led to important advances in the description of the stochastic dynamics of Hamiltonian systems. Here, the long-time behavior of the basic transport processes obeying the fractional FPK equation is analyzed. A derivation of the large-scale turbulent transport coefficient for a Hamiltonian system with 11 / 2 degrees of freedom is proposed in connection with the fractal structure of the particle chaotic trajectories. The principal transport regimes (i.e., a diffusion-type process, ballistic motion, subdiffusion in the limit of the frozen Hamiltonian, and behavior associated with self-organized criticality) are obtained as partial cases of the generalized transport law. A comparison with recent numerical and experimental studies is given. PMID:11308983
NASA Astrophysics Data System (ADS)
Palombi, Filippo; Toti, Simona
2014-07-01
The stochastic dynamics of the multi-state voter model is investigated on a class of complex networks made of non-overlapping cliques, each hosting a political candidate and interacting with the others via Erdős-Rényi links. Numerical simulations of the model are interpreted in terms of an ad-hoc mean field theory, specifically tuned to resolve the inter/intra-clique interactions. Under a proper definition of the thermodynamic limit (with the average degree of the agents kept fixed while increasing the network size), the model is found to display the empirical scaling discovered by Fortunato and Castellano (Phys Rev Lett 99(13):138701, 2007) , while the vote distribution resembles roughly that observed in Brazilian elections.
Technology Transfer Automated Retrieval System (TEKTRAN)
The objective of this study was to develop a daily stochastic dynamic dairy simulation model which included multi-trait genetics, and to evaluate the effects of various reproduction and selection strategies on the genetic, technical and financial performance of a dairy herd. The 12 correlated geneti...
NASA Astrophysics Data System (ADS)
Raso, Luciano; Dorchies, David; Malaterre, Pierre-Olivier
2015-04-01
We developed an Objective Oriented Programming (OOP) tool for optimal management of complex water systems by use of Stochastic Dual Dynamic Programming (SDDP). OOP is a powerful programming paradigm. OOP minimizes code redundancies, making code modification and maintenance very effective. This is especially welcome in research, in which, often, code must be modified to meet new requirements that were not initially considered. SDDP is an advanced method for optimal operation of complex dynamic systems under uncertainty. SDDP can deal with large and complex systems, such as a multi-reservoir system. The objective of this tool is making SDDP usable for Water Management Analysts. Thanks to this tool, the Analyst can bypass the SDDP programming complexity, and his/her task is simplified to the definition of system elements, topology and objectives, and experiments characteristics. In this tool, the main classes are: Experiment, System, Element, and Objective. Experiments are run on a system. A system is made of many elements interconnected among them. Class Element is made of the following sub-classes: (stochastic) hydrological scenario, (deterministic) water demand scenario, reservoir, river reach, off-take, and irrigation basin. Objectives are used in the optimization procedure to find the optimal operational rules, for a given system and experiment. OOP flexibility allows the Water Management Analyst to extend easily existing classes in order to answer his/her specific research questions. The tool is implemented in Python, and will be initially tested on two applications: the Senegal River water system, in West Africa, and the Seine River, in France.
Bidirectional Classical Stochastic Processes with Measurements and Feedback
NASA Technical Reports Server (NTRS)
Hahne, G. E.
2005-01-01
A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.
NASA Astrophysics Data System (ADS)
Vardaci, E.; Nadtochy, P. N.; Di Nitto, A.; Brondi, A.; La Rana, G.; Moro, R.; Rath, P. K.; Ashaduzzaman, M.; Kozulin, E. M.; Knyazheva, G. N.; Itkis, I. M.; Cinausero, M.; Prete, G.; Fabris, D.; Montagnoli, G.; Gelli, N.
2015-09-01
The system of intermediate fissility 132Ce has been studied experimentally and theoretically to investigate the dissipation properties of nuclear matter. Cross sections of fusion-fission and evaporation-residue channels together with light charged particle multiplicities in both channels, their spectra, light charged particle-evaporation residue angular correlations, and mass-energy distribution of fission fragments have been measured. Theoretical analysis has been performed using a multidimensional stochastic approach coupled with a Hauser-Feshbach treatment of particle evaporation. The main conclusions are that the full one-body shape-dependent dissipation mechanism allows the reproduction of the full set of experimental data and that after a time τd=5 ×10-21 s from the equilibrium configuration of the compound nucleus, fission decay can occur in a time that can span several orders of magnitude.
NASA Astrophysics Data System (ADS)
Wu, Zhizhang; Huang, Zhongyi
2016-07-01
In this paper, we consider the numerical solution of the one-dimensional Schrödinger equation with a periodic lattice potential and a random external potential. This is an important model in solid state physics where the randomness results from complicated phenomena that are not exactly known. Here we generalize the Bloch decomposition-based time-splitting pseudospectral method to the stochastic setting using the generalized polynomial chaos with a Galerkin procedure so that the main effects of dispersion and periodic potential are still computed together. We prove that our method is unconditionally stable and numerical examples show that it has other nice properties and is more efficient than the traditional method. Finally, we give some numerical evidence for the well-known phenomenon of Anderson localization.
Asymptotically optimal production policies in dynamic stochastic jobshops with limited buffers
NASA Astrophysics Data System (ADS)
Hou, Yumei; Sethi, Suresh P.; Zhang, Hanqin; Zhang, Qing
2006-05-01
We consider a production planning problem for a jobshop with unreliable machines producing a number of products. There are upper and lower bounds on intermediate parts and an upper bound on finished parts. The machine capacities are modelled as finite state Markov chains. The objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production. Finding an optimal control policy for this problem is difficult. Instead, we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity. The asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities. The value function for the original problem is shown to converge to the value function of the limiting problem. The convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established.
Stochasticity enhances the gaining of bet-hedging strategies in contact-process-like dynamics.
Hidalgo, Jorge; Pigolotti, Simone; Muñoz, Miguel A
2015-03-01
In biology and ecology, individuals or communities of individuals living in unpredictable environments often alternate between different evolutionary strategies to spread and reduce risks. Such behavior is commonly referred to as "bet-hedging." Long-term survival probabilities and population sizes can be much enhanced by exploiting such hybrid strategies. Here, we study the simplest possible birth-death stochastic model in which individuals can choose among a poor but safe strategy, a better but risky alternative, or a combination of both. We show analytically and computationally that the benefits derived from bet-hedging strategies are much stronger for higher environmental variabilities (large external noise) and/or for small spatial dimensions (large intrinsic noise). These circumstances are typically encountered by living systems, thus providing us with a possible justification for the ubiquitousness of bet-hedging in nature. PMID:25871061
Dynamic phasing of multichannel cw laser radiation by means of a stochastic gradient algorithm
Volkov, V A; Volkov, M V; Garanin, S G; Dolgopolov, Yu V; Kopalkin, A V; Kulikov, S M; Starikov, F A; Sukharev, S A; Tyutin, S V; Khokhlov, S V; Chaparin, D A
2013-09-30
The phasing of a multichannel laser beam by means of an iterative stochastic parallel gradient (SPG) algorithm has been numerically and experimentally investigated. The operation of the SPG algorithm is simulated, the acceptable range of amplitudes of probe phase shifts is found, and the algorithm parameters at which the desired Strehl number can be obtained with a minimum number of iterations are determined. An experimental bench with phase modulators based on lithium niobate, which are controlled by a multichannel electronic unit with a real-time microcontroller, has been designed. Phasing of 16 cw laser beams at a system response bandwidth of 3.7 kHz and phase thermal distortions in a frequency band of about 10 Hz is experimentally demonstrated. The experimental data are in complete agreement with the calculation results. (control of laser radiation parameters)
NASA Astrophysics Data System (ADS)
Nagel, Hannes; Janke, Wolfhard
2016-05-01
Driven diffusive systems such as the zero-range process (ZRP) and the pair-factorized steady states (PFSS) stochastic transport process are versatile tools that lend themselves to the study of transport phenomena on a generic level. While their mathematical structure is simple enough to allow significant analytical treatment, they offer a variety of interesting phenomena. With appropriate dynamics, the ZRP and PFSS models feature a condensation transition where, for a supercritical density, the translational symmetry breaks spontaneously and excess particles form a single-site or spatially extended condensate, respectively. In this paper we numerically study the typical time scales of the two stages of this condensation process: Nucleation and coarsening. Nucleation is the first stage of condensation where the bulk system relaxes to its stationary distribution and droplet nuclei form in the system. These droplets then gradually grow or evaporate in the coarsening regime to coalesce in a single condensate when the system finally relaxes to the stationary state. We use the ZRP condensation model to discuss the choice of the estimation method for the nucleation time scale and present scaling exponents for the ZRP and PFSS condensation models with respect to the choice of the typical droplet nuclei mass. We then proceed to present scaling exponents in the coarsening regime of the ZRP for partially asymmetric dynamics and the PFSS model for symmetric and asymmetric dynamics.
Strong ground-motion prediction from Stochastic-dynamic source models
Guatteri, Mariagiovanna; Mai, P.M.; Beroza, G.C.; Boatwright, J.
2003-01-01
In the absence of sufficient data in the very near source, predictions of the intensity and variability of ground motions from future large earthquakes depend strongly on our ability to develop realistic models of the earthquake source. In this article we simulate near-fault strong ground motion using dynamic source models. We use a boundary integral method to simulate dynamic rupture of earthquakes by specifying dynamic source parameters (fracture energy and stress drop) as spatial random fields. We choose these quantities such that they are consistent with the statistical properties of slip heterogeneity found in finite-source models of past earthquakes. From these rupture models we compute theoretical strong-motion seismograms up to a frequency of 2 Hz for several realizations of a scenario strike-slip Mw 7.0 earthquake and compare empirical response spectra, spectra obtained from our dynamic models, and spectra determined from corresponding kinematic simulations. We find that spatial and temporal variations in slip, slip rise time, and rupture propagation consistent with dynamic rupture models exert a strong influence on near-source ground motion. Our results lead to a feasible approach to specify the variability in the rupture time distribution in kinematic models through a generalization of Andrews' (1976) result relating rupture speed to apparent fracture energy, stress drop, and crack length to 3D dynamic models. This suggests that a simplified representation of dynamic rupture may be obtained to approximate the effects of dynamic rupture without having to do full dynamic simulations.
NASA Astrophysics Data System (ADS)
Serva, Federico; Cagnazzo, Chiara; Riccio, Angelo
2016-04-01
version of the model, the default and a new stochastic version, in which the value of the perturbation field at launching level is not constant and uniform, but extracted at each time-step and grid-point from a given PDF. With this approach we are trying to add further variability to the effects given by the deterministic NOGW parameterization: the impact on the simulated climate will be assessed focusing on the Quasi-Biennial Oscillation of the equatorial stratosphere (known to be driven also by gravity waves) and on the variability of the mid-to-high latitudes atmosphere. The different characteristics of the circulation will be compared with recent reanalysis products in order to determine the advantages of the stochastic approach over the traditional deterministic scheme.
Lecca, Paola; Ihekwaba, Adaoha E C; Dematté, Lorenzo; Priami, Corrado
2010-01-01
Reaction-diffusion systems are mathematical models that describe how the concentrations of substances distributed in space change under the influence of local chemical reactions, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose solution predicts how diffusion causes the concentration field to change with time. This change is proportional to the diffusion coefficient. If the solute moves in a homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and solute. However, in nonhomogeneous and structured media the assumption of constant intracellular diffusion coefficient is not necessarily valid, and, consequently, the diffusion coefficient is a function of the local concentration of solvent and solutes. In this paper we propose a stochastic model of reaction-diffusion systems, in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces. We then describe the software tool Redi (REaction-DIffusion simulator) which we have developed in order to implement this model into a Gillespie-like stochastic simulation algorithm. Finally, we show the ability of our model implemented in the Redi tool to reproduce the observed gradient of the bicoid protein in the Drosophila Melanogaster embryo. With Redi, we were able to simulate with an accuracy of 1% the experimental spatio-temporal dynamics of the bicoid protein, as recorded in time-lapse experiments obtained by direct measurements of transgenic bicoidenhanced green fluorescent protein. PMID:21098882
Fouchet, David; Leblanc, Guillaume; Sauvage, Frank; Guiserix, Micheline; Poulet, Hervé; Pontier, Dominique
2009-01-01
Background In natural cat populations, Feline Immunodeficiency Virus (FIV) is transmitted through bites between individuals. Factors such as the density of cats within the population or the sex-ratio can have potentially strong effects on the frequency of fight between individuals and hence appear as important population risk factors for FIV. Methodology/Principal Findings To study such population risk factors, we present data on FIV prevalence in 15 cat populations in northeastern France. We investigate five key social factors of cat populations; the density of cats, the sex-ratio, the number of males and the mean age of males and females within the population. We overcome the problem of dependence in the infective status data using sexually-structured dynamic stochastic models. Only the age of males and females had an effect (p = 0.043 and p = 0.02, respectively) on the male-to-female transmission rate. Due to multiple tests, it is even likely that these effects are, in reality, not significant. Finally we show that, in our study area, the data can be explained by a very simple model that does not invoke any risk factor. Conclusion Our conclusion is that, in host-parasite systems in general, fluctuations due to stochasticity in the transmission process are naturally very large and may alone explain a larger part of the variability in observed disease prevalence between populations than previously expected. Finally, we determined confidence intervals for the simple model parameters that can be used to further aid in management of the disease. PMID:19888418
NASA Astrophysics Data System (ADS)
Salehi Fashami, Mohammad; Atulasimha, Jayasimha; Bandyopadhyay, Supriyo
2013-03-01
Straintronic nanomagnetic logic (SML), where Boolean computation is elicited from dipole coupled multiferroic nanomagnets switched with electrically generated strain, has emerged as an extremely energy-efficient computing paradigm. We have studied the reliability of such logic circuits by computing the gate error rates in the presence of thermal noise by simulating switching trajectories with the stochastic Landau-Lifshitz-Gilbert (LLG) equation. In addition, we examine the lower bound of energy dissipation as a function of switching error and explain how the out-of-plane excursion of the magnetization vector leads to excess energy dissipation over this bound for a given switching error. This analysis is performed to understand the connection between reliability and energy dissipation for a single switch and then extended to larger nanomagnetic logic circuits to assess the viability of dipole coupled SML. This work is supported by the US National Science Foundation under the SHF-Small grant CCF-1216614, NEB 2020 grant ECCS-1124714 and by the Semiconductor Research Corporation (SRC) under NRI Task 2203.001.
Benedek, C; Descombes, X; Zerubia, J
2012-01-01
In this paper, we introduce a new probabilistic method which integrates building extraction with change detection in remotely sensed image pairs. A global optimization process attempts to find the optimal configuration of buildings, considering the observed data, prior knowledge, and interactions between the neighboring building parts. We present methodological contributions in three key issues: 1) We implement a novel object-change modeling approach based on Multitemporal Marked Point Processes, which simultaneously exploits low-level change information between the time layers and object-level building description to recognize and separate changed and unaltered buildings. 2) To answer the challenges of data heterogeneity in aerial and satellite image repositories, we construct a flexible hierarchical framework which can create various building appearance models from different elementary feature-based modules. 3) To simultaneously ensure the convergence, optimality, and computation complexity constraints raised by the increased data quantity, we adopt the quick Multiple Birth and Death optimization technique for change detection purposes, and propose a novel nonuniform stochastic object birth process which generates relevant objects with higher probability based on low-level image features. PMID:21576749
Critical Dynamics in the Evolution of Stochastic Strategies for the Iterated Prisoner's Dilemma
Adami, Christoph
2010-01-01
The observed cooperation on the level of genes, cells, tissues, and individuals has been the object of intense study by evolutionary biologists, mainly because cooperation often flourishes in biological systems in apparent contradiction to the selfish goal of survival inherent in Darwinian evolution. In order to resolve this paradox, evolutionary game theory has focused on the Prisoner's Dilemma (PD), which incorporates the essence of this conflict. Here, we encode strategies for the iterated Prisoner's Dilemma (IPD) in terms of conditional probabilities that represent the response of decision pathways given previous plays. We find that if these stochastic strategies are encoded as genes that undergo Darwinian evolution, the environmental conditions that the strategies are adapting to determine the fixed point of the evolutionary trajectory, which could be either cooperation or defection. A transition between cooperative and defective attractors occurs as a function of different parameters such as mutation rate, replacement rate, and memory, all of which affect a player's ability to predict an opponent's behavior. These results imply that in populations of players that can use previous decisions to plan future ones, cooperation depends critically on whether the players can rely on facing the same strategies that they have adapted to. Defection, on the other hand, is the optimal adaptive response in environments that change so quickly that the information gathered from previous plays cannot usefully be integrated for a response. PMID:20949101
NASA Astrophysics Data System (ADS)
Song, Jiyun; Wang, Zhi-Hua
2016-05-01
Urban land-atmosphere interactions can be captured by numerical modeling framework with coupled land surface and atmospheric processes, while the model performance depends largely on accurate input parameters. In this study, we use an advanced stochastic approach to quantify parameter uncertainty and model sensitivity of a coupled numerical framework for urban land-atmosphere interactions. It is found that the development of urban boundary layer is highly sensitive to surface characteristics of built terrains. Changes of both urban land use and geometry impose significant impact on the overlying urban boundary layer dynamics through modification on bottom boundary conditions, i.e., by altering surface energy partitioning and surface aerodynamic resistance, respectively. Hydrothermal properties of conventional and green roofs have different impacts on atmospheric dynamics due to different surface energy partitioning mechanisms. Urban geometry (represented by the canyon aspect ratio), however, has a significant nonlinear impact on boundary layer structure and temperature. Besides, managing rooftop roughness provides an alternative option to change the boundary layer thermal state through modification of the vertical turbulent transport. The sensitivity analysis deepens our insight into the fundamental physics of urban land-atmosphere interactions and provides useful guidance for urban planning under challenges of changing climate and continuous global urbanization.
NASA Astrophysics Data System (ADS)
Taneri, Sencer
We investigate the folding dynamics of the plant-seed protein Crambin in a liquid environment, that usually happens to be water with some certain viscosity. To take into account the viscosity, necessitates a stochastic approach. This can be summarized by a 2D-Langevin equation, even though the simulation is still carried out in 3D. Solution of the Langevin equation will be the basic task in order to proceed with a Molecular Dynamics simulation, which will accompany a delicate Monte Carlo technique. The potential wells, used to engineer the energy space assuming the interaction of monomers constituting the protein-chain, are simply modeled by a combination of two parabola. This combination will approximate the real physical interactions, that is given by the well known Lennard-Jones potential. Contributions to the total potential from torsion, bending and distance dependent potentials are good to the fourth nearest neighbor. The final image is in a very good geometric agreement with the real shape of the protein chain, which can be obtained from the protein data bank. The quantitative measure of this agreement is the similarity parameter with the native structure, which is found to be 0.91 < 1 for the best sample. The folding time can be determined from Debye-relaxation process. We apply two regimes and calculate the folding time, corresponding to the elastic domain mode, which yields 5.2 ps for the same sample.
NASA Astrophysics Data System (ADS)
Xu, Jun; Li, Jie
2016-05-01
Viscoelastic dampers, where fractional derivatives are involved, are often considered for use to mitigate dynamic response of structures. However, it is not an easy task to obtain the probabilistic dynamic response and the reliability of controlled structures with fractional terms. For this purpose, an efficient methodology based on the probability density evolution method is proposed, where the generalized density evolution equation is present to capture the instantaneous probabilistic dynamic response and the dynamic reliability can be evaluated from the standpoint of probability dissipation. Numerical solution is of practical necessity, where a deterministic procedure to solve the equation of motion with fractional derivatives is embedded. Therefore, the precise integration method (PIM) is extended to numerically integrate the equation of motion with fractional terms, which offers high accuracy. The numerical results verify the effectiveness of the advocated methodology, but also indicate the viscoelastic dampers can enhance the seismic performance of structures significantly.
A framework for stochastic simulations and visualization of biological electron-transfer dynamics
NASA Astrophysics Data System (ADS)
Nakano, C. Masato; Byun, Hye Suk; Ma, Heng; Wei, Tao; El-Naggar, Mohamed Y.
2015-08-01
Electron transfer (ET) dictates a wide variety of energy-conversion processes in biological systems. Visualizing ET dynamics could provide key insight into understanding and possibly controlling these processes. We present a computational framework named VizBET to visualize biological ET dynamics, using an outer-membrane Mtr-Omc cytochrome complex in Shewanella oneidensis MR-1 as an example. Starting from X-ray crystal structures of the constituent cytochromes, molecular dynamics simulations are combined with homology modeling, protein docking, and binding free energy computations to sample the configuration of the complex as well as the change of the free energy associated with ET. This information, along with quantum-mechanical calculations of the electronic coupling, provides inputs to kinetic Monte Carlo (KMC) simulations of ET dynamics in a network of heme groups within the complex. Visualization of the KMC simulation results has been implemented as a plugin to the Visual Molecular Dynamics (VMD) software. VizBET has been used to reveal the nature of ET dynamics associated with novel nonequilibrium phase transitions in a candidate configuration of the Mtr-Omc complex due to electron-electron interactions.
A stochastic chemical dynamic approach to correlate autoimmunity and optimal vitamin-D range.
Roy, Susmita; Shrinivas, Krishna; Bagchi, Biman
2014-01-01
Motivated by several recent experimental observations that vitamin-D could interact with antigen presenting cells (APCs) and T-lymphocyte cells (T-cells) to promote and to regulate different stages of immune response, we developed a coarse grained but general kinetic model in an attempt to capture the role of vitamin-D in immunomodulatory responses. Our kinetic model, developed using the ideas of chemical network theory, leads to a system of nine coupled equations that we solve both by direct and by stochastic (Gillespie) methods. Both the analyses consistently provide detail information on the dependence of immune response to the variation of critical rate parameters. We find that although vitamin-D plays a negligible role in the initial immune response, it exerts a profound influence in the long term, especially in helping the system to achieve a new, stable steady state. The study explores the role of vitamin-D in preserving an observed bistability in the phase diagram (spanned by system parameters) of immune regulation, thus allowing the response to tolerate a wide range of pathogenic stimulation which could help in resisting autoimmune diseases. We also study how vitamin-D affects the time dependent population of dendritic cells that connect between innate and adaptive immune responses. Variations in dose dependent response of anti-inflammatory and pro-inflammatory T-cell populations to vitamin-D correlate well with recent experimental results. Our kinetic model allows for an estimation of the range of optimum level of vitamin-D required for smooth functioning of the immune system and for control of both hyper-regulation and inflammation. Most importantly, the present study reveals that an overdose or toxic level of vitamin-D or any steroid analogue could give rise to too large a tolerant response, leading to an inefficacy in adaptive immune function. PMID:24971516
NASA Astrophysics Data System (ADS)
Cottrell, Paul Edward
There is a lack of research in the area of hedging future contracts, especially in illiquid or very volatile market conditions. It is important to understand the volatility of the oil and currency markets because reduced fluctuations in these markets could lead to better hedging performance. This study compared different hedging methods by using a hedging error metric, supplementing the Receding Horizontal Control and Stochastic Programming (RHCSP) method by utilizing the London Interbank Offered Rate with the Levy process. The RHCSP hedging method was investigated to determine if improved hedging error was accomplished compared to the Black-Scholes, Leland, and Whalley and Wilmott methods when applied on simulated, oil, and currency futures markets. A modified RHCSP method was also investigated to determine if this method could significantly reduce hedging error under extreme market illiquidity conditions when applied on simulated, oil, and currency futures markets. This quantitative study used chaos theory and emergence for its theoretical foundation. An experimental research method was utilized for this study with a sample size of 506 hedging errors pertaining to historical and simulation data. The historical data were from January 1, 2005 through December 31, 2012. The modified RHCSP method was found to significantly reduce hedging error for the oil and currency market futures by the use of a 2-way ANOVA with a t test and post hoc Tukey test. This study promotes positive social change by identifying better risk controls for investment portfolios and illustrating how to benefit from high volatility in markets. Economists, professional investment managers, and independent investors could benefit from the findings of this study.
Numerical analysis for finite-range multitype stochastic contact financial market dynamic systems
NASA Astrophysics Data System (ADS)
Yang, Ge; Wang, Jun; Fang, Wen
2015-04-01
In an attempt to reproduce and study the dynamics of financial markets, a random agent-based financial price model is developed and investigated by the finite-range multitype contact dynamic system, in which the interaction and dispersal of different types of investment attitudes in a stock market are imitated by viruses spreading. With different parameters of birth rates and finite-range, the normalized return series are simulated by Monte Carlo simulation method and numerical studied by power-law distribution analysis and autocorrelation analysis. To better understand the nonlinear dynamics of the return series, a q-order autocorrelation function and a multi-autocorrelation function are also defined in this work. The comparisons of statistical behaviors of return series from the agent-based model and the daily historical market returns of Shanghai Composite Index and Shenzhen Component Index indicate that the proposed model is a reasonable qualitative explanation for the price formation process of stock market systems.
Numerical analysis for finite-range multitype stochastic contact financial market dynamic systems
Yang, Ge; Wang, Jun; Fang, Wen
2015-04-15
In an attempt to reproduce and study the dynamics of financial markets, a random agent-based financial price model is developed and investigated by the finite-range multitype contact dynamic system, in which the interaction and dispersal of different types of investment attitudes in a stock market are imitated by viruses spreading. With different parameters of birth rates and finite-range, the normalized return series are simulated by Monte Carlo simulation method and numerical studied by power-law distribution analysis and autocorrelation analysis. To better understand the nonlinear dynamics of the return series, a q-order autocorrelation function and a multi-autocorrelation function are also defined in this work. The comparisons of statistical behaviors of return series from the agent-based model and the daily historical market returns of Shanghai Composite Index and Shenzhen Component Index indicate that the proposed model is a reasonable qualitative explanation for the price formation process of stock market systems.
NASA Astrophysics Data System (ADS)
Bouzat, Sebastián
2016-01-01
One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.
Bouzat, Sebastián
2016-01-01
One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models. PMID:26871095
Stochastic aspects of one-dimensional discrete dynamical systems: Benford's law
NASA Astrophysics Data System (ADS)
Snyder, Mark A.; Curry, James H.; Dougherty, Anne M.
2001-08-01
Benford's law owes its discovery to the ``Grubby Pages Hypothesis,'' a 19th century observation made by Simon Newcomb that the beginning pages of logarithm books were grubbier than the last few pages, implying that scientists referenced the values toward the front of the books more frequently. If a data set satisfies Benford's law, then it's significant digits will have a logarithmic distribution, which favors smaller significant digits. In this article we demonstrate two ways of creating discrete one-dimensional dynamical systems that satisfy Benford's law. We also develop a numerical simulation methodology that we use to study dynamical systems when analytical results are not readily available.
Stochastic aspects of one-dimensional discrete dynamical systems: Benford's law.
Snyder, M A; Curry, J H; Dougherty, A M
2001-08-01
Benford's law owes its discovery to the "Grubby Pages Hypothesis," a 19th century observation made by Simon Newcomb that the beginning pages of logarithm books were grubbier than the last few pages, implying that scientists referenced the values toward the front of the books more frequently. If a data set satisfies Benford's law, then it's significant digits will have a logarithmic distribution, which favors smaller significant digits. In this article we demonstrate two ways of creating discrete one-dimensional dynamical systems that satisfy Benford's law. We also develop a numerical simulation methodology that we use to study dynamical systems when analytical results are not readily available. PMID:11497692
Henty, Jessica L.; Bledsoe, Samuel W.; Khurana, Parul; Meagher, Richard B.; Day, Brad; Blanchoin, Laurent; Staiger, Christopher J.
2011-01-01
Actin filament arrays are constantly remodeled as the needs of cells change as well as during responses to biotic and abiotic stimuli. Previous studies demonstrate that many single actin filaments in the cortical array of living Arabidopsis thaliana epidermal cells undergo stochastic dynamics, a combination of rapid growth balanced by disassembly from prolific severing activity. Filament turnover and dynamics are well understood from in vitro biochemical analyses and simple reconstituted systems. However, the identification in living cells of the molecular players involved in controlling actin dynamics awaits the use of model systems, especially ones where the power of genetics can be combined with imaging of individual actin filaments at high spatial and temporal resolution. Here, we test the hypothesis that actin depolymerizing factor (ADF)/cofilin contributes to stochastic filament severing and facilitates actin turnover. A knockout mutant for Arabidopsis ADF4 has longer hypocotyls and epidermal cells when compared with wild-type seedlings. This correlates with a change in actin filament architecture; cytoskeletal arrays in adf4 cells are significantly more bundled and less dense than in wild-type cells. Several parameters of single actin filament turnover are also altered. Notably, adf4 mutant cells have a 2.5-fold reduced severing frequency as well as significantly increased actin filament lengths and lifetimes. Thus, we provide evidence that ADF4 contributes to the stochastic dynamic turnover of actin filaments in plant cells. PMID:22010035
Swimming motility plays a key role in the stochastic dynamics of cell clumping
NASA Astrophysics Data System (ADS)
Qi, Xianghong; Nellas, Ricky B.; Byrn, Matthew W.; Russell, Matthew H.; Bible, Amber N.; Alexandre, Gladys; Shen, Tongye
2013-04-01
Dynamic cell-to-cell interactions are a prerequisite to many biological processes, including development and biofilm formation. Flagellum induced motility has been shown to modulate the initial cell-cell or cell-surface interaction and to contribute to the emergence of macroscopic patterns. While the role of swimming motility in surface colonization has been analyzed in some detail, a quantitative physical analysis of transient interactions between motile cells is lacking. We examined the Brownian dynamics of swimming cells in a crowded environment using a model of motorized adhesive tandem particles. Focusing on the motility and geometry of an exemplary motile bacterium Azospirillum brasilense, which is capable of transient cell-cell association (clumping), we constructed a physical model with proper parameters for the computer simulation of the clumping dynamics. By modulating mechanical interaction (‘stickiness’) between cells and swimming speed, we investigated how equilibrium and active features affect the clumping dynamics. We found that the modulation of active motion is required for the initial aggregation of cells to occur at a realistic time scale. Slowing down the rotation of flagellar motors (and thus swimming speeds) is correlated to the degree of clumping, which is consistent with the experimental results obtained for A. brasilense.
Das, Sonjoy; Goswami, Kundan; Datta, Biswa N.
2014-12-10
Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.
Schneider, T.
1986-06-01
Much effort has been devoted to the subjects of dynamic, quantum, and classical critical phenomena, although these research fields developed rather independently. Recently, however, remarkable connections have been established, achieved by using the connection between the time-dependent Ginzburg-Landau equation (TDGL) in d dimensions, describing critical dynamics, and the Fokker-Planck equation. The latter is then reduced to an imaginary-time Schrodinger equation, defining the Hamiltonian of the quantum system, which in turn can be mapped onto a static and classical (d + 1)-dimensional counterpart. Another interesting aspect of these mappings is the simulation of quantum systems in terms of Langevin equations and the construction of quantum systems with soluble ground-state expectative values.
NASA Astrophysics Data System (ADS)
Das, S.; Goswami, K.; Datta, B. N.
2016-05-01
Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of a loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Finally the most robust set of feedback matrices is selected from the set of probabilistically characterized optimal closed-loop system to implement the new methodology for design of active controlled structures. Numerical examples are presented to illustrate the proposed methodology.
NASA Astrophysics Data System (ADS)
Das, Sonjoy; Goswami, Kundan; Datta, Biswa N.
2014-12-01
Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.
Stochastic modeling of the time-averaged equations for climate dynamics
NASA Technical Reports Server (NTRS)
Spreiter, J. R.
1979-01-01
Two analyses on climate dynamics are presented, both based on a simplified set of barotropic equations for representing large scale non-linear atmospheric circulation characteristics. The statistical properties of the set of equations were investigated for small values of a parameter k sub o, corresponding to the physical case of large zonal westerlies and relatively weak eddy motions. The effect of seasonal type forcing on the solution of these equations was also studied and some preliminary numerical results are presented.
Inertial stochastic dynamics. II. Influence of inertia on slow kinetic processes of supercoiled DNA
NASA Astrophysics Data System (ADS)
Beard, Daniel A.; Schlick, Tamar
2000-05-01
We apply our new algorithms presented in the companion paper (LTID: long-time-step inertial dynamics, IBD: inertial Brownian dynamics) for mass-dependent Langevin dynamics (LD) with hydrodynamics, as well as the standard Brownian dynamical (BD) propagator, to study the thermal fluctuations of supercoiled DNA minicircles. Our DNA model accounts for twisting, bending, and salt-screened electrostatic interactions. Though inertial relaxation times are on the order of picoseconds, much slower kinetic processes are affected by the Brownian (noninertial) approximation typically employed. By comparing results of LTID and IBD to those generated using the standard (BD) algorithm, we find that the equilibrium fluctuations in writhing number, Wr, and radius of gyration, Rg, are influenced by mass-dependent terms. The autocorrelation functions for these quantities differ between the BD simulations and the inertial LD simulations by as much as 10%. In contrast, when the nonequilibrium process of relaxation from a perturbed state is examined, all methods (inertial and diffusive) yield similar results with no detectable statistical differences between the mean folding pathways. Thus, while the evolution of an ensemble toward equilibrium is equally well described by the inertial and the noninertial methods, thermal fluctuations are influenced by inertia. Examination of such equilibrium fluctuations in a biologically relevant macroscopic property—namely the two-site intermolecular distance—reveals mass-dependent behavior: The rate of juxtaposition of linearly distant sites along a 1500-base pair DNA plasmid, occurring over time scales of milliseconds and longer, is increased by about 8% when results from IBD are compared to those from BD. Since inertial modes that decay on the picosecond time scale in the absence of thermal forces exert an influence on slower fluctuations in macroscopic properties, we advocate that IBD be used for generating long-time trajectories of supercoiled
NASA Astrophysics Data System (ADS)
Klinkusch, Stefan; Tremblay, Jean Christophe
2016-05-01
In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.
Klinkusch, Stefan; Tremblay, Jean Christophe
2016-05-14
In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN. PMID:27179472
NASA Astrophysics Data System (ADS)
Wen, Xing-Chun; He, Ling-Yun
2015-08-01
There is a bitter controversy over what drives the housing price in China in the existing literature. In this paper, we investigate the underlying driving force behind housing price fluctuations in China, especially focusing on the role of housing demand shock with that of money supply shock in explaining housing price movements, by a new Keynesian dynamic stochastic general equilibrium model. Empirical results suggest that it is housing demand, instead of money supply, that mainly drives China's housing price movements. Relevant policy implication is further discussed, namely, whether to consider the housing price fluctuations in the conduct of monetary policy. By means of the policy simulations, we find that a real house price-augmented money supply rule is a better monetary policy for China's economy stabilization. 1. Investment refers to fixed capital investment. 2. Housing price refers to national average housing price. Quarterly data on housing price during the period of our work are not directly available. However, monthly data of the value of sales on housing and sale volume on housing can be directly obtained from National Bureau of Statistics of China. We add up the monthly data and calculate one quarter's housing price by dividing the value of housing sales by its sale volume in one quarter. 3. M2 means the broad money supply in China.
NASA Astrophysics Data System (ADS)
Thomas, Michael A.; Quinodoz, Sofia; Schötz, Eva-Maria
2012-09-01
Asexual reproduction by division in higher organisms is rare, because a prerequisite is the ability to regenerate an entire organism from a piece of the original body. Freshwater planarians are one of the few animals that can reproduce this way, but little is known about the regulation of their reproduction cycles or strategies. We have previously shown that a planarian's reproduction strategy is randomized to include fragmentations, producing multiple offspring, as well as binary fissions, and can be partially explained by a maximum relative entropy principle. In this study we attempt to decompose the factors controlling their reproduction cycle. Based on recent studies on the cell cycle of budding yeast, which suggest that molecular noise in gene expression and cell size at birth together control cell cycle variability, we investigated whether the variability in planarian reproduction waiting times could be similarly regulated. We find that such a model can indeed explain the observed distribution of waiting times between birth and next reproductive event, suggesting that birth size and a stochastic noise term govern the reproduction dynamics of asexual planarians.
NASA Astrophysics Data System (ADS)
Martin, A.; Pascal, C.; Leconte, R.
2014-12-01
Stochastic Dynamic Programming (SDP) is known to be an effective technique to find the optimal operating policy of hydropower systems. In order to improve the performance of SDP, this project evaluates the impact of re-updating the policy at every time step by using Ensemble Streamflow Prediction (ESP). We present a case study of the Kemano's hydropower system on the Nechako River in British Columbia, Canada. Managed by Rio Tinto Alcan (RTA), this system is subject to large streamflow volumes in spring due to important amount of snow depth during the winter season. Therefore, the operating policy should not only maximize production but also minimize the risk of flooding. The hydrological behavior of the system is simulated with CEQUEAU, a distributed and deterministic hydrological model developed by the Institut national de la recherche scientifique - Eau, Terre et Environnement (INRS-ETE) in Quebec, Canada. On each decision time step, CEQUEAU is used to generate ESP scenarios based on historical meteorological sequences and the current state of the hydrological model. These scenarios are used into the SDP to optimize the new release policy for the next time steps. This routine is then repeated over the entire simulation period. Results are compared with those obtained by using SDP on historical inflow scenarios.
Cirit, Murat; Krajcovic, Matej; Choi, Colin K.; Welf, Erik S.; Horwitz, Alan F.; Haugh, Jason M.
2010-01-01
Productive cell migration requires the spatiotemporal coordination of cell adhesion, membrane protrusion, and actomyosin-mediated contraction. Integrins, engaged by the extracellular matrix (ECM), nucleate the formation of adhesive contacts at the cell's leading edge(s), and maturation of nascent adhesions to form stable focal adhesions constitutes a functional switch between protrusive and contractile activities. To shed additional light on the coupling between integrin-mediated adhesion and membrane protrusion, we have formulated a quantitative model of leading edge dynamics combining mechanistic and phenomenological elements and studied its features through classical bifurcation analysis and stochastic simulation. The model describes in mathematical terms the feedback loops driving, on the one hand, Rac-mediated membrane protrusion and rapid turnover of nascent adhesions, and on the other, myosin-dependent maturation of adhesions that inhibit protrusion at high ECM density. Our results show that the qualitative behavior of the model is most sensitive to parameters characterizing the influence of stable adhesions and myosin. The major predictions of the model, which we subsequently confirmed, are that persistent leading edge protrusion is optimal at an intermediate ECM density, whereas depletion of myosin IIA relieves the repression of protrusion at higher ECM density. PMID:20195494
NASA Astrophysics Data System (ADS)
da Silva, Roberto; Hentz, Agenor; Alves, Alexandre
2015-11-01
In this work we propose a model to describe the fluctuations of self-driven objects (species A) walking against a crowd of particles in the opposite direction (species B) in order to simulate the spatial properties of the particle distribution from a stochastic point of view. Driven by concepts from pedestrian dynamics, in a particular regime known as stop-and-go waves, we propose a particular single-biased random walk (SBRW). This setup is modeled both via partial differential equations (PDE) and by using a probabilistic cellular automaton (PCA) method. The problem is non-interacting until the opposite particles visit the same cell of the target particles, which generates delays on the crossing time that depends on the concentration of particles of opposite species per cell. We analyzed the fluctuations on the position of particles and our results show a non-regular propagation characterized by long-tailed and asymmetric distributions which are better fitted by some chromatograph distributions found in the literature. We also show that effects of the crowd of particles in this situation are able to generate a pattern where we observe a small decrease of the target particle dispersion followed by an increase, differently from the observed straightforward non-interacting case. For a particular initial condition we present an interesting solution via constant density approximation (CDA).
NASA Astrophysics Data System (ADS)
Khatiwala, Samar; Shaw, Bruce E.; Cane, Mark A.
Low-dimensional models can give insight into the climate system, in particular its response to externally imposed forcing such as the anthropogenic emission of green-house gases. Here, we use the Lorenz system, a chaotic dynamical system characterized by two “regimes”, to examine the effect of a weak imposed forcing. We show that the probability density functions (PDF's) of time-spent in the two regimes are exponential, and that the most dramatic response to forcing is a change in the frequency of occurrence of extremely persistent events, rather than the weaker change in the mean persistence time. This enhanced sensitivity of the “tails” of the PDF's to forcing is quantitatively explained by changes in the stability of the regimes. We demonstrate similar behavior in a stochastically forced double well system. Our results suggest that the most significant effect of anthropogenic forcing may be to change the frequency of occurrence of persistent climate events, such as droughts, rather than the mean.
Xi, Yi-Bin; Li, Chen; Cui, Long-Biao; Liu, Jian; Guo, Fan; Li, Liang; Liu, Ting-Ting; Liu, Kang; Chen, Gang; Xi, Min; Wang, Hua-Ning; Yin, Hong
2016-01-01
Familial risk plays a significant role in the etiology of schizophrenia (SZ). Many studies using neuroimaging have demonstrated structural and functional alterations in relatives of SZ patients, with significant results found in diverse brain regions involving the anterior cingulate cortex (ACC), caudate, dorsolateral prefrontal cortex (DLPFC), and hippocampus. This study investigated whether unaffected relatives of first episode SZ differ from healthy controls (HCs) in effective connectivity measures among these regions. Forty-six unaffected first-degree relatives of first episode SZ patients-according to the DSM-IV-were studied. Fifty HCs were included for comparison. All subjects underwent resting state functional magnetic resonance imaging (fMRI). We used stochastic dynamic causal modeling (sDCM) to estimate the directed connections between the left ACC, right ACC, left caudate, right caudate, left DLPFC, left hippocampus, and right hippocampus. We used Bayesian parameter averaging (BPA) to characterize the differences. The BPA results showed hyperconnectivity from the left ACC to right hippocampus and hypoconnectivity from the right ACC to right hippocampus in SZ relatives compared to HCs. The pattern of anterior cingulate cortico-hippocampal connectivity in SZ relatives may be a familial feature of SZ risk, appearing to reflect familial susceptibility for SZ. PMID:27512370
Xi, Yi-Bin; Li, Chen; Cui, Long-Biao; Liu, Jian; Guo, Fan; Li, Liang; Liu, Ting-Ting; Liu, Kang; Chen, Gang; Xi, Min; Wang, Hua-Ning; Yin, Hong
2016-01-01
Familial risk plays a significant role in the etiology of schizophrenia (SZ). Many studies using neuroimaging have demonstrated structural and functional alterations in relatives of SZ patients, with significant results found in diverse brain regions involving the anterior cingulate cortex (ACC), caudate, dorsolateral prefrontal cortex (DLPFC), and hippocampus. This study investigated whether unaffected relatives of first episode SZ differ from healthy controls (HCs) in effective connectivity measures among these regions. Forty-six unaffected first-degree relatives of first episode SZ patients—according to the DSM-IV—were studied. Fifty HCs were included for comparison. All subjects underwent resting state functional magnetic resonance imaging (fMRI). We used stochastic dynamic causal modeling (sDCM) to estimate the directed connections between the left ACC, right ACC, left caudate, right caudate, left DLPFC, left hippocampus, and right hippocampus. We used Bayesian parameter averaging (BPA) to characterize the differences. The BPA results showed hyperconnectivity from the left ACC to right hippocampus and hypoconnectivity from the right ACC to right hippocampus in SZ relatives compared to HCs. The pattern of anterior cingulate cortico-hippocampal connectivity in SZ relatives may be a familial feature of SZ risk, appearing to reflect familial susceptibility for SZ. PMID:27512370
NASA Astrophysics Data System (ADS)
Andrews, Blake M.; Song, Junho; Fahnestock, Larry A.
2009-09-01
Buckling-restrained braces (BRBs) have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame (BRBF) reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that: (1) quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; (2) quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and (3) evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves (i.e., conditional probabilities of brace failure given ground shaking intensity parameters) were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.
NASA Astrophysics Data System (ADS)
Huang, Wen-Cheng; Yuan, Lun-Chin; Lee, Chi-Ming
2002-12-01
The objective of this paper is to present a genetic algorithm-based stochastic dynamic programming (GA-based SDP) to cope with the dimensionality problem of a multiple-reservoir system. The joint long-term operation of a parallel reservoir system in the Feitsui and Shihmen reservoirs in northern Taiwan demonstrates the successful application of the proposed GA-based SDP model. Within the case study system it is believed that GA is a useful technique in supporting optimization. Though the employment of GA-based SDP may be time consuming as it proceeds through generation by generation, the model can overcome the "dimensionality curse" in searching solutions. Simulation results show Feitsui's surplus water can be utilized efficiently to fill Shihmen's deficit water without affecting Feitsui's main purpose as Taipei city's water supply. The optimal joint operation suggests that Feitsui, on average, can provide 650,000 m3/day and 920,000 m3/day to Shihmen during the wet season and dry season, respectively.
Solution of deterministic-stochastic epidemic models by dynamical Monte Carlo method
NASA Astrophysics Data System (ADS)
Aièllo, O. E.; Haas, V. J.; daSilva, M. A. A.; Caliri, A.
2000-07-01
This work is concerned with dynamical Monte Carlo (MC) method and its application to models originally formulated in a continuous-deterministic approach. Specifically, a susceptible-infected-removed-susceptible (SIRS) model is used in order to analyze aspects of the dynamical MC algorithm and achieve its applications in epidemic contexts. We first examine two known approaches to the dynamical interpretation of the MC method and follow with the application of one of them in the SIRS model. The working method chosen is based on the Poisson process where hierarchy of events, properly calculated waiting time between events, and independence of the events simulated, are the basic requirements. To verify the consistence of the method, some preliminary MC results are compared against exact steady-state solutions and other general numerical results (provided by Runge-Kutta method): good agreement is found. Finally, a space-dependent extension of the SIRS model is introduced and treated by MC. The results are interpreted under and in accordance with aspects of the herd-immunity concept.
Numerical analysis for finite-range multitype stochastic contact financial market dynamic systems.
Yang, Ge; Wang, Jun; Fang, Wen
2015-04-01
In an attempt to reproduce and study the dynamics of financial markets, a random agent-based financial price model is developed and investigated by the finite-range multitype contact dynamic system, in which the interaction and dispersal of different types of investment attitudes in a stock market are imitated by viruses spreading. With different parameters of birth rates and finite-range, the normalized return series are simulated by Monte Carlo simulation method and numerical studied by power-law distribution analysis and autocorrelation analysis. To better understand the nonlinear dynamics of the return series, a q-order autocorrelation function and a multi-autocorrelation function are also defined in this work. The comparisons of statistical behaviors of return series from the agent-based model and the daily historical market returns of Shanghai Composite Index and Shenzhen Component Index indicate that the proposed model is a reasonable qualitative explanation for the price formation process of stock market systems. PMID:25933659
NASA Astrophysics Data System (ADS)
Klarenberg, G.
2015-12-01
Infrastructure projects such as road paving have proven to bring a variety of (mainly) socio-economic advantages to countries and populations. However, many studies have also highlighted the negative socio-economic and biophysical effects that these developments have at local, regional and even larger scales. The "MAP" area (Madre de Dios in Peru, Acre in Brazil, and Pando in Bolivia) is a biodiversity hotspot in the southwestern Amazon where sections of South America's Inter-Oceanic Highway were paved between 2006 and 2010. We are interested in vegetation dynamics in the area since it plays an important role in ecosystem functions and ecosystem services in socio-ecological systems: it provides information on productivity and structure of the forest. In preparation of more complex and mechanistic simulation of vegetation, non-linear time series analysis and Dynamic Factor Analysis (DFA) was conducted on Enhanced Vegetation Index (EVI) time series - which is a remote sensing product and provides information on vegetation dynamics as it detects chlorophyll (productivity) and structural change. Time series of 30 years for EVI2 (from MODIS and AVHRR) were obtained for 100 communities in the area. Through specific time series cluster analysis of the vegetation data, communities were clustered to facilitate data analysis and pattern recognition. The clustering is spatially consistent, and appears to be driven by median road paving progress - which is different for each cluster. Non-linear time series analysis (multivariate singular spectrum analysis, MSSA) separates common signals (or low-dimensional attractors) across clusters. Despite the presence of this deterministic structure though, time series behavior is mostly stochastic. Granger causality analysis between EVI2 and possible response variables indicates which variables (and with what lags) are to be included in DFA, resulting in unique Dynamic Factor Models for each cluster.
NASA Astrophysics Data System (ADS)
Polin, Marco; Tuval, Idan; Drescher, Knut; Goldstein, Raymond
2009-03-01
The biflagellated alga Chlamydomonas reinhardtii is a good model organism to study the origin of flagellar synchronization. Here we employ high-speed imaging to study the beating of the two flagella of Chlamydomonas, and show that a single cell can alternate between two distinct dynamical regimes: asynchronous and synchronous. The asynchronous state is characterized by a large interflagellar frequency difference. In the synchronous state, the flagella beat in phase for lengthy periods, interrupted episodically by an extra beat of either flagellum. The statistics of these events are consistent with a model of hydrodynamically coupled noisy oscillators. Previous observations have suggested that the two flagella have well separated intrinsic beat frequencies, and are synchronized by their mutual coupling. Our analysis shows instead that the synchronized state is incompatible with coupling-induced synchronization of flagella with those intrinsic frequencies. This suggests that the beat frequencies themselves are under the control of the cell. Moreover, high-resolution three-dimensional tracking of swimming cells provides strong evidence that these dynamical states are related to non-phototactic reorientation events in the trajectories, yielding a eukaryotic equivalent of the ``run and tumble'' motion of peritrichously flagellated bacteria.
Stochastic dynamics and phase-field roughening in optomechanical oscillator arrays
NASA Astrophysics Data System (ADS)
Lauter, Roland; Mitra, Aditi; Marquardt, Florian
We consider arrays of coupled optomechanical systems, each of which consists of a laser-driven optical mode interacting with a mechanical (vibrational) mode. For sufficiently strong laser driving, the mechanical modes can settle into stable finite-amplitude oscillations on a limit cycle. We study the collective classical nonlinear dynamics of the phases of these oscillators, which is effectively described by an extension of the well-known Kuramoto model. In this extended model, we study the effect of noise on the dynamics in the case of homogeneous-phase initial conditions. We analytically establish a connection to the physics of surface growth as described by the Kardar-Parisi-Zhang model. Simulations of one-dimensional arrays of our model indeed show roughening of the phase field and universal scaling of the phase-field width. In contrast to the continuum Kardar-Parisi-Zhang model, our model is a genuine lattice model. We discuss interesting effects due to this difference, including crossover timescales and the role of instabilities of the roughening process.
NASA Astrophysics Data System (ADS)
Daryanoosh, Shakib; Wiseman, Howard M.; Brandes, Tobias
2016-02-01
A Markovian open quantum system which relaxes to a unique steady state ρss of finite rank can be decomposed into a finite physically realizable ensemble (PRE) of pure states. That is, as shown by R. I. Karasik and H. M. Wiseman [Phys. Rev. Lett. 106, 020406 (2011), 10.1103/PhysRevLett.106.020406], in principle there is a way to monitor the environment so that in the long-time limit the conditional state jumps between a finite number of possible pure states. In this paper we show how to apply this idea to the dynamics of a double quantum dot arising from the feedback control of quantum transport, as previously considered by C. Pöltl, C. Emary, and T. Brandes [Phys. Rev. B 84, 085302 (2011), 10.1103/PhysRevB.84.085302]. Specifically, we consider the limit where the system can be described as a qubit, and show that while the control scheme can always realize a two-state PRE, in the incoherent-tunneling regime there are infinitely many PREs compatible with the dynamics that cannot be so realized. For the two-state PREs that are realized, we calculate the counting statistics and see a clear distinction between the coherent and incoherent regimes.
Spatial stochastic modeling of intracellular Ca2+ dynamics using two-regime methods
NASA Astrophysics Data System (ADS)
Dobramysl, Ulrich; Robinson, Martin; Erban, Radek
2014-03-01
The signaling pathways in many cell types depend on the controlled release of calcium ions from the endoplasmatic reticulum (ER) into the cytoplasm, via clusters of inisitol triphosphate (IP3) receptor channels. At low concentrations, Ca2+ ions facilitate channel activation, while acting as inhibitory agents at high concentrations. An activation event causes the opening of other channels in a cluster, resulting in a calcium puff. We simulate calcium ion dynamics using a recently-developed hybrid two-regime technique, wherein the positions of calcium ions in the vicinity of a channel cluster are tracked by employing an off-lattice Brownian dynamics algorithm. An efficient compartment-based algorithm is used in the remainder of the computational domain to correctly capture the diffusive spread of ions. We characterize calcium puffs via the distributions of inter-puff times and amplitudes and investigate the influence of diffusive noise on the puff characteristics by comparing our results with data obtained from an effective non-spatial model. The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no. 239870.
Delayed feedback control of stochastic spatiotemporal dynamics in a resonant tunneling diode.
Stegemann, G; Balanov, A G; Schöll, E
2006-01-01
The influence of time-delayed feedback upon the spatiotemporal current density patterns is investigated in a model of a semiconductor nanostructure, namely a double-barrier resonant tunneling diode. The parameters are chosen below the Hopf bifurcation, where the only stable state of the system is a spatially inhomogeneous "filamentary" steady state. The addition of weak Gaussian white noise to the system gives rise to spatially inhomogeneous self-sustained temporal oscillations that can be quite coherent. We show that applying a time-delayed feedback can either increase or decrease the regularity of the noise-induced dynamics in this spatially extended system. Using linear stability analysis, we can explain these effects, depending on the length of the delay interval. Furthermore, we study the influence of this additional control term upon the deterministic behavior of the system, which can change significantly depending on the choice of parameters. PMID:16486254
A stochastic-dynamic model for global atmospheric mass field statistics
NASA Technical Reports Server (NTRS)
Ghil, M.; Balgovind, R.; Kalnay-Rivas, E.
1981-01-01
A model that yields the spatial correlation structure of atmospheric mass field forecast errors was developed. The model is governed by the potential vorticity equation forced by random noise. Expansion in spherical harmonics and correlation function was computed analytically using the expansion coefficients. The finite difference equivalent was solved using a fast Poisson solver and the correlation function was computed using stratified sampling of the individual realization of F(omega) and hence of phi(omega). A higher order equation for gamma was derived and solved directly in finite differences by two successive applications of the fast Poisson solver. The methods were compared for accuracy and efficiency and the third method was chosen as clearly superior. The results agree well with the latitude dependence of observed atmospheric correlation data. The value of the parameter c sub o which gives the best fit to the data is close to the value expected from dynamical considerations.
Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion
Olšina, Jan; Mančal, Tomáš; Kramer, Tobias; Kreisbeck, Christoph
2014-10-28
A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.
Dirac dynamics on stochastic phase spaces for spin 1/2 particles
NASA Astrophysics Data System (ADS)
Prugovečki, Eduard
1980-06-01
The Foldy-Wouthuysen representation of the dynamics of a free spin {1}/{2} particle is formulated in a Hilbert space H(Γ) of spinor-valued functions over Γ-space. H(Γ) carries a reducible Wigner-type representation of the Poincaré group. The transition to the Dirac representation in a new bispinor Hilbert space K(Γ) is effected by means of a generalized inverse Foldy-Wouthuysen transformation. Explicit expressions are derived for the resolution generators η of invariant subspaces K±(Γ η) carrying irreducible representations of the resulting representations of the Poincaré group. The formalism is recast in a manifestly covariant form and the Dirac equation on H(Γ s) with minimal coupling to a four-potential is examined. It is shown that the resulting external field theory is gauge-invariant and relativistically covariant.
Majer, Niels; Schöll, Eckehard
2009-01-01
We study the control of noise-induced spatiotemporal current density patterns in a semiconductor nanostructure (double-barrier resonant tunneling diode) by multiple time-delayed feedback. We find much more pronounced resonant features of noise-induced oscillations compared to single time feedback, rendering the system more sensitive to variations in the delay time tau . The coherence of noise-induced oscillations measured by the correlation time exhibits sharp resonances as a function of tau , and can be strongly increased by optimal choices of tau . Similarly, the peaks in the power spectral density are sharpened. We provide analytical insight into the control mechanism by relating the correlation times and mean frequencies of noise-induced breathing oscillations to the stability properties of the deterministic stationary current density filaments under the influence of the control loop. Moreover, we demonstrate that the use of multiple time delays enlarges the regime in which the deterministic dynamical properties of the system are not changed by delay-induced bifurcations. PMID:19257003
NASA Astrophysics Data System (ADS)
Mobilia, Mauro
2013-10-01
The fixation properties of a simple prisoner's dilemma game in the presence of “cooperation facilitators” have recently been investigated in finite and well-mixed populations for various dynamics [Mobilia, Phys. Rev. EPRESCM1539-375510.1103/PhysRevE.86.011134 86, 011134 (2012)]. In a Comment, Miękisz claims that, for cooperation to be favored by selection in the standard prisoner's dilemma games with facilitators, it suffices that fC>fD (where fC/D are the respective fitnesses of cooperators and defectors). In this Reply, we show that, in generic prisoner's dilemma games with ℓ cooperation facilitators, it is generally not sufficient that a single cooperator has a higher fitness than defectors to ensure that selection favors cooperation. In fact, it is also necessary that selection promotes the replacement of defection by cooperation in a population of size N, which requires that the fixation probability of a single cooperator exceeds (N-ℓ)-1. This replacement condition is independent of fC>fD and, when the payoff for mutual defection is negative, it is shown to be more stringent than the invasion condition. Our results, illustrated by a series of examples, considerably generalize those reported in the paper [Phys. Rev. EPRESCM1539-375510.1103/PhysRevE.86.011134 86, 011134 (2012)] and in the aforementioned Comment whose claims are demonstrated to be relevant only for a special subclass of prisoner's dilemma games.
Probing the permeability of porous media by NMR measurement of stochastic dispersion dynamics
NASA Astrophysics Data System (ADS)
Brosten, Tyler; Maier, Robert; Codd, Sarah; Vogt, Sarah; Seymour, Joseph
2011-11-01
A generalized short-time expansion of hydrodynamic dispersion is derived using non-linear response theory. The result is in accordance with the well-known reduced cases of shear flow in ducts and pipes. In terms of viscous dominated (low Reynolds number) flow in porous media the generalized expansion facilitates the measurement of permeability by PGSE-NMR measurement of time dependent molecular displacement dynamics. To be more precise, for porous media characterized by a homogeneous permeability coefficient along the direction of flow K, and fluid volume fraction ɛ, the effective dispersion coefficient D (t) = < | R-
A stochastic dynamic model for human error analysis in nuclear power plants
NASA Astrophysics Data System (ADS)
Delgado-Loperena, Dharma
Nuclear disasters like Three Mile Island and Chernobyl indicate that human performance is a critical safety issue, sending a clear message about the need to include environmental press and competence aspects in research. This investigation was undertaken to serve as a roadmap for studying human behavior through the formulation of a general solution equation. The theoretical model integrates models from two heretofore-disassociated disciplines (behavior specialists and technical specialists), that historically have independently studied the nature of error and human behavior; including concepts derived from fractal and chaos theory; and suggests re-evaluation of base theory regarding human error. The results of this research were based on comprehensive analysis of patterns of error, with the omnipresent underlying structure of chaotic systems. The study of patterns lead to a dynamic formulation, serving for any other formula used to study human error consequences. The search for literature regarding error yielded insight for the need to include concepts rooted in chaos theory and strange attractors---heretofore unconsidered by mainstream researchers who investigated human error in nuclear power plants or those who employed the ecological model in their work. The study of patterns obtained from the rupture of a steam generator tube (SGTR) event simulation, provided a direct application to aspects of control room operations in nuclear power plant operations. In doing so, the conceptual foundation based in the understanding of the patterns of human error analysis can be gleaned, resulting in reduced and prevent undesirable events.
Within-Host Stochastic Emergence Dynamics of Immune-Escape Mutants
Hartfield, Matthew; Alizon, Samuel
2015-01-01
Predicting the emergence of new pathogenic strains is a key goal of evolutionary epidemiology. However, the majority of existing studies have focussed on emergence at the population level, and not within a host. In particular, the coexistence of pre-existing and mutated strains triggers a heightened immune response due to the larger total pathogen population; this feedback can smother mutated strains before they reach an ample size and establish. Here, we extend previous work for measuring emergence probabilities in non-equilibrium populations, to within-host models of acute infections. We create a mathematical model to investigate the emergence probability of a fitter strain if it mutates from a self-limiting strain that is guaranteed to go extinct in the long-term. We show that ongoing immune cell proliferation during the initial stages of infection causes a drastic reduction in the probability of emergence of mutated strains; we further outline how this effect can be accurately measured. Further analysis of the model shows that, in the short-term, mutant strains that enlarge their replication rate due to evolving an increased growth rate are more favoured than strains that suffer a lower immune-mediated death rate (‘immune tolerance’), as the latter does not completely evade ongoing immune proliferation due to inter-parasitic competition. We end by discussing the model in relation to within-host evolution of human pathogens (including HIV, hepatitis C virus, and cancer), and how ongoing immune growth can affect their evolutionary dynamics. PMID:25785434
Ma, Liangsuo; Steinberg, Joel L.; Cunningham, Kathryn A.; Lane, Scott D.; Bjork, James M.; Neelakantan, Harshini; Price, Amanda E.; Narayana, Ponnada A.; Kosten, Thomas R.; Bechara, Antoine; Moeller, F. Gerard
2015-01-01
Cocaine dependence is associated with increased impulsivity in humans. Both cocaine dependence and impulsive behavior are under the regulatory control of cortico-striatal networks. One behavioral laboratory measure of impulsivity is response inhibition (ability to withhold a prepotent response) in which altered patterns of regional brain activation during executive tasks in service of normal performance are frequently found in cocaine dependent (CD) subjects studied with functional magnetic resonance imaging (fMRI). However, little is known about aberrations in specific directional neuronal connectivity in CD subjects. The present study employed fMRI-based dynamic causal modeling (DCM) to study the effective (directional) neuronal connectivity associated with response inhibition in CD subjects, elicited under performance of a Go/NoGo task with two levels of NoGo difficulty (Easy and Hard). The performance on the Go/NoGo task was not significantly different between CD subjects and controls. The DCM analysis revealed that prefrontal–striatal connectivity was modulated (influenced) during the NoGo conditions for both groups. The effective connectivity from left (L) anterior cingulate cortex (ACC) to L caudate was similarly modulated during the Easy NoGo condition for both groups. During the Hard NoGo condition in controls, the effective connectivity from right (R) dorsolateral prefrontal cortex (DLPFC) to L caudate became more positive, and the effective connectivity from R ventrolateral prefrontal cortex (VLPFC) to L caudate became more negative. In CD subjects, the effective connectivity from L ACC to L caudate became more negative during the Hard NoGo conditions. These results indicate that during Hard NoGo trials in CD subjects, the ACC rather than DLPFC or VLPFC influenced caudate during response inhibition. PMID:26082893
Steinberg, Joel L.; Cunningham, Kathryn A.; Lane, Scott D.; Kramer, Larry A.; Narayana, Ponnada A.; Kosten, Thomas R.; Bechara, Antoine; Moeller, F. Gerard
2015-01-01
Abstract This study employed functional magnetic resonance imaging (fMRI)-based dynamic causal modeling (DCM) to study the effective (directional) neuronal connectivity underlying inhibitory behavioral control. fMRI data were acquired from 15 healthy subjects while they performed a Go/NoGo task with two levels of NoGo difficulty (Easy and Hard NoGo conditions) in distinguishing spatial patterns of lines. Based on the previous inhibitory control literature and the present fMRI activation results, 10 brain regions were postulated as nodes in the effective connectivity model. Due to the large number of potential interconnections among these nodes, the number of models for final analysis was reduced to a manageable level for the whole group by conducting DCM Network Discovery, which is a recently developed option within the Statistical Parametric Mapping software package. Given the optimum network model, the DCM Network Discovery analysis found that the locations of the driving input into the model from all the experimental stimuli in the Go/NoGo task were the amygdala and the hippocampus. The strengths of several cortico-subcortical connections were modulated (influenced) by the two NoGo conditions. Specifically, connectivity from the middle frontal gyrus (MFG) to hippocampus was enhanced by the Easy condition and further enhanced by the Hard NoGo condition, possibly suggesting that compared with the Easy NoGo condition, stronger control from MFG was needed for the hippocampus to discriminate/learn the spatial pattern in order to respond correctly (inhibit), during the Hard NoGo condition. PMID:25336321
Ma, Liangsuo; Steinberg, Joel L; Cunningham, Kathryn A; Lane, Scott D; Bjork, James M; Neelakantan, Harshini; Price, Amanda E; Narayana, Ponnada A; Kosten, Thomas R; Bechara, Antoine; Moeller, F Gerard
2015-01-01
Cocaine dependence is associated with increased impulsivity in humans. Both cocaine dependence and impulsive behavior are under the regulatory control of cortico-striatal networks. One behavioral laboratory measure of impulsivity is response inhibition (ability to withhold a prepotent response) in which altered patterns of regional brain activation during executive tasks in service of normal performance are frequently found in cocaine dependent (CD) subjects studied with functional magnetic resonance imaging (fMRI). However, little is known about aberrations in specific directional neuronal connectivity in CD subjects. The present study employed fMRI-based dynamic causal modeling (DCM) to study the effective (directional) neuronal connectivity associated with response inhibition in CD subjects, elicited under performance of a Go/NoGo task with two levels of NoGo difficulty (Easy and Hard). The performance on the Go/NoGo task was not significantly different between CD subjects and controls. The DCM analysis revealed that prefrontal-striatal connectivity was modulated (influenced) during the NoGo conditions for both groups. The effective connectivity from left (L) anterior cingulate cortex (ACC) to L caudate was similarly modulated during the Easy NoGo condition for both groups. During the Hard NoGo condition in controls, the effective connectivity from right (R) dorsolateral prefrontal cortex (DLPFC) to L caudate became more positive, and the effective connectivity from R ventrolateral prefrontal cortex (VLPFC) to L caudate became more negative. In CD subjects, the effective connectivity from L ACC to L caudate became more negative during the Hard NoGo conditions. These results indicate that during Hard NoGo trials in CD subjects, the ACC rather than DLPFC or VLPFC influenced caudate during response inhibition. PMID:26082893
Ma, Liangsuo; Steinberg, Joel L; Cunningham, Kathryn A; Lane, Scott D; Kramer, Larry A; Narayana, Ponnada A; Kosten, Thomas R; Bechara, Antoine; Moeller, F Gerard
2015-04-01
This study employed functional magnetic resonance imaging (fMRI)-based dynamic causal modeling (DCM) to study the effective (directional) neuronal connectivity underlying inhibitory behavioral control. fMRI data were acquired from 15 healthy subjects while they performed a Go/NoGo task with two levels of NoGo difficulty (Easy and Hard NoGo conditions) in distinguishing spatial patterns of lines. Based on the previous inhibitory control literature and the present fMRI activation results, 10 brain regions were postulated as nodes in the effective connectivity model. Due to the large number of potential interconnections among these nodes, the number of models for final analysis was reduced to a manageable level for the whole group by conducting DCM Network Discovery, which is a recently developed option within the Statistical Parametric Mapping software package. Given the optimum network model, the DCM Network Discovery analysis found that the locations of the driving input into the model from all the experimental stimuli in the Go/NoGo task were the amygdala and the hippocampus. The strengths of several cortico-subcortical connections were modulated (influenced) by the two NoGo conditions. Specifically, connectivity from the middle frontal gyrus (MFG) to hippocampus was enhanced by the Easy condition and further enhanced by the Hard NoGo condition, possibly suggesting that compared with the Easy NoGo condition, stronger control from MFG was needed for the hippocampus to discriminate/learn the spatial pattern in order to respond correctly (inhibit), during the Hard NoGo condition. PMID:25336321
NASA Astrophysics Data System (ADS)
Mao, G.; Vogl, S.; Laux, P.; Wagner, S.; Kunstmann, H.
2014-07-01
Dynamically downscaled precipitation fields from regional climate model (RCM) often cannot be used directly for local climate change impact studies. Due to their inherent biases, i.e. systematic over- or underestimations compared to observations, several correction approaches have been developed. Most of the bias correction procedures such as the quantile mapping approach employ a transfer function that based on the statistical differences between RCM output and observations. Apart from such transfer function based statistical correction algorithms, a stochastic bias correction technique, based on the concept of Copula theory, is developed here and applied to correct precipitation fields from the Weather Research and Forecasting (WRF) model. As Dynamically downscaled precipitation fields we used high resolution (7 km, daily) WRF simulations for Germany driven by ERA40 reanalysis data for 1971-2000. The REGNIE data set from Germany Weather Service is used as gridded observation data (1 km, daily) and rescaled to 7 km for this application. The 30 year time series are splitted into a calibration (1971-1985) and validation (1986-2000) period of equal length. Based on the estimated dependence structure between WRF and REGNIE data and the identified respective marginal distributions in calibration period, separately analyzed for the different seasons, conditional distribution functions are derived for each time step in validation period. This finally allows to get additional information about the range of the statistically possible bias corrected values. The results show that the Copula-based approach efficiently corrects most of the errors in WRF derived precipitation for all seasons. It is also found that the Copula-based correction performs better for wet bias correction than for dry bias correction. In autumn and winter, the correction introduced a small dry bias in the Northwest of Germany. The average relative bias of daily mean precipitation from WRF for the
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
NASA Astrophysics Data System (ADS)
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.
Weinberg, Seth H.; Smith, Gregory D.
2012-01-01
Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers. PMID:23509597
Ying, Xiaoguo; Liu, Wei; Hui, Guohua
2015-01-01
In this paper, litchi freshness rapid non-destructive evaluating method using electronic nose (e-nose) and non-linear stochastic resonance (SR) was proposed. EN responses to litchi samples were continuously detected for 6 d Principal component analysis (PCA) and non-linear stochastic resonance (SR) methods were utilized to analyze EN detection data. PCA method could not totally discriminate litchi samples, while SR signal-to-noise ratio (SNR) eigen spectrum successfully discriminated all litchi samples. Litchi freshness predictive model developed using SNR eigen values shows high predictive accuracy with regression coefficients R2 = 0 .99396. PMID:25920547
Ali, Qasim; Bauch, Chris T.; Anand, Madhur
2015-01-01
Background The transportation of camp firewood infested by non-native forest pests such as Asian long-horned beetle (ALB) and emerald ash borer (EAB) has severe impacts on North American forests. Once invasive forest pests are established, it can be difficult to eradicate them. Hence, preventing the long-distance transport of firewood by individuals is crucial. Methods Here we develop a stochastic simulation model that captures the interaction between forest pest infestations and human decisions regarding firewood transportation. The population of trees is distributed across 10 patches (parks) comprising a “low volume” partition of 5 patches that experience a low volume of park visitors, and a “high volume” partition of 5 patches experiencing a high visitor volume. The infestation spreads within a patch—and also between patches—according to the probability of between-patch firewood transportation. Individuals decide to transport firewood or buy it locally based on the costs of locally purchased versus transported firewood, social norms, social learning, and level of concern for observed infestations. Results We find that the average time until a patch becomes infested depends nonlinearly on many model parameters. In particular, modest increases in the tree removal rate, modest increases in public concern for infestation, and modest decreases in the cost of locally purchased firewood, relative to baseline (current) values, cause very large increases in the average time until a patch becomes infested due to firewood transport from other patches, thereby better preventing long-distance spread. Patches that experience lower visitor volumes benefit more from firewood movement restrictions than patches that experience higher visitor volumes. Also, cross–patch infestations not only seed new infestations, they can also worsen existing infestations to a surprising extent: long-term infestations are more intense in the high volume patches than the low volume
NASA Astrophysics Data System (ADS)
Davidsen, Claus; Liu, Suxia; Mo, Xingguo; Engelund Holm, Peter; Trapp, Stefan; Rosbjerg, Dan; Bauer-Gottwein, Peter
2015-04-01
Few studies address water quality in hydro-economic models, which often focus primarily on optimal allocation of water quantities. Water quality and water quantity are closely coupled, and optimal management with focus solely on either quantity or quality may cause large costs in terms of the oth-er component. In this study, we couple water quality and water quantity in a joint hydro-economic catchment-scale optimization problem. Stochastic dynamic programming (SDP) is used to minimize the basin-wide total costs arising from water allocation, water curtailment and water treatment. The simple water quality module can handle conservative pollutants, first order depletion and non-linear reactions. For demonstration purposes, we model pollutant releases as biochemical oxygen demand (BOD) and use the Streeter-Phelps equation for oxygen deficit to compute the resulting min-imum dissolved oxygen concentrations. Inelastic water demands, fixed water allocation curtailment costs and fixed wastewater treatment costs (before and after use) are estimated for the water users (agriculture, industry and domestic). If the BOD concentration exceeds a given user pollution thresh-old, the user will need to pay for pre-treatment of the water before use. Similarly, treatment of the return flow can reduce the BOD load to the river. A traditional SDP approach is used to solve one-step-ahead sub-problems for all combinations of discrete reservoir storage, Markov Chain inflow clas-ses and monthly time steps. Pollution concentration nodes are introduced for each user group and untreated return flow from the users contribute to increased BOD concentrations in the river. The pollutant concentrations in each node depend on multiple decision variables (allocation and wastewater treatment) rendering the objective function non-linear. Therefore, the pollution concen-tration decisions are outsourced to a genetic algorithm, which calls a linear program to determine the remainder of the decision
NASA Astrophysics Data System (ADS)
Brasseur, Pierre; Candille, Guillem; Bouttier, Pierre-Antoine; Brankart, Jean-Michel; Verron, Jacques
2015-04-01
The objective of this study is to explicitly simulate and quantify the uncertainty related to sea-level anomalies diagnosed from eddy-resolving ocean circulation models, in order to develop advanced methods suitable for addressing along-track altimetric data assimilation into such models. This work is carried out jointly with the MyOcean and SANGOMA (Stochastic Assimilation for the Next Generation Ocean Model Applications) consortium, funded by EU under the GMES umbrella over the 2012-2015 period. In this framework, a realistic circulation model of the North Atlantic ocean at 1/4° resolution (NATL025 configuration) has been adapted to include effects of unresolved scales on the dynamics. This is achieved by introducing stochastic perturbations of the equation of state to represent the associated model uncertainty. Assimilation experiments are designed using altimetric data from past and on-going missions (Jason-2 and Saral/AltiKA experiments, and Cryosat-2 for fully independent altimetric validation) to better control the Gulf Stream circulation, especially the frontal regions which are predominantly affected by the non-resolved dynamical scales. An ensemble based on such stochastic perturbations is then produced and evaluated -through the probabilistic criteria: the reliability and the resolution- using the model equivalent of along-track altimetric observations. These three elements (stochastic parameterization, ensemble simulation and 4D observation operator) are used together to perform optimal 4D analysis of along-track altimetry over 10-day assimilation windows. In this presentation, the results show that the free ensemble -before starting the assimilation process- well reproduces the climatological variability over the Gulf Stream area: the system is then pretty reliable but no informative (null probabilistic resolution). Updating the free ensemble with altimetric data leads to a better reliability and to an improvement of the information (resolution
Zerbetto, Mirco; Kotsyubynskyy, Dmytro; Kowalewski, Jozef; Widmalm, Göran; Polimeno, Antonino
2012-11-01
In this work, we address the description of the dynamics of cyclodextrins in relation with nuclear magnetic resonance (NMR) relaxation data collected for hydroxymethyl groups. We define an integrated computational approach based on the definition and parametrization of a stochastic equation able to describe the relevant degrees of freedom affecting the NMR observables. The computational protocol merges molecular dynamics simulations and hydrodynamics approaches for the evaluation of most of the molecular parameters entering the stochastic description of the system. We apply the method to the interpretation of the (13)C NMR relaxation of the -CH(2)OH group of cyclodextrins. We use γ-cyclodextrin as a case study. Results are in agreement with quantitative and qualitative analyses performed in the past with simpler models and molecular dynamics simulations. The element of novelty in our approach is in the treatment of the coupling of the relevant internal (glucopyranose ring twisting/tilting and hydroxymethyl group jumps) and global (molecular tumbling) degrees of freedom. PMID:23057513
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Choustova, Olga
2008-01-01
We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Through comparing properties of trajectories we come to the conclusion that the only possibility to proceed with real financial data is to apply the stochastic version of the pilot wave theory—the model of Bohm Vigier.
NASA Astrophysics Data System (ADS)
Kovalevsky, Valery O.; Lobachev, Vitaly V.
2002-02-01
Detail analysis of active medium flow structure is presented. Schlieren method photography of flow is processed to reconstruct parameters both stochastic and order phase components. Properties of random part including correlation function, spectrum of spatial frequency, scale of turbulence, are determined by digital filtering. It was possible to compare influence of random and regular phase distortions on radiation divergence structure.
NASA Astrophysics Data System (ADS)
Qian, Hong
2010-12-01
Based on a stochastic, nonlinear, open biochemical reaction system perspective, we present an analytical theory for cellular biochemical processes. The chemical master equation (CME) approach provides a unifying mathematical framework for cellular modeling. We apply this theory to both self-regulating gene networks and phosphorylation-dephosphorylation signaling modules with feedbacks. Two types of bistability are illustrated in mesoscopic biochemical systems: one that has a macroscopic, deterministic counterpart and another that does not. In certain cases, the latter stochastic bistability is shown to be a "ghost" of the extinction phenomenon. We argue the thermal fluctuations inherent in molecular processes do not disappear in mesoscopic cell-sized nonlinear systems; rather they manifest themselves as isogenetic variations on a different time scale. Isogenetic biochemical variations in terms of the stochastic attractors can have extremely long lifetime. Transitions among discrete stochastic attractors spend most of the time in "waiting", exhibit punctuated equilibria. It can be naturally passed to "daughter cells" via a simple growth and division process. The CME system follows a set of nonequilibrium thermodynamic laws that include non-increasing free energy F( t) with external energy drive Q hk ≥0, and total entropy production rate e p =- dF/ dt+ Q hk ≥0. In the thermodynamic limit, with a system's size being infinitely large, the nonlinear bistability in the CME exhibits many of the characteristics of macroscopic equilibrium phase transition.
NASA Astrophysics Data System (ADS)
Mao, G.; Vogl, S.; Laux, P.; Wagner, S.; Kunstmann, H.
2015-04-01
Dynamically downscaled precipitation fields from regional climate models (RCMs) often cannot be used directly for regional climate studies. Due to their inherent biases, i.e., systematic over- or underestimations compared to observations, several correction approaches have been developed. Most of the bias correction procedures such as the quantile mapping approach employ a transfer function that is based on the statistical differences between RCM output and observations. Apart from such transfer function-based statistical correction algorithms, a stochastic bias correction technique, based on the concept of Copula theory, is developed here and applied to correct precipitation fields from the Weather Research and Forecasting (WRF) model. For dynamically downscaled precipitation fields we used high-resolution (7 km, daily) WRF simulations for Germany driven by ERA40 reanalysis data for 1971-2000. The REGNIE (REGionalisierung der NIEderschlagshöhen) data set from the German Weather Service (DWD) is used as gridded observation data (1 km, daily) and aggregated to 7 km for this application. The 30-year time series are split into a calibration (1971-1985) and validation (1986-2000) period of equal length. Based on the estimated dependence structure (described by the Copula function) between WRF and REGNIE data and the identified respective marginal distributions in the calibration period, separately analyzed for the different seasons, conditional distribution functions are derived for each time step in the validation period. This finally allows to get additional information about the range of the statistically possible bias-corrected values. The results show that the Copula-based approach efficiently corrects most of the errors in WRF derived precipitation for all seasons. It is also found that the Copula-based correction performs better for wet bias correction than for dry bias correction. In autumn and winter, the correction introduced a small dry bias in the
NASA Technical Reports Server (NTRS)
Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.
2006-01-01
In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.
Biochemical simulations: stochastic, approximate stochastic and hybrid approaches
2009-01-01
Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem. PMID:19151097
Yifat, Jonathan; Gannot, Israel
2015-03-01
Early detection of malignant tumors plays a crucial role in the survivability chances of the patient. Therefore, new and innovative tumor detection methods are constantly searched for. Tumor-specific magnetic-core nano-particles can be used with an alternating magnetic field to detect and treat tumors by hyperthermia. For the analysis of the method effectiveness, the bio-heat transfer between the nanoparticles and the tissue must be carefully studied. Heat diffusion in biological tissue is usually analyzed using the Pennes Bio-Heat Equation, where blood perfusion plays an important role. Malignant tumors are known to initiate an angiogenesis process, where endothelial cell migration from neighboring vasculature eventually leads to the formation of a thick blood capillary network around them. This process allows the tumor to receive its extensive nutrition demands and evolve into a more progressive and potentially fatal tumor. In order to assess the effect of angiogenesis on the bio-heat transfer problem, we have developed a discrete stochastic 3D model & simulation of tumor-induced angiogenesis. The model elaborates other angiogenesis models by providing high resolution 3D stochastic simulation, capturing of fine angiogenesis morphological features, effects of dynamic sprout thickness functions, and stochastic parent vessel generator. We show that the angiogenesis realizations produced are well suited for numerical bio-heat transfer analysis. Statistical study on the angiogenesis characteristics was derived using Monte Carlo simulations. According to the statistical analysis, we provide analytical expression for the blood perfusion coefficient in the Pennes equation, as a function of several parameters. This updated form of the Pennes equation could be used for numerical and analytical analyses of the proposed detection and treatment method. PMID:24462603
NASA Astrophysics Data System (ADS)
Chiavico, Mattia; Raso, Luciano; Dorchies, David; Malaterre, Pierre-Olivier
2015-04-01
Seine river region is an extremely important logistic and economic junction for France and Europe. The hydraulic protection of most part of the region relies on four controlled reservoirs, managed by EPTB Seine-Grands Lacs. Presently, reservoirs operation is not centrally coordinated, and release rules are based on empirical filling curves. In this study, we analyze how a centralized release policy can face flood and drought risks, optimizing water system efficiency. The optimal and centralized decisional problem is solved by Stochastic Dual Dynamic Programming (SDDP) method, minimizing an operational indicator for each planning objective. SDDP allows us to include into the system: 1) the hydrological discharge, specifically a stochastic semi-distributed auto-regressive model, 2) the hydraulic transfer model, represented by a linear lag and route model, and 3) reservoirs and diversions. The novelty of this study lies on the combination of reservoir and hydraulic models in SDDP for flood and drought protection problems. The study case covers the Seine basin until the confluence with Aube River: this system includes two reservoirs, the city of Troyes, and the Nuclear power plant of Nogent-Sur-Seine. The conflict between the interests of flood protection, drought protection, water use and ecology leads to analyze the environmental system in a Multi-Objective perspective.
NASA Astrophysics Data System (ADS)
Zhang, Yue; Zhang, Qingling; Yan, Xing-Gang
2014-06-01
In this paper, a class of singular Leslie-Gower predator-prey bioeconomic models with environment fluctuations and time delays is investigated. Local stability analysis of the model reveals that there is a phenomenon of singularity induced bifurcation due to variation of economic interest of harvesting. By choosing the delay as a bifurcation parameter, it is shown that the Hopf bifurcations can occur as the delay crosses some critical values. Then, the effect of a fluctuating environment on the singular stochastic delayed predator-prey bioeconomic model is discussed. Finally numerical simulations demonstrate that the amplitude of oscillation for population is enhanced when compared with the oscillation observed in the deterministic environment.
Karakulov, Valerii V.; Smolin, Igor Yu. E-mail: skrp@ftf.tsu.ru; Skripnyak, Vladimir A. E-mail: skrp@ftf.tsu.ru
2014-11-14
Mechanical behavior of stochastic metal-ceramic composites with the aluminum matrix under high-rate deformation at shock-wave loading is numerically simulated with consideration for structural evolution. Effective values of mechanical parameters of metal-ceramic composites Al
Assaraf, Roland; Caffarel, Michel; Kollias, A C
2011-04-15
We present a method to efficiently evaluate small energy differences of two close N-body systems by employing stochastic processes having a stability versus chaos property. By using the same random noise, energy differences are computed from close trajectories without reweighting procedures. The approach is presented for quantum systems but can be applied to classical N-body systems as well. It is exemplified with diffusion Monte Carlo simulations for long chains of hydrogen atoms and molecules for which it is shown that the long-standing problem of computing energy derivatives is solved. PMID:21568537
NASA Astrophysics Data System (ADS)
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
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.
NASA Astrophysics Data System (ADS)
Khazanov, G. V.; Tel'Nikhin, A. A.; Kronberg, T. K.
2008-03-01
In the Hamiltonian approach, electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing particle motion are transformed into a closed pair of nonlinear difference equations. The solutions of these equations show there exists a threshold in initial electron energy, below which electron motion is regular and above which electron motion is stochastic. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. A calculation of the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studied. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.
NASA Astrophysics Data System (ADS)
Munsky, Brian
2015-03-01
MAPK signal-activated transcription plays central roles in myriad biological processes including stress adaptation responses and cell fate decisions. Recent single-cell and single-molecule experiments have advanced our ability to quantify the spatial, temporal, and stochastic fluctuations for such signals and their downstream effects on transcription regulation. This talk explores how integrating such experiments with discrete stochastic computational analyses can yield quantitative and predictive understanding of transcription regulation in both space and time. We use single-molecule mRNA fluorescence in situ hybridization (smFISH) experiments to reveal locations and numbers of multiple endogenous mRNA species in 100,000's of individual cells, at different times and under different genetic and environmental perturbations. We use finite state projection methods to precisely and efficiently compute the full joint probability distributions of these mRNA, which capture measured spatial, temporal and correlative fluctuations. By combining these experimental and computational tools with uncertainty quantification, we systematically compare models of varying complexity and select those which give optimally precise and accurate predictions in new situations. We use these tools to explore two MAPK-activated gene regulation pathways. In yeast adaptation to osmotic shock, we analyze Hog1 kinase activation of transcription for three different genes STL1 (osmotic stress), CTT1 (oxidative stress) and HSP12 (heat shock). In human osteosarcoma cells under serum induction, we analyze ERK activation of c-Fos transcription.
NASA Technical Reports Server (NTRS)
Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.
2007-01-01
In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.
NASA Astrophysics Data System (ADS)
Piantadosi, J.; Metcalfe, A. V.; Howlett, P. G.
2008-01-01
SummaryWe present a new approach to stochastic dynamic programming (SDP) to determine a policy for management of urban storm-water that minimises conditional value-at-risk (CVaR). Storm-water flows into a large capture dam and is subsequently pumped to a holding dam. Water is then supplied directly to users or stored in an underground aquifer. We assume random inflow and constant demand. SDP is used to find a pumping policy that minimises CVaR, with a penalty for increased risk of environmental damage, and a pumping policy that maximises expected monetary value (EMV). We use both value iteration and policy improvement to show that the optimal policy under CVaR differs from the optimal policy under EMV.
Stochastic superparameterization in quasigeostrophic turbulence
Grooms, Ian; Majda, Andrew J.
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
Quantum Spontaneous Stochasticity
NASA Astrophysics Data System (ADS)
Drivas, Theodore; Eyink, Gregory
Classical Newtonian dynamics is expected to be deterministic, but recent fluid turbulence theory predicts that a particle advected at high Reynolds-numbers by ''nearly rough'' flows moves nondeterministically. Small stochastic perturbations to the flow velocity or to the initial data lead to persistent randomness, even in the limit where the perturbations vanish! Such ``spontaneous stochasticity'' has profound consequences for astrophysics, geophysics, and our daily lives. We show that a similar effect occurs with a quantum particle in a ''nearly rough'' force, for the semi-classical (large-mass) limit, where spreading of the wave-packet is usually expected to be negligible and dynamics to be deterministic Newtonian. Instead, there are non-zero probabilities to observe multiple, non-unique solutions of the classical equations. Although the quantum wave-function remains split, rapid phase oscillations prevent any coherent superposition of the branches. Classical spontaneous stochasticity has not yet been seen in controlled laboratory experiments of fluid turbulence, but the corresponding quantum effects may be observable by current techniques. We suggest possible experiments with neutral atomic-molecular systems in repulsive electric dipole potentials.
Samuelson, P A
1971-02-01
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
From Complex to Simple: Interdisciplinary Stochastic Models
ERIC Educational Resources Information Center
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…
NASA Astrophysics Data System (ADS)
Nishino, Masamichi; Miyashita, Seiji
2015-04-01
It is crucially important to investigate the effects of temperature on magnetic properties such as critical phenomena, nucleation, pinning, domain wall motion, and coercivity. The Landau-Lifshitz-Gilbert (LLG) equation has been applied extensively to study dynamics of magnetic properties. Approaches of Langevin noises have been developed to introduce the temperature effect into the LLG equation. To have the thermal equilibrium state (canonical distribution) as the steady state, the system parameters must satisfy some condition known as the fluctuation-dissipation relation. In inhomogeneous magnetic systems in which spin magnitudes are different at sites, the condition requires that the ratio between the amplitude of the random noise and the damping parameter depend on the magnitude of the magnetic moment at each site. Focused on inhomogeneous magnetic systems, we systematically showed agreement between the stationary state of the stochastic LLG equation and the corresponding equilibrium state obtained by Monte Carlo simulations in various magnetic systems including dipole-dipole interactions. We demonstrated how violations of the condition result in deviations from the true equilibrium state. We also studied the characteristic features of the dynamics depending on the choice of the parameter set. All the parameter sets satisfying the condition realize the same stationary state (equilibrium state). In contrast, different choices of parameter set cause seriously different relaxation processes. We show two relaxation types, i.e., magnetization reversals with uniform rotation and with nucleation.
Hughes, Samantha Jane; Cabral, João Alexandre; Bastos, Rita; Cortes, Rui; Vicente, Joana; Eitelberg, David; Yu, Huirong; Honrado, João; Santos, Mário
2016-09-15
This method development paper outlines an integrative stochastic dynamic methodology (StDM) framework to anticipate land use (LU) change effects on the ecological status of monitored and non-monitored lotic surface waters under the Water Framework Directive (WFD). Tested in the Alto Minho River Basin District in North West Portugal, the model is an innovative step towards developing a decision-making and planning tool to assess the influence impacts such as LU change and climate change on these complex systems. Comprising a series of sequential steps, a Generalized Linear Model based, competing model Multi Model Inference (MMI) approach was used for parameter estimation to identify principal land use types (distal factors) driving change in biological and physicochemical support elements (proximal factors) in monitored water bodies. The framework integrated MMI constants and coefficients of selected LU categories in the StDM simulations and spatial projections to simulate the ecological status of monitored and non-monitored lotic waterbodies in the test area under 2 scenarios of (1) LU intensification and (2) LU extensification. A total of 100 simulations were run for a 50year period for each scenario. Spatially dynamic projections of WFD metrics were obtained, taking into account the occurrence of stochastic wildfire events which typically occur in the study region and are exacerbated by LU change. A marked projected decline to "Moderate" ecological status for most waterbodies was detected under intensification but little change under extensification; only a few waterbodies fell to "moderate" status. The latter scenario describes the actual regional socio-economic situation of agricultural abandonment due to rural poverty, partly explaining the projected lack of change in ecological status. Based on the WFD "one out all out" criterion, projected downward shifts in ecological status were due to physicochemical support elements, namely increased phosphorus levels
Stochastic ontogenetic growth model
NASA Astrophysics Data System (ADS)
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.
Stochastic thermodynamics of resetting
NASA Astrophysics Data System (ADS)
Fuchs, Jaco; Goldt, Sebastian; Seifert, Udo
2016-03-01
Stochastic dynamics with random resetting leads to a non-equilibrium steady state. Here, we consider the thermodynamics of resetting by deriving the first and second law for resetting processes far from equilibrium. We identify the contributions to the entropy production of the system which arise due to resetting and show that they correspond to the rate with which information is either erased or created. Using Landauer's principle, we derive a bound on the amount of work that is required to maintain a resetting process. We discuss different regimes of resetting, including a Maxwell demon scenario where heat is extracted from a bath at constant temperature.
J.A. Krommes
2009-05-19
Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-χ theorem is discussed. An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.
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. PMID:26133418
Stochastic resonance on a circle
Wiesenfeld, K. ); Pierson, D.; Pantazelou, E.; Dames, C.; Moss, F. )
1994-04-04
We describe a new realization of stochastic resonance, applicable to a broad class of systems, based on an underlying excitable dynamics with deterministic reinjection. A simple but general theory of such single-trigger'' systems is compared with analog simulations of the Fitzhugh-Nagumo model, as well as experimental data obtained from stimulated sensory neurons in the crayfish.
Stochastic Resonance and Information Processing
NASA Astrophysics Data System (ADS)
Nicolis, C.
2014-12-01
A dynamical system giving rise to multiple steady states and subjected to noise and a periodic forcing is analyzed from the standpoint of information theory. It is shown that stochastic resonance has a clearcut signature on information entropy, information transfer and other related quantities characterizing information transduction within the system.
Wang Rubin; Yu Wei
2005-08-25
In this paper, we investigate how the population of neuronal oscillators deals with information and the dynamic evolution of neural coding when the external stimulation acts on it. Numerically computing method is used to describe the evolution process of neural coding in three-dimensioned space. The numerical result proves that only the suitable stimulation can change the coupling structure and plasticity of neurons.
Quadratic Stochastic Operators with Countable State Space
NASA Astrophysics Data System (ADS)
Ganikhodjaev, Nasir
2016-03-01
In this paper, we provide the classes of Poisson and Geometric quadratic stochastic operators with countable state space, study the dynamics of these operators and discuss their application to economics.
Stochastic structure formation in random media
NASA Astrophysics Data System (ADS)
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.
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.
NASA Astrophysics Data System (ADS)
Ritto, T. G.; Soize, Christian; Sampaio, R.
2010-04-01
This work proposes a strategy for the robust optimization of the nonlinear dynamics of a drill-string, which is a structure that rotates and digs into the rock to search for oil. The nonparametric probabilistic approach is employed to model the uncertainties of the structure as well as the uncertainties of the bit-rock interaction model. This paper is particularly concerned with the robust optimization of the rate of penetration of the column, i.e., we aim to maximize the mathematical expectation of the mean rate of penetration, respecting the integrity of the system. The variables of the optimization problem are the rotational speed at the top and the initial reaction force at the bit; they are considered deterministic. The goal is to find the set of variables that maximizes the expected mean rate of penetration, respecting, vibration limits, stress limit and fatigue limit of the dynamical system.
Johnson, Todd; Bartol, Tom; Sejnowski, Terrence; Mjolsness, Eric
2015-01-01
Astochastic reaction network model of Ca2+ dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, ‘graph-constrained correlation dynamics’, requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice. PMID:26086598
Soudackov, Alexander V; Hazra, Anirban; Hammes-Schiffer, Sharon
2011-10-14
A theoretical approach for the multidimensional treatment of photoinduced proton-coupled electron transfer (PCET) processes in solution is presented. This methodology is based on the multistate continuum theory with an arbitrary number of diabatic electronic states representing the relevant charge distributions in a general PCET system. The active electrons and transferring proton(s) are treated quantum mechanically, and the electron-proton vibronic free energy surfaces are represented as functions of multiple scalar solvent coordinates corresponding to the single electron and proton transfer reactions involved in the PCET process. A dynamical formulation of the dielectric continuum theory is used to derive a set of coupled generalized Langevin equations of motion describing the time evolution of these collective solvent coordinates. The parameters in the Langevin equations depend on the solvent properties, such as the dielectric constants, relaxation time, and molecular moment of inertia, as well as the solute properties. The dynamics of selected intramolecular nuclear coordinates, such as the proton donor-acceptor distance or a torsional angle within the PCET complex, may also be included in this formulation. A surface hopping method in conjunction with the Langevin equations of motion is used to simulate the nonadiabatic dynamics on the multidimensional electron-proton vibronic free energy surfaces following photoexcitation. This theoretical treatment enables the description of both sequential and concerted mechanisms, as well as more complex processes involving a combination of these mechanisms. The application of this methodology to a series of model systems corresponding to collinear and orthogonal PCET illustrates fundamental aspects of these different mechanisms and elucidates the significance of proton vibrational relaxation and nonequilibrium solvent dynamics. PMID:22010706
Stochastic kinetic mean field model
NASA Astrophysics Data System (ADS)
Erdélyi, Zoltán; Pasichnyy, Mykola; Bezpalchuk, Volodymyr; Tomán, János J.; Gajdics, Bence; Gusak, Andriy M.
2016-07-01
This paper introduces a new model for calculating the change in time of three-dimensional atomic configurations. The model is based on the kinetic mean field (KMF) approach, however we have transformed that model into a stochastic approach by introducing dynamic Langevin noise. The result is a stochastic kinetic mean field model (SKMF) which produces results similar to the lattice kinetic Monte Carlo (KMC). SKMF is, however, far more cost-effective and easier to implement the algorithm (open source program code is provided on
Strasser, Michael; Theis, Fabian J; Marr, Carsten
2012-01-01
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
Noiseless compression using non-Markov models
NASA Technical Reports Server (NTRS)
Blumer, Anselm
1989-01-01
Adaptive data compression techniques can be viewed as consisting of a model specified by a database common to the encoder and decoder, an encoding rule and a rule for updating the model to ensure that the encoder and decoder always agree on the interpretation of the next transmission. The techniques which fit this framework range from run-length coding, to adaptive Huffman and arithmetic coding, to the string-matching techniques of Lempel and Ziv. The compression obtained by arithmetic coding is dependent on the generality of the source model. For many sources, an independent-letter model is clearly insufficient. Unfortunately, a straightforward implementation of a Markov model requires an amount of space exponential in the number of letters remembered. The Directed Acyclic Word Graph (DAWG) can be constructed in time and space proportional to the text encoded, and can be used to estimate the probabilities required for arithmetic coding based on an amount of memory which varies naturally depending on the encoded text. The tail of that portion of the text which was encoded is the longest suffix that has occurred previously. The frequencies of letters following these previous occurrences can be used to estimate the probability distribution of the next letter. Experimental results indicate that compression is often far better than that obtained using independent-letter models, and sometimes also significantly better than other non-independent techniques.
NASA Astrophysics Data System (ADS)
Piccardi, Carlo; Soncini-Sessa, Rodolfo
1991-05-01
The solution via dynamic programming (DP) of a reservoir optimal control problem is often computationally prohibitive when the proper description of the inflow process leads to a system model having several state variables and/or when a sufficiently dense state discretization is required to achieve numerical accuracy. Thus, to simplify, the inflow correlation is usually neglected and/or a coarse state discretization is adopted. However, these simplifications may significantly affect the reliability of the solution of the optimization problem. Nowadays, the availability of very powerful computers based on innovative architectures (vector and parallel machines), even in the domain of personal computers (transputer architectures), stimulates the reformulation of the standard dynamic programming algorithm in a form able to exploit these new machine architectures. The reformulated DP algorithm and new machines enable faster and less costly solution of optimization problems involving a system model having two state variables (storage and previous period inflow, then taking into account the inflow correlation) and a number of states (of the order of 104) such as to guarantee a high numerical accuracy.
Shit, Anindita; Chattopadhyay, Sudip; Chaudhuri, Jyotipratim Ray
2013-09-12
Escape from a metastable state in the presence of a high-frequency field (where the driving becomes nonadiabatic) underlies a broad range of phenomena of physics and chemistry, and thus its understanding is of paramount importance. We study the problem of intermediate-to-high-damping escape from a metastable state of a dissipative system driven by a rapidly oscillating field, one of the most important classes of nonequilibrium systems, in a broad range of field driving frequencies (ω) and amplitudes (a). We construct a Langevin equation using quantum gauge transformation in the light of Floquet theorem and exploiting a systematic perturbative expansion in powers of 1/ω using "Kapitza-Landau time window". The quantum dynamics in a high-frequency field are found to be described by an effective time-independent potential. The temperature dependence of escape rate and the change of its form with varying parameters of the field have been analyzed. It may decrease upon increasing the temperature which is contingent on the effects of intricate interplay between external modulation and dissipation. The crossover temperature between tunnelling and thermal hopping increases with an increase in external modulation so that quantum effects in the escape are relevant at higher temperatures. These observations are uncommon and counterintuitive and, therefore, of considerable interest. Our results might be valuable for the exploration of the dynamics of cold atoms in electromagnetic fields. PMID:23627350
Stochastic ion acceleration by beating electrostatic waves.
Jorns, B; Choueiri, E Y
2013-01-01
A study is presented of the stochasticity in the orbit of a single, magnetized ion produced by the particle's interaction with two beating electrostatic waves whose frequencies differ by the ion cyclotron frequency. A second-order Lie transform perturbation theory is employed in conjunction with a numerical analysis of the maximum Lyapunov exponent to determine the velocity conditions under which stochasticity occurs in this dynamical system. Upper and lower bounds in ion velocity are found for stochastic orbits with the lower bound approximately equal to the phase velocity of the slower wave. A threshold condition for the onset of stochasticity that is linear with respect to the wave amplitudes is also derived. It is shown that the onset of stochasticity occurs for beating electrostatic waves at lower total wave energy densities than for the case of a single electrostatic wave or two nonbeating electrostatic waves. PMID:23410446
Bastos-Leite, António J.; Ridgway, Gerard R.; Silveira, Celeste; Norton, Andreia; Reis, Salomé; Friston, Karl J.
2015-01-01
We report the first stochastic dynamic causal modeling (sDCM) study of effective connectivity within the default mode network (DMN) in schizophrenia. Thirty-three patients (9 women, mean age = 25.0 years, SD = 5) with a first episode of psychosis and diagnosis of schizophrenia—according to the Diagnostic and Statistic Manual of Mental Disorders, 4th edition, revised criteria—were studied. Fifteen healthy control subjects (4 women, mean age = 24.6 years, SD = 4) were included for comparison. All subjects underwent resting state functional magnetic resonance imaging (fMRI) interspersed with 2 periods of continuous picture viewing. The anterior frontal (AF), posterior cingulate (PC), and the left and right parietal nodes of the DMN were localized in an unbiased fashion using data from 16 independent healthy volunteers (using an identical fMRI protocol). We used sDCM to estimate directed connections between and within nodes of the DMN, which were subsequently compared with t tests at the between subject level. The excitatory effect of the PC node on the AF node and the inhibitory self-connection of the AF node were significantly weaker in patients (mean values = 0.013 and −0.048 Hz, SD = 0.09 and 0.05, respectively) relative to healthy subjects (mean values = 0.084 and −0.088 Hz, SD = 0.15 and 0.77, respectively; P < .05). In summary, sDCM revealed reduced effective connectivity to the AF node of the DMN—reflecting a reduced postsynaptic efficacy of prefrontal afferents—in patients with first-episode schizophrenia. PMID:24939881
Stochastic string models with continuous semimartingales
NASA Astrophysics Data System (ADS)
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.
Smith, Jason F.; Chen, Kewei; Pillai, Ajay S.; Horwitz, Barry
2013-01-01
The number and variety of connectivity estimation methods is likely to continue to grow over the coming decade. Comparisons between methods are necessary to prune this growth to only the most accurate and robust methods. However, the nature of connectivity is elusive with different methods potentially attempting to identify different aspects of connectivity. Commonalities of connectivity definitions across methods upon which base direct comparisons can be difficult to derive. Here, we explicitly define “effective connectivity” using a common set of observation and state equations that are appropriate for three connectivity methods: dynamic causal modeling (DCM), multivariate autoregressive modeling (MAR), and switching linear dynamic systems for fMRI (sLDSf). In addition while deriving this set, we show how many other popular functional and effective connectivity methods are actually simplifications of these equations. We discuss implications of these connections for the practice of using one method to simulate data for another method. After mathematically connecting the three effective connectivity methods, simulated fMRI data with varying numbers of regions and task conditions is generated from the common equation. This simulated data explicitly contains the type of the connectivity that the three models were intended to identify. Each method is applied to the simulated data sets and the accuracy of parameter identification is analyzed. All methods perform above chance levels at identifying correct connectivity parameters. The sLDSf method was superior in parameter estimation accuracy to both DCM and MAR for all types of comparisons. PMID:23717258
Complexity and synchronization in stochastic chaotic systems
NASA Astrophysics Data System (ADS)
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.
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.
The Sharma-Parthasarathy stochastic two-body problem
Cresson, J.
2015-03-15
We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed two-body problem,” Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case.
A stochastic model of AIDS and condom use
NASA Astrophysics Data System (ADS)
Dalal, Nirav; Greenhalgh, David; Mao, Xuerong
2007-01-01
In this paper we introduce stochasticity into a model of AIDS and condom use via the technique of parameter perturbation which is standard in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as desired in any population dynamics. We also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment. Our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system.
Suboptimal stochastic controller for an n-body spacecraft
NASA Technical Reports Server (NTRS)
Larson, V.
1973-01-01
The problem is studied of determining a stochastic optimal controller for an n-body spacecraft. The approach used in obtaining the stochastic controller involves the application, interpretation, and combination of advanced dynamical principles and the theoretical aspects of modern control theory. The stochastic controller obtained for a complicated model of a spacecraft uses sensor angular measurements associated with the base body to obtain smoothed estimates of the entire state vector, can be easily implemented, and enables system performance to be significantly improved.
Stochastic resonance in passive and active electronic circuits
Anishchenko, V.S.; Khovanov, I.A.; Shulgin, B.V.
1996-06-01
The phenomenon of stochastic resonance in a bistable system modeling overdamped oscillator is studied by numerical simulations and experiments. Experimental data are compared with theoretical results. Stochastic resonance in Chua{close_quote}s circuit is investigated in detail for different regimes of its own dynamics. The main characteristics of stochastic resonance for different regimes under the adiabatic approximation are compared. {copyright} {ital 1996 American Institute of Physics.}
Solving the Langevin equation with stochastic algebraically correlated noise
NASA Astrophysics Data System (ADS)
Płoszajczak, M.; Srokowski, T.
1997-05-01
The long time tail in the velocity and force autocorrelation function has been found recently in molecular dynamics simulations of peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. In this paper we propose a Markovian process, the multidimensional kangaroo process, which permits the description of various algebraically correlated stochastic processes.
Multiple fields in stochastic inflation
NASA Astrophysics Data System (ADS)
Assadullahi, Hooshyar; Firouzjahi, Hassan; Noorbala, Mahdiyar; Vennin, Vincent; Wands, David
2016-06-01
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 numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δ N formalism.
Stochastic resonance during a polymer translocation process
NASA Astrophysics Data System (ADS)
Mondal, Debasish; Muthukumar, Murugappan
We study the translocation of a flexible polymer in a confined geometry subjected to a time-periodic external drive to explore stochastic resonance. We describe the equilibrium translocation process in terms of a Fokker-Planck description and use a discrete two-state model to describe the effect of the external driving force on the translocation dynamics. We observe that no stochastic resonance is possible if the associated free-energy barrier is purely entropic in nature. The polymer chain experiences a stochastic resonance effect only in presence of an energy threshold in terms of polymer-pore interaction. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.
Stochastic processes in muon ionization cooling
NASA Astrophysics Data System (ADS)
Errede, D.; Makino, K.; Berz, M.; Johnstone, C. J.; Van Ginneken, A.
2004-02-01
A muon ionization cooling channel consists of three major components: the magnet optics, an acceleration cavity, and an energy absorber. The absorber of liquid hydrogen contained by thin aluminum windows is the only component which introduces stochastic processes into the otherwise deterministic acceleration system. The scattering dynamics of the transverse coordinates is described by Gaussian distributions. The asymmetric energy loss function is represented by the Vavilov distribution characterized by the minimum number of collisions necessary for a particle undergoing loss of the energy distribution average resulting from the Bethe-Bloch formula. Examples of the interplay between stochastic processes and deterministic beam dynamics are given.
Stochastic cellular automata model of neural networks.
Goltsev, A V; de Abreu, F V; Dorogovtsev, S N; Mendes, J F F
2010-06-01
We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers, and spontaneous activity. This model has a complex phase diagram with self-organized active neural states, hybrid phase transitions, and a rich array of behaviors. We show that if spontaneous activity (noise) reaches a threshold level then global neural oscillations emerge. Stochastic resonance is a precursor of this dynamical phase transition. These oscillations are an intrinsic property of even small groups of 50 neurons. PMID:20866454
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. PMID:18517590
Fluctuations as stochastic deformation
NASA Astrophysics Data System (ADS)
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.
Analysis of stochastically forced quasi-periodic attractors
Ryashko, Lev
2015-11-30
A problem of the analysis of stochastically forced quasi-periodic auto-oscillations of nonlinear dynamic systems is considered. A stationary distribution of random trajectories in the neighborhood of the corresponding deterministic attractor (torus) is studied. A parametric description of quadratic approximation of the quasipotential based on the stochastic sensitivity functions (SSF) technique is given. Using this technique, we analyse a dispersion of stochastic flows near the torus. For the case of two-torus in three-dimensional space, the stochastic sensitivity function is constructed.
Stochastic approach to equilibrium and nonequilibrium thermodynamics
NASA Astrophysics Data System (ADS)
Tomé, Tânia; de Oliveira, Mário J.
2015-04-01
We develop the stochastic approach to thermodynamics based on stochastic dynamics, which can be discrete (master equation) and continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second the definition of entropy production rate, which is non-negative and vanishes in thermodynamic equilibrium. Based on these assumptions, we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasiequilibrium processes; the convexity of the equilibrium surface; the monotonic time behavior of thermodynamic potentials, including entropy; the bilinear form of the entropy production rate; the Onsager coefficients and reciprocal relations; and the nonequilibrium steady states of chemical reactions.
Stochastic approach to equilibrium and nonequilibrium thermodynamics.
Tomé, Tânia; de Oliveira, Mário J
2015-04-01
We develop the stochastic approach to thermodynamics based on stochastic dynamics, which can be discrete (master equation) and continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second the definition of entropy production rate, which is non-negative and vanishes in thermodynamic equilibrium. Based on these assumptions, we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasiequilibrium processes; the convexity of the equilibrium surface; the monotonic time behavior of thermodynamic potentials, including entropy; the bilinear form of the entropy production rate; the Onsager coefficients and reciprocal relations; and the nonequilibrium steady states of chemical reactions. PMID:25974471
Stochastic effects in a seasonally forced epidemic model
NASA Astrophysics Data System (ADS)
Rozhnova, G.; Nunes, A.
2010-10-01
The interplay of seasonality, the system’s nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.
Problems of Mathematical Finance by Stochastic Control Methods
NASA Astrophysics Data System (ADS)
Stettner, Łukasz
The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.
A Stochastic Employment Problem
ERIC Educational Resources Information Center
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…
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models
NASA Astrophysics Data System (ADS)
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models.
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D W; Stumpf, Michael P H
2015-09-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs. PMID:26342359
Stochastic neural nets and vision
NASA Astrophysics Data System (ADS)
Fall, Thomas C.
1991-03-01
A stochastic neural net shares with the normally defined neural nets the concept that information is processed by a system consisting of a set of nodes (neurons) connected by weighted links (axons). The normal neural net takes in inputs on an initial layer of neurons which fire appropriately; a neuron of the next layer fires depending on the sum of weights of the axons leading to it from fired neurons of the first layer. The stochastic neural net differs in that the neurons are more complex and that the vision activity is a dynamic process. The first layer (viewing layer) of neurons fires stochastically based on the average brightness of the area it sees and then has a refractory period. The viewing layer looks at the image for several clock cycles. The effect is like those photo sensitive sunglasses that darken in bright light. The neurons over the bright areas are most likely in a refractory period (and this can't fire) and the neurons over the dark areas are not. Now if we move the sensing layer with respect to the image so that a portion of the neurons formerly over the dark are now over the bright, they will likely all fire on that first cycle. Thus, on that cycle, one would see a flash from that portion significantly stronger than surrounding regions. Movement the other direction would produce a patch that is darker, but this effect is not as noticeable. These effects are collected in a collection layer. This paper will discuss the use of the stochastic neural net for edge detection and segmentation of some simple images.
Control of stochastic sensitivity in a stabilization problem for gas discharge system
Bashkirtseva, Irina
2015-11-30
We consider a nonlinear dynamic stochastic system with control. A problem of stochastic sensitivity synthesis of the equilibrium is studied. A mathematical technique of the solution of this problem is discussed. This technique is applied to the problem of the stabilization of the operating mode for the stochastic gas discharge system. We construct a feedback regulator that reduces the stochastic sensitivity of the equilibrium, suppresses large-amplitude oscillations, and provides a proper operation of this engineering device.
Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats
2014-05-01
In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods. PMID:24631177
Stochastic resonance in neuron models: Endogenous stimulation revisited
NASA Astrophysics Data System (ADS)
Plesser, Hans E.; Geisel, Theo
2001-03-01
The paradigm of stochastic resonance (SR)-the idea that signal detection and transmission may benefit from noise-has met with great interest in both physics and the neurosciences. We investigate here the consequences of reducing the dynamics of a periodically driven neuron to a renewal process (stimulation with reset or endogenous stimulation). This greatly simplifies the mathematical analysis, but we show that stochastic resonance as reported earlier occurs in this model only as a consequence of the reduced dynamics.
Stochastic Processes in Electrochemistry.
Singh, Pradyumna S; Lemay, Serge G
2016-05-17
Stochastic behavior becomes an increasingly dominant characteristic of electrochemical systems as we probe them on the smallest scales. Advances in the tools and techniques of nanoelectrochemistry dictate that stochastic phenomena will become more widely manifest in the future. In this Perspective, we outline the conceptual tools that are required to analyze and understand this behavior. We draw on examples from several specific electrochemical systems where important information is encoded in, and can be derived from, apparently random signals. This Perspective attempts to serve as an accessible introduction to understanding stochastic phenomena in electrochemical systems and outlines why they cannot be understood with conventional macroscopic descriptions. PMID:27120701
A suboptimal stochastic controller for an N-body spacecraft
NASA Technical Reports Server (NTRS)
Larson, V.
1973-01-01
Considerable attention, in the open literature, is being focused on the problem of developing a suitable set of deterministic dynamical equations for a complex spacecraft. This paper considers the problem of determining a stochastic optimal controller for an n-body spacecraft. The approach used in obtaining the stochastic controller involves the application, interpretation, and combination of advanced dynamical principles and the theoretical aspects of modern control theory. The stochastic controller obtained herein for a complicated model of a spacecraft uses sensor angular measurements associated with the base body to obtain smoothed estimates of the entire state vector. It can be easily implemented, and it enables system performance to be significantly improved.
Spring, William Joseph
2009-04-13
We consider quantum analogues of n-parameter stochastic processes, associated integrals and martingale properties extending classical results obtained in [1, 2, 3], and quantum results in [4, 5, 6, 7, 8, 9, 10].
Random musings on stochastics (Lorenz Lecture)
NASA Astrophysics Data System (ADS)
Koutsoyiannis, D.
2014-12-01
In 1960 Lorenz identified the chaotic nature of atmospheric dynamics, thus highlighting the importance of the discovery of chaos by Poincare, 70 years earlier, in the motion of three bodies. Chaos in the macroscopic world offered a natural way to explain unpredictability, that is, randomness. Concurrently with Poincare's discovery, Boltzmann introduced statistical physics, while soon after Borel and Lebesgue laid the foundation of measure theory, later (in 1930s) used by Kolmogorov as the formal foundation of probability theory. Subsequently, Kolmogorov and Khinchin introduced the concepts of stochastic processes and stationarity, and advanced the concept of ergodicity. All these areas are now collectively described by the term "stochastics", which includes probability theory, stochastic processes and statistics. As paradoxical as it may seem, stochastics offers the tools to deal with chaos, even if it results from deterministic dynamics. As chaos entails uncertainty, it is more informative and effective to replace the study of exact system trajectories with that of probability densities. Also, as the exact laws of complex systems can hardly be deduced by synthesis of the detailed interactions of system components, these laws should inevitably be inferred by induction, based on observational data and using statistics. The arithmetic of stochastics is quite different from that of regular numbers. Accordingly, it needs the development of intuition and interpretations which differ from those built upon deterministic considerations. Using stochastic tools in a deterministic context may result in mistaken conclusions. In an attempt to contribute to a more correct interpretation and use of stochastic concepts in typical tasks of nonlinear systems, several examples are studied, which aim (a) to clarify the difference in the meaning of linearity in deterministic and stochastic context; (b) to contribute to a more attentive use of stochastic concepts (entropy, statistical
Computational stochastic model of ions implantation
Zmievskaya, Galina I. Bondareva, Anna L.; Levchenko, Tatiana V.; Maino, Giuseppe
2015-03-10
Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.
Self-generated stochastic heating in an rf discharge
Lichtenberg, A.
1992-01-01
We have studied the nonlinear dynamics of stochastic heating arising from the reflection of electrons from moving sheaths as an underlying mechanism for electron power deposition in r.f. discharges. We examined the dynamics of the electron collision with the sheaths in the regime in which the sheath motion is small compared to the average electron velocity to de rive a mop that describes the electron motion. We have shown that for high frequency, ({omega}/2{pi}{approx gt}50MHz), the electrons will strike the moving wall with random phase. At low pressures this stochasticity is an intrinsic property of the dynamics. The stochastic electron heating leads to a power law electron distribution. The stochastic heating was determined in both the slow sheath and fast sheath velocity regimes assuming an incident Maxwellian distribution.
Criteria for stochastic pinning control of networks of chaotic maps
Mwaffo, Violet; Porfiri, Maurizio; DeLellis, Pietro
2014-03-15
This paper investigates the controllability of discrete-time networks of coupled chaotic maps through stochastic pinning. In this control scheme, the network dynamics are steered towards a desired trajectory through a feedback control input that is applied stochastically to the network nodes. The network controllability is studied by analyzing the local mean square stability of the error dynamics with respect to the desired trajectory. Through the analysis of the spectral properties of salient matrices, a toolbox of conditions for controllability are obtained, in terms of the dynamics of the individual maps, algebraic properties of the network, and the probability distribution of the pinning control. We demonstrate the use of these conditions in the design of a stochastic pinning control strategy for networks of Chirikov standard maps. To elucidate the applicability of the approach, we consider different network topologies and compare five different stochastic pinning strategies through extensive numerical simulations.